Advanced NFL Stats Community

Comeback Wins/Losses: The Comeback Kings

2012-04-13T18:45:00.000-04:00

by Clark Heins

For every comeback win there is a corresponding comeback loss, and one cannot be considered without the other. A comeback win occurs when the winning team overcomes a deficit at the start of the fourth quarter, at sometime during the fourth quarter or, if necessary, in overtime. Comeback wins have little to do with “comeback opportunities,” as the latter deal specifically with a point spread of eight or fewer points and include games that are tied in the fourth quarter. A comeback win can occur from any deficit and doesn’t deal with ties.

For the purposes of this study, I have made no attempt to credit a QB’s total of comeback wins/losses based upon whether or not he deserves them, as luck always plays a role. My totals are entirely based upon one criteria---who was the QB of record when the comeback win or loss was attained, regardless of how it was attained. As an example, I didn't credit Dan Marino, John Elway, Kerry Collins, and Warren Moon with comeback wins when they were injured during a game-winning drive and replaced by another QB. To do so would ignore the element of luck. Also, my calculations are based upon “QB starts” rather than “games played”, as it would be extremely unfair to use the latter stat for many of the QBs. “QB starts” isn’t perfect either, as several of the QBs mentioned here scored comeback wins or losses in relief.

My interest in comeback wins began when I read an article about “comeback opportunities” by Jason McKinley ("Quarterbacks and Fourth Quarter Comebacks”, Football Outsiders, June 26, 2006). McKinley formulated the concept of “QB of record”. In doing so, he created a level playing field for all the QBs who could be judged by one common standard while, at the same time, eliminating any personal bias or value judgments on the part of the researcher. However, little data existed concerning comeback wins, and my frustration to find information fueled my interest. Fortune smiled when Doug Drinen published over 10,000 NFL box scores on his website, pro-football-reference.com. Given the box scores, I could easily figure out who the winning QBs of record were for about 90 percent of the games. The remaining 10 percent I had to look up in newspaper articles. Foolishly, I did not record the losing QBs of record and have had to go back and correct that mistake because I realized I had only half of the equation that would lead to the answer to the question I was interested in: “Who were the real comeback kings?”

Okay, let’s look at the raw figures: Twenty-five NFL QBs have attained 20 or more comeback wins in their careers with Drew Brees, Ben Roethlisberger and Eli Manning reaching that figure in 2011. Taken together, these 25 QBs have totaled 636 comeback wins and 474 comeback losses. It should be noted that in 32 of these comeback wins (5%), the winning points were scored by either a defensive or special teams player. However, this does not diminish the role that the winning QB of record plays in the outcome as, on average, the go-ahead points in a comeback win are scored with eight minutes and ten seconds remaining in the contest---which means that the winning QB of record must help his team maintain and protect the lead for nearly eight minutes of the fourth quarter while, at the same time, the losing QB of record has nearly eight minutes to overcome a deficit which, on average is 4.8 points (see McKinley's article for a full discussion). Acknowledging the fact that football is the ultimate team sport and that QBs are merely the titular representatives of their teams, these are their comeback wins minus their comeback losses and the difference, in plus or minus terms:

	Wins	Losses	Difference
Dan Marino	37	26	11
Peyton Manning	36	24	12
Johnny Unitas	35	17	18
John Elway	33	18	15
Brett Favre	32	26	6

Joe Montana	31	16	15
Vinny Testaverde	29	28	1
Fran Tarkenton	29	30	-1
Drew Bledsoe	27	22	5
Warren Moon	25	25	0

Tom Brady	25	10	15
Dave Krieg	24	17	7
Jim Kelly	24	19	5
Dan Fouts	23	23	0
Randall Cunningham	22	19	3

Jake Plummer	21	11	10
Joe Theismann	21	8	13
Steve Bartkowski	20	22	-2
Boomer Esiason	20	26	-6
Y.A. Tittle	20	11	9

Joe Ferguson	20	17	3
Kerry Collins	20	17	3
Eli Manning	22	10	12
Ben Roethlisberger	20	10	10
Drew Brees	20	22	-2

Terry Bradshaw	19	11	8
Ken Stabler	19	13	6
Jim Plunkett	19	14	5
Jon Kitna	19	19	0
Donovan McNabb	18	22	-4

John Brodie	18	16	2
Jake Delhomme	18	13	5
Ron Jaworski	17	20	-3
Steve DeBerg	17	22	-5
Norm Van Brocklin (one CBW from 1949)	17	9	8

Doug Williams	17	9	8
Jim Hart	17	17	0
Brian Sipe	17	15	2
Steve McNair	17	14	3
Mark Brunell	17	20	-3

George Blanda	16	12	4
Roger Staubach	16	11	5
Trent Green	16	13	3
Bart Starr	16	11	5
Rich Gannon	16	25	-9

Troy Aikman	16	19	-3
Neil O’Donnell	16	6	10
Jay Schroeder	16	12	4
Tommy Kramer	16	13	3
Charlie Conerly (one CBW from 1949)	15	14	1

Bobby Layne (one CBW from 1949)	15	10	5
Danny White	15	10	5
Bernie Kosar	15	14	1
Jim Harbaugh	15	18	-3
Steve Young	14	15	-1

Sonny Jurgensen	14	13	1
Steve Grogan	14	18	-4
Ken O’Brien	14	12	2
Brad Johnson	14	13	1
Trent Dilfer	14	8	6

Dan Pastorini	14	10	4
Bob Griese	14	14	0
Steve Beuerlein	14	13	1
Daryle Lamonica	14	2	12

The raw results show that, while Dan Marino has the most comeback wins and Fran Tarkenton has the most comeback losses, Johnny Unitas has the best differential – all the more remarkable in that he did not have the benefit of overtime games to pad his figures. The two big surprises have to be Joe Theismann and Jake Plummer, neither of whom is considered among the elite QBs, but both of whom performed well under fourth-quarter pressure; indeed, McKinley had Plummer as the top-rated QB in his survey which covered the years 1996-05.

Neil O’Donnell and Daryle Lamonica are the seventh and eighth NFL QBs who had at least 10 more comeback wins than losses during their careers. Currently, Peyton Manning, Tom Brady, Ben Rothlisberger and Eli Manning also have at least ten more comeback wins than losses. The big disappointment has to be Brett Favre who, despite his 32 comeback wins, recorded only six of those wins on the road! Meanwhile, Joe Montana and Peyton Manning share the record for the most road comeback wins (22), while Vinny Testaverde racked up an impressive 18.

Other interesting stats include Daryle Lamonica never suffering a comeback loss at home, Tom Brady having only one comeback loss at home, and the Steelers not having a single comeback loss at home during an entire decade, the 1970s. Remarkably, Lamonica had only one comeback loss in 91 starts (ties not counted) and only two comeback losses altogether. Peyton Manning holds the record for most comeback wins in a single decade (29) while Drew Brees has the dubious record for most comeback losses in a single decade (20).

Perhaps the oddest single stat I came across occurred in the 1998 season when, from November 8 through December 6, 18 consecutive comeback wins were recorded by home teams! Overall, home teams have a slight advantage over road teams in achieving a comeback win, but this advantage is not as large as one might expect. Since 1950, there have been 12,105 games played in the NFL (ties omitted) and 2,678 of those have been decided by comeback wins: 1,252 on the road, 1,412 at home, and 14 at neutral sites.

As interesting as these raw figures are, there are better ways to calculate who the real “comeback kings” were. One method simply involves figuring the percentage of comeback wins (excluding those in relief) versus the total number of games started (ties omitted) for each QB. Unitas, Favre, Montana, Testaverde, and Krieg each had one comeback win in relief; Esiason had two and Tittle had five. Among others, Earl Morrall and Chariie Conerly also had five comeback wins in relief. The following percentages emerge for the QBs listed above:

	Comeback Wins	Total Starts (less ties)	Percentage
Johnny Unitas	34	190	17.9
Eli Manning	22	130	16.9
Joe Montana	30	187	16
Peyton Manning	36	226	15.9
Joe Theismann	21	132	15.9

Ben Roethlisberger	20	127	15.7
Randall Cunningham	22	143	15.4
Steve Bartkowski	20	131	15.3
Jake Plummer	20	142	14.8
Dan Marino	37	258	14.3

Tom Brady	25	181	13.8
Drew Bledsoe	27	199	13.6
Jim Kelly	24	177	13.6
John Elway	33	251	13.1
Dan Fouts	23	177	13

Vinny Testaverde	28	218	12.8
Dave Krieg	23	184	12.5
Drew Brees	20	162	12.3
Fran Tarkenton	29	244	11.9
Warren Moon	25	213	11.7

Joe Ferguson	20	175	11.4
Y.A. Tittle	15	134	11.2
Kerry Collins	20	187	10.7
Boomer Esiason	18	178	10.1
Brett Favre	31	322	9.6

Johnny Unitas is the runaway winner here, even more so when we consider that during the 1950s and 1960s, the NFL average for all games was only 10.2 percent, which includes comeback wins by QBs who came off the bench. The AFL average was only 8.8 percent during the 1960s. Compare those figures with 11.7 percent, the percentage attained by NFL QBs (including those in relief) for all games over the last 30 years. Aside from Unitas, Y.A. Tittle also played during the 1950s and 1960s. Of the 25 QBs considered, only Joe Ferguson, Fran Tarkenton and Dan Fouts spent a significant portion of their careers during the 1970s when the percentages were 8.4 percent from 1970-73 (no overtime) and 10.7 percent from 1974-79 (overtime). The big surprise on this list has to be Joe Theismann, while the biggest bust is, once again, Brett Favre.

There is another way to look at these figures – namely, by comparing the number of comeback wins (as starters) against career victories. These numbers represent the fact that some QBs just had to work a lot harder than other QBs to attain their wins. The 25 QBs from above:

	Comeback Wins	Total Wins	Percentage
Steve Barkowski	20	60	33.3
Vinny Testaverde	28	92	30.4
Jake Plummer	21	71	29.6
Eli Manning	22	77	28.6
Johnny Unitas	34	124	27.4

Drew Bledsoe	27	101	26.7
Randall Cunningham	22	85	25.9
Dan Fouts	23	89	25.8
Joe Theismann	21	83	25.3
Joe Ferguson	20	80	25.0

Peyton Manning	36	150	24.0
Dan Marino	37	155	23.9
Warren Moon	25	105	23.8
Kerry Collins	20	84	23.8
Dave Krieg	23	101	22.8

Joe Montana	30	133	22.6
Fran Tarkenton	29	130	22.3
Ben Roethlisberger	20	90	22.2
Jim Kelly	24	110	21.8
Boomer Esiason	18	83	21.7

Drew Brees	20	97	20.6
John Elway	33	162	20.4
Y.A. Tittle	15	78	19.2
Tom Brady	25	140	17.9
Brett Favre	31	199	15.6

In this case, Brett Favre being at the tail-end of the pack may be a good thing, because it could represent dominance on Favre’s part. In other words, Favre’s teams were often so far ahead by the time the fourth quarter rolled around that there was little need for a comeback win. Remember, among the things that comeback wins tell us is that the losing team actually dominated the game through the first three quarters – which really is a very good thing, as teams that have the lead after three quarters will win well over 70 percent of those games. Bucking this trend was Warren Moon, whose teams held the lead entering the fourth quarter only once in his 25 comeback wins! On the opposite end of the spectrum, in Brett Favre’s 32 roller-coaster comeback wins, his teams had the lead in 15 of those games after three quarters, lost a fourth quarter lead in 17 of those games, only to regain it by game’s end.

	Comeback Losses	Total Starts	Percentage
Joe Theismann	7	132	5.3
Tom Brady	10	181	5.5
Jake Plummer	10	142	7.1
John Elway	18	251	7.2
Y.A. Tittle	10	134	7.5

Eli Manning	10	130	7.7
Ben Roethlisberger	10	127	7.9
Joe Montana	15	187	8.0
Brett Favre	26	322	8.1
Dave Krieg	16	184	8.7

Johnny Unitas	17	190	8.9
Kerry Collins	17	187	9.1
Joe Ferguson	17	175	9.7
Dan Marino	26	258	10.1
Peyton Manning	24	226	10.6

Jim Kelly	19	177	10.7
Drew Bledsoe	22	199	11.1
Warren Moon	25	213	11.7
Fran Tarkenton	30	244	12.3
Vinny Testaverde	27	218	12.4

Dan Fouts	22	177	12.4
Randall Cunningham	19	143	13.3
Drew Brees	22	162	13.6
Boomer Esiason	26	178	14.6
Steve Bartkowski	22	131	16.8

Again, the NFL average over the last 30 years (which includes comeback losses in relief) is 11.7 percent. Tom Brady is a big winner here, but, as noted below, he had certain advantages that many others did not. Joe Theismann is once again the big surprise. Y.A. Tittle deserves recognition among the old-timers. Steve Bartkowski lived on the razor’s edge, as he had only 131 starts, but 42 of them were decided by a comeback win or loss. Ironically, Elway and Favre, famous for comeback wins, were actually superior at preventing comeback losses. As Joe Montana once wisely commented, “It is much harder maintaining a slight lead in the fourth quarter than overcoming one.”

Kurt Warner suffered only five comeback losses in 129 starts and Jack Kemp had only three comeback losses in 108 starts!

Okay, so what does this tell us? We can probably narrow our candidates for the all-time “comeback king” down to three selections – the brilliant all-around achievements of Unitas, who ranks at or near the top in every category and towers over all the other QBs from his own era. Also, Unitas had a personal hand in 21 of his 35 comeback wins (20 game-winning TD passes and one rushing touchdown), although it should be noted that his contemporary Y.A. Tittle had a personal hand in 15 of his 20 comeback wins (12 game-winning TD passes and three rushing TDs). Unitas and Tittle had a big advantage playing during an era that featured man-to-man defenses, rather than zones. Then there is the remarkable comeback ability on the road of Montana and Manning. After all, the single most difficult feat for any QB is to win consistently on the road before a hostile crowd and on a foreign field. Montana and Manning are both exceptional in this capacity. Unitas wasn’t shabby on the road either, as he had 15 comeback wins away from home. Of Montana’s 31 comeback wins, he had 14 game-winning TD passes and one TD run. Of Manning’s 36 comeback wins, he has twelve game-winning TD passes and three TD runs.

Honorable mention goes to John Elway, Dan Marino and Tom Brady. Elway gets eliminated because he had a tremendous physical and psychological advantage playing at Mile High, which greatly padded his figures; 21 of his 33 comeback wins occurred at home and he had a personal hand in only eleven of his comeback wins (nine game-winning TD passes and two rushing TDs). Marino gets eliminated because, while he was very good in all areas (16 game-winning TD passes in his 37 comeback wins), he doesn’t overwhelm you in any particular category and, like Unitas, he had a very lackluster career winning percentage (44.7%) against winning teams; this latter factor is further emphasized by the fact that only twelve of his 37 comeback wins were achieved against teams with a winning record.

Meanwhile, Brady appears likely to overtake Unitas in comeback win/loss differential and, among his many records, also has the best winning percentage against winning teams in NFL history – and 14 of his 25 comeback wins have come against teams with a winning record, which is tops among the 25 QBs considered, followed by Fouts (12 of 23), Montana (see below) and Kelly (12 of 24). However, he has had a personal hand in only ten of his 25 comeback wins, as nine of them came via a field goal and one by a defensive score. Also, a recent study by Nicholas Higgins ("Adjusted Comeback Efficiency”, Football Outsiders, February 2, 2010) indicates that Brady, despite having the highest percentage rate of converting “comeback opportunities”, had the third easiest “degree of difficulty” in achieving his remarkable record when compared with 59 other QBs who were active from 1998-2009. In contrast, Jake Plummer had the fifth harshest “degree of difficulty” during this same period, and thus Higgins has Plummer and twelve other QBs (including Peyton Manning) rated ahead of Brady in “Adjusted Comeback Efficiency”. Eli Manning, who has had 12 game-winning TD passes among his 22 comeback wins, was the top-rated QB in Higgins' survey.

Unfortunately, we can only measure “degree of difficulty” for QBs who were active over the last 15 years or so, as it requires documenting the time and outcome of every single play. However, we do know that Brady, like Montana, had the advantage of playing in a poor division and, as a result, his overall strength of schedule is fairly weak. Also, as McKinley and Higgins pointed out, Brady has greatly benefited from having a defensive genius as his head coach, one of the best, if not the best, teams of all time, the best field goal kickers, among the easiest of on-the-field situational circumstances, and, beginning with the infamous “tuck” game, an extraordinary run of luck that borders on the unbelievable. With Brady, more than any other QB, it is extremely difficult trying to separate the “dancer from the dance”.

But, have we gone far enough in our analysis? Well, as usual, the answer is no. We have barely touched the tip of the iceberg. Among the many nuances we have not even fathomed are these two factors: the ability of a QB to put his team in a position to win the game, and the ability of a QB, once he has attained a lead, to hold onto it. Both of these abilities are difficult to measure statistically, yet each plays a very important role in comeback wins and losses.

There are two other factors that should be obvious, but are often overlooked when trying to determine who the “comeback kings” really are. Simply stated, they are the relative strength of the teams the QB is pitted against during the course of his career and the relative strength of the teams he plays for. Fortunately, Doug Drinen has provided us with avenues to explore these two factors.

The relative strength of the teams that a QB opposed during his career has been given to us not once, but twice in recent articles (March 30 and April 12, 2009) by Mr. Drinen. Sadly, the great disparity between the results of these two articles draws into question the validity of either. However, both appear to show that Peyton Manning had a much more difficult strength of schedule than Unitas, who had a more difficult strength of schedule than Montana. As pointed out above with Tom Brady, strength of schedule, inherent in “degree of difficulty”, must, of necessity, be a major consideration. This latter factor suggests that Manning, given everything else, might be the one true “comeback king” – although it should be pointed out that, in another one of Drinen’s articles (August 6, 2008), Montana is given credit for a far better winning percentage (65.2%) against winning teams than Manning (49.1%) or Unitas (42.0%). Of Montana’s 31 comeback wins, 16 were achieved against teams with a winning record; Manning’s figure is 16 of 36, while Unitas totaled a lowly 9 of 35! Montana, as usual, was at his best when the pressure was greatest.

The second factor is much more difficult to analyze. The relative strength of the teams that a QB plays for can be loosely determined by examining the “expected” won-loss records of those teams from year to year against their actual won-loss records and then determining the variance between the two. Any variance between “expected” and real won-loss records can, in large part, be explained by just how good or how bad that team really was. Using data from pro-football-reference.com, Manning has had thirteen full seasons with the Colts, who have managed to win thirteen more games than expected, Montana had ten full seasons with the 49ers and Chiefs, who won 3.4 more games than expected, and Unitas had thirteen full seasons with the Colts, who won 0.4 more games than expected. Inversely, these figures seem to tip the scales toward Unitas as the NFL’s one true “comeback king”, as Unitas’ teams were inferior to those of Montana, whose teams were inferior to those of Manning – thus making Unitas’ comeback win/loss differential all the more impressive.

What all of this suggests is that, while Manning may have had a tougher schedule than either Unitas or Montana, he also had a better team surrounding him; thus, these two facets tend to offset each other. Team success and QB success most often go hand-in-hand. How to qualitatively separate the two presents us with our greatest mystery. When and if we are finally able to overcome this mystery should provide us with the last chapter to our story, but my suspicion is that Peyton Manning will eventually emerge as the NFL’s true “comeback king”.

Until then, like Tennyson’s Ulysses, I shall continue to “Follow knowledge like a sinking star, Beyond the utmost bound of human thought.”

Spygate: The Effectiveness of Cheating

2012-02-24T23:29:00.001-05:00

by Paul Benjamin

Enough time has passed to evaluate the effect of Bill Belichick's cheating. The cheating took place from 2000-2006, and was ended early in 2007, giving 5 years of data since.

The known cheating consisted of two components, as revealed by Eric Mangini. First, the Patriots would tape opponents defensive hand signals. This permitted coaches to correlate the signals with the defensive alignments and figure out what each signal meant. Second, the Patriots used unregistered radio frequencies, so that the second time they played that team the offensive coordinator could watch the defensive signals and choose the perfect play to tell the quarterback. Normally, the referee cuts the registered radio frequency 15 seconds before the snap, so the offensive coordinator cannot communicate with the quarterback after the defense makes its substitutions, but the Patriots were the only team in the league that had radio equipment that could broadcast on multiple frequencies simultaneously. After the referee would cut the registered frequency, the quarterback could still hear the coordinator on the other frequency, so he could be told the defensive alignment he was facing and what play to call.

So the plays and blocking schemes were always perfect ones to exploit each defensive alignment.

To measure the effect of this scheme, we need to isolate pairs of games in which the Patriots would be obtaining tape then using it. Some teams are played only every three years, so that data is not likely to show much. Teams in the same division are played twice every year and tape from the previous year can be used, so the effect of the cheating scheme may be harder to detect. I started by analyzing games played in the same season against out-of-division opponents. The second game against such an opponent is always a postseason game, so this has the advantage of measuring postseason success. After looking at these games, I saw that the Patriots have twice faced a division opponent (Jets) in the postseason, so I added those games, too. So the analysis below is of all opponents the Patriots played in the regular season and postseason of the same year. There are 30 such games.

The overall result is that during the spying era, the Patriots were 4-5 during the regular season but went 6-2 against the same teams in the postseason, so they did much better the second time. Since the cheating was ended, the Patriots have gone 5-2 in the regular season but dropped to 2-4 in the postseason, with their offense per game dropping by 10 points in the postseason, so they are doing much worse the second time, and primarily because their offense is tanking. This is despite the Patriot offense scoring more points per game during 2007-2011 than they did in 2000-2006, which reflects they have more talent.

The numbers indicate that the cheating scheme was worth more than a touchdown a game.

Results of Patriots' games, showing only opponents they played both in regular season and postseason:

After cheating was ended:

	Opponent	Regular Season	Postseason
2011	Denver Broncos	W 41-23 (Away, week 15)	W 45-10
	New York Giants	L 20-24 (Home, week 9)	L 17-21
2010	New York Jets	L 14-28 (Away, week 2)	L 21-28
	New York Jets	W 45-3 (Home, week 13)
2009	Baltimore Ravens	W 27-21 (Home, week 4)	L 14-33
2007	San Diego Chargers	W 38-14 (Home, week 2)	W 21-12
	New York Giants	W 38-35 (Away, week 17)	L 14-17 (Superbowl)

Summary	Regular Season	Postseason
Record	5-2	2-4
Points Scored per Game;	31.9	22.0
Points Allowed per Game	21.1	20.2

While cheating:

	Opponent	Regular Season	Postseason
2006	New York Jets	W 24-17 (Away, week 2)	W 37-16
	New York Jets	L 14-17 (Home, week 10)
	Indianapolis Colts	L 20-27 (Home, week 9)	L 34-38
2005	Denver Broncos	L 20-28 (Away, week 6)	L 13-27
2004	Indianapolis Colts	W 27-24 (Home, week 1)	W 20-3
	Pittsburgh Steelers	L 20-34 (Away, week 8)	W 41-27
2003	Tennessee Titans	W 38-30 (Home, week 5)	W 17-14 (Superbowl)
	Indianapolis Colts	W 38-34 (Away, week 13)	W 24-17
2001	St. Louis Rams	L 17-24 (Home, week 10)	W 20-17 (Superbowl)

Summary	Regular Season	Postseason
Record	4-5	6-2
Points Scored per Game;	24.2	25.8
Points Allowed per Game	26.1	19.9

Ring Probability Added

2012-02-06T19:55:00.000-05:00

by Joe Harris
When arguing a QB's "greatness" people often quote the number of rings a player has as a definitive conclusion to a debate. For example, Dilfer is obviously greater than Marino because he has a ring. And there is nothing else to it. That statement takes the logic a bit further than most people would, but that is essentially how a lot of fans view the world. Whilst I am not a fan of this form of logic, I thought that it would be interesting to look at this concept through the lens of WPA or, more specically, RPA - Ring Probability Added.

Ring Probability Added
The basic idea is to take Brian's WPA stats and weight it depending on the magnitude of the game. For example, in 2004 when New England beat Carolina, Tom Brady essentially did enough to win the game single-handedly with +0.97 WPA. This corresponds to +0.49 RPA - he increased New England's chances of winning the Superbowl by 49%.

The game magnitudes I assigned were:

Superbowl: 50%

Conference Championship: 25%

Divisional Round: 12.5%

Wild Card Round: 6.25%

Regular Season Game: 0.4% The logic behind the Regular Season weighting was that I wanted to keep all the games equal. So I used a weighting of 1/256 (the number of games in a season). What this doesn't do is account for the fact that, when it comes to winning a Superbowl, 0 wins for the season is just as useful as 6 wins - either way your team misses the playoffs. But in the end the regular season had very little impact on the final results.
I thought it would also be fun to think about the Total Rings a player wins for himself and his teammates. Based on the assumption of 53 players on an NFL roster, I multiply the RPA by 53. Using this logic I conclude that in Brady's career he has won 73 rings for himself and his teammates.

It should go without saying that every QBs RPA is extremely dependent on the performance of the O-line and receivers in the same games.

The Results
The results are not hugely surprising. Brady leads the way with +1.38 RPA, followed by the Manning brothers, Roethlisberger and Brees - the winners of 5 of the last 6 Superbowls.

My favourite result is that Rex Grossman managed to total -0.38 RPA or -20 Total Rings in just one season. This is amazing but it is really a testament to that Bears defence; Not only did he play badly enough to lose each playoff game, the rest of the team bailed him out just enough that he had a chance to further hurt their chances in the next round.

Rank	Name	RPA	Total Rings
1	T. Brady	+1.38	73
2	P.Manning	+0.75	40
3	B.Roethlisberger	+0.57	30
4	E.Manning	+0.56	30
5	D.Brees	+0.52	27
6	K.Warner	+0.49	26
7	J.Delhomme	+0.30	16
8	A.Rodgers	+0.27	14
9	D.Culpepper	+0.16	9
10	S.McNair	+0.16	8
11	M.Sanchez	+0.15	8
12	M.Bulger	+0.12	6
13	J.Garcia	+0.09	5
14	P.Rivers	+0.08	4
15	B.Johnson	+0.08	4

145	J.Flacco	-0.11	-6
146	T.Dilfer	-0.12	-6
147	R.Gannon	-0.14	-7
148	K.Collins	-0.23	-12
149	R.Grossman	-0.37	-20

Some Final Thoughts
When I started this analysis I was hoping that the results would show Peyton in a more favourable light. Whilst I obviously wasn't expecting him to outperform Tom Brady, I did think that he would do slightly better vs Eli and Big Ben. However, if you account for the number of seasons each QB has played all three QBs have just over 3.5 RPA per season.

For good quarterbacks, having a good defence and running game is still very important when it comes to accumulating RPA. The chart below shows that Peyton has actual done more to get his teams to Superbowls than Tom Brady. Unfortunately for him this only translated to 2 Superbowls in real life vs Brady's 5.

(click on the chart for a larger, clearer version.)

Conversely, for bad quarterbacks, it can be better to have a bad defence - as highlighted by Rex Grossman who otherwise would never have been in a position to post such terrible stats in big games.

Betting Market Power Rankings – Conference Finals Edition

2012-01-22T11:03:00.002-05:00

by Michael Beuoy

Editor's Note: Michael submitted this earlier this week and I was late in posting it. EA

Here are the final Betting Market Power Rankings of the season, updated with the results of the prior week and the lines for this week. As promised last week, I will also revisit my predictions for the lines and over/unders for the conference final games.

Refer to last week’s post for more detail on the weights used.
Here is a glossary of terms:

LSTWK - The betting market rank as of the prior week
GPF - Stands for Generic Points Favored. It’s what you would expect a team to be favored by against a league average opponent at a neutral site.
oGPF – Offensive Generic Points Favored. The component of a team’s total GPF attributable to its ability to score points.
dGPF – Defensive Generic Points Favored. The component of a team’s total GPF attributable to its ability to prevent the other team from scoring points
O RANK – The team’s oGPF ranking.
D RANK – The team’s dGPF ranking.
GWP - Stands for Generic Win Probability. I converted the GPF into a generic win probability using the following formula: GWP = 1/(1+exp(-GPF/7)).

And here is the ranking table (the Rank column is relative to all 32 teams, but I’m only showing the 12 playoff teams):

Rank	Team	LSTWK	GPF	oGPF	dGPF	GWP	ORank	DRank
1	NO	1	10.0	10.5	-0.5	0.81	1	21
2	NE	3	9.0	8.5	0.5	0.79	2	12
4	GB	2	6.5	6.5	0.0	0.72	3	18
5	NYG	8	4.5	3.5	1.0	0.66	6	9
6	SF	5	4.5	0.0	4.5	0.66	14	2
7	BAL	7	4.5	1.0	3.5	0.66	11	3
8	PIT	6	4.0	-0.5	4.5	0.64	16	1
9	ATL	11	3.5	1.0	2.5	0.62	12	6
11	DET	9	2.5	3.5	-1.0	0.60	5	23
15	TEX	16	0.5	-2.5	3.0	0.52	23	5
18	CIN	19	-1.0	-1.0	0.0	0.47	20	16
24	DEN	24	-4.0	-3.0	-1.0	0.37	25	22

New England is the clear favorite among the field of four.

The remaining three teams all have identical GPF, indicating a competitive matchup in the Superbowl should New England happen to lose this weekend.

Here is how the model predicted the point spreads and over/unders for the two Conference Finals. I’ll show two versions of the predictions. The first is just copied from last week’s post. The second includes one more piece of information, which is how each team performed against the market’s expectation. As noted in my original post on this topic, the market appears to trust the outcome of each game with 15% credibility.

Last Week

Game	Pred Line	ActLine	Diff	Pred OU	Act OU	OU Diff
BAL @ NE	6.5	7.0	0.5	49.0	50.5	1.5
NYG @ SF	3.5	2.5	-1.0	42.0	42.0	0.0

This Week (factors in Divisional Round results)

Game	Pred Line	ActLine	Diff	Pred OU	Act OU	OU Diff
BAL @ NE	7.5	7.0	-0.5	49.0	50.5	1.5
NYG @ SF	2.5	2.5	0.0	42.0	42.0	0.0

Last week’s prediction was fairly close (not as close as Brian’s tweet, but this week’s nudged closer due to the model factoring in the Giants and Patriots beating the market’s expectation by about 25 points and 20 points, respectively. SF also beat expectations, but only by about 7 points, while the Ravens performed as expected by beating the Texans by a touchdown.

Editor's note: The last two tables are a revision from the original post. The tables had been switched in the original version.

Best (And Worst) Post-Season Coaching Records Since 1950, via a Binomial View

2012-01-13T02:30:00.000-05:00

by Jim Glass

Vince Lombardi's post-season coaching W-L record of 9-1, .900, is the best ever. Or maybe not, some say Joe Gibb's record of 17-7 is standard to beat - "only" .708, but over a run of 2.4 times as many games it is much harder to keep a big winning record. How can we compare them?

One way is to compute the binomial probability of a coach attaining a given won-loss record by random chance. For instance, in Herm Edwards' first year coaching my Jets, he went 10-6. I was happy. That .625 winning record was better than Tom Landry's .607 and our former coach Bill Parcells' .570 - better than a Hall of Famer's and sure future Hall of Famer's! It looked like we had a great coach. Except that Parcells earned his .570 over 303 games and Landry earned his .607 over 418, while Herm had earned his .625 over only 16.

The binomial calculation can give the probability of winning a given number of games out of any number played, and so providea a common standard to apply to the W-L performances of different coaches with different W-L percentages over differing numbers of games. It told me that, assuming game outcomes were random with a 50% chance of winning/losing, Herm's record of .625 (or better) had only a 22% probability of occurring by random chance, which was pretty encouraging - but Bill's .570 record had only a 1% chance, and Tom's .607 had only a 0.001% chance. So perhaps it was premature to declare Herm a better coach than Tuna and Tom (as indeed it turned out to be).

Now it's playoff time, so I wondered: what if we applied this common standard when looking at the playoff coaching records of Belichick, McCarthy, Dungy, and all the other coaches of all post-season games back to 1950? And suppose we set the random probability of winning each playoff game not at 50%, but at the actual probability of winning indicated by the relative strength of the competing teams and home field advantage?

Which coaches would we see to have beaten the odds, which not, and who would the surprises be? This is the exercise followed below.

Method
I used the PFR.com data base to compile a list of all NFL post-season games and coaches from 1950 through 2010, using teams' "Simple Rating System" numbers to gauge their relative strength. The SRS gives a team's strength-of-schedule adjusted average net points per game (points for minus points against) compared to the league average. To this I added 2.5 points to the rating of the home team (when there was one). From the resulting point differential the conventional Pythagorean formula provides a winning probability for each team in each game.

Taking all the games for each coach, the resulting "Unit Pythagorean" rating provides his expected W-L percentage.
Using this percentage instead of 50% as the probability of winning, the binomial calculation gives the probability of the coach's actual W-L record resulting from random chance.

Take Dick Vermeil as an example. His 6-5 winning record with a Super Bowl championship appears very credible on its face. But his teams averaged a full touchdown better than the opposition by SRS, were the higher rated in every single game, and on top of that had home field advantage seven times to only twice for the opponent. All this gives him a .689 expecting winning rate, the highest of any coach with three or more post-season games. Put that into the calculator and it says his actual 6-5, .545 record was better than only a meager 9% of those expected by chance - random chance would beat his playoff record 91% of the time.

At the other extreme, Blanton Collier as the successor to the great Paul Brown disappointed the Browns fans of his day by going only 3-4 in the post-season. But as he had only a .255 expected winning percentage, his .429 winning record was superior to .746 of those expected by chance, the highest binomial rating of any coach with a losing record.

More recently, Ken Whisenhunt has gone 4-2, .667, in the playoffs with only a .281 expected winning rate, giving him a winning record better than .944 of those expected by chance - the highest binomial rating among all the 128 coaches to take a team to the playoffs since 1950. (Lombardi is #2.)

The numbers, and interpreting them
I've limited the list below to the 70 coaches who have coached five or more playoff games since 1950.

Given for each is the number of playoff games coached, his W-L count, actual winning percentage, expected winning percentage, and the binomial calculation of the percentage of random results his record exceeds. Thus, a figure of .612 indicates the coach's record is better than 61.2% of the records produced by chance (given his expected winning percentage).

Personally, I do not consider these numbers to be very persuasive evidence of "how good" a coach is or was. The sample sizes for all are small to very small and vary greatly, and random results in just a few close games can make a very big difference in the binomial result.

But this data does show, objectively, how well each coach's actual record in the playoffs compares to reasonable expectation. Is Coach X's "great" record in the playoffs really as good as it looks? Is Coach Y's "poor" record actually better than it looks? Does Marty Schottenheimer really have the worst playoff coaching record of all time? (No, but close.)

For perspective on (and arguments about) such questions, I think this data is useful.

Rank	Name	Games	Won	Lost	Won Lost%	Expected WL%	Binomial Performance
1	Ken Whisenhunt	6	4	2	0.667	0.281	0.944
2	Vince Lombardi	10	9	1	0.900	0.662	0.901
3	Weeb Ewbank	5	4	1	0.800	0.448	0.871
4	Bum Phillips	7	4	3	0.571	0.308	0.863
5	Joe Gibbs	24	17	7	0.708	0.578	0.862
6	Jimmy Johnson	13	9	4	0.692	0.504	0.860
7	Tom Flores	11	8	3	0.727	0.521	0.857
8	Chuck Noll	24	16	8	0.667	0.545	0.839
9	Bill Belichick	21	15	6	0.714	0.601	0.797
10	Tom Coughlin	15	8	7	0.533	0.396	0.796

11	John Fox	8	5	3	0.625	0.422	0.790
12	Bill Walsh	14	10	4	0.714	0.574	0.783
13	Hank Stram	8	5	3	0.625	0.427	0.782
14	Don McCafferty	5	4	1	0.800	0.530	0.773
15	Blanton Collier	7	3	4	0.429	0.255	0.746
16	Rex Ryan	6	4	2	0.667	0.452	0.741
17	Raymond Berry	5	3	2	0.600	0.379	0.718
18	Bill Parcells	19	11	8	0.579	0.500	0.676
19	Jerry Burns	6	3	3	0.500	0.340	0.667
20	Marv Levy	19	11	8	0.579	0.504	0.663

21	Brian Billick	8	5	3	0.625	0.512	0.610
22	Barry Switzer	7	5	2	0.714	0.594	0.593
23	Dan Reeves	20	11	9	0.550	0.499	0.592
24	Jeff Fisher	11	5	6	0.455	0.379	0.591
25	John Madden	16	9	7	0.563	0.504	0.586
26	Mark Holmgren	24	13	11	0.542	0.503	0.569
27	Mike Shanahan	13	8	5	0.615	0.556	0.556
28	Bill Cowher	21	12	9	0.571	0.534	0.548
29	John Harbaugh	7	4	3	0.571	0.479	0.546
30	Ray Malavasi	6	3	3	0.500	0.402	0.540

31	Mike Tomlin	7	5	2	0.714	0.630	0.513
32	Sam Wyche	5	3	2	0.600	0.495	0.509
33	Mike McCarthy	7	5	2	0.714	0.634	0.504
34	John Robinson	10	4	6	0.400	0.355	0.500
35	Tom Landry	36	20	16	0.556	0.543	0.492
36	George Seifert	15	10	5	0.667	0.636	0.482
37	Norv Turner	8	4	4	0.500	0.458	0.458
38	Jerry Glanville	7	3	4	0.429	0.403	0.413
39	Andy Reid	19	10	9	0.526	0.526	0.409
40	John Gruden	9	5	4	0.556	0.541	0.400

41	Tony Dungy	19	9	10	0.474	0.479	0.393
42	Sean Payton	6	4	2	0.667	0.631	0.392
43	Dave Wannstedt	5	2	3	0.400	0.378	0.376
44	Ted Marchibroda	6	2	4	0.333	0.327	0.364
45	Pete Carroll	5	2	3	0.400	0.393	0.349
46	Art Shell	5	2	3	0.400	0.427	0.292
47	Herm Edwards	6	2	4	0.333	0.375	0.274
48	Dick Nolan	5	2	3	0.400	0.458	0.244
49	Bud Grant	22	10	12	0.455	0.514	0.220
50	Steve Mariucci	7	3	4	0.429	0.513	0.206

51	Mike Ditka	12	6	6	0.500	0.586	0.184
52	Bobby Ross	8	3	5	0.375	0.474	0.181
53	Jim Fassel	5	2	3	0.400	0.506	0.180
54	Chuck Knox	18	7	11	0.389	0.474	0.169
55	Don Shula	36	19	17	0.528	0.595	0.161
56	Red Miller	5	2	3	0.400	0.532	0.150
57	Lovie Smith	6	3	3	0.500	0.631	0.139
58	Mike Martz	7	3	4	0.429	0.587	0.109
59	Don Coryell	9	3	6	0.333	0.485	0.106
60	Dick Vermeil	11	6	5	0.545	0.689	0.091

61	Mike Sherman	6	2	4	0.250	0.531	0.083
62	Wayne Fontes	5	1	4	0.200	0.409	0.072
63	Dennis Green	12	4	8	0.333	0.519	0.056
64	George Allen	9	2	7	0.222	0.432	0.048
65	Paul Brown	12	4	8	0.333	0.541	0.041
66	Sid Gillman	6	1	5	0.167	0.420	0.038
67	Jack Pardee	6	1	5	0.167	0.552	0.008
68	Wade Phillips	6	1	5	0.167	0.560	0.007
69	Marty Schottenheimer	18	5	13	0.278	0.534	0.007
70	Jim Mora, Sr.	6	0	6	0.000	0.597	0.000

Betting Market Power Rankings – Divisional Round Edition

2012-01-12T13:32:00.000-05:00

by Michael Beuoy

In last week’s post, I showed how one can use the betting over/under in conjunction with the point spread to decompose team strength into an offensive and defensive Generic Points Favored (GPF = oGPF + dGPF). The post was essentially a redo of the Week 16 rankings, and unfortunately, I did not have enough time to apply the new method to the Wildcard Round of the playoffs. This week, I do have time, so here is a peek into the mind of the Betting Market for the Divisional Round of the Playoffs. In addition, I’ve laid out a table of the predicted lines and over/unders for each possible matchup in the Conference Finals and Superbowl. I’ll return to the predictions in the following weeks to see how the model did (testable predictions! science!).

For those of you that are interested, I’ve decided to start a blog for the purposes of publishing these rankings for various sports. I’ll start off with the NBA (see the first set of rankings here). After that, I’ll take a crack at NCAA Basketball, and then hopefully move on to Major League Baseball (which presents some interesting opportunities for decomposing team strength into offense, defense, and pitching, and creating a separate set of starting pitcher rankings). The blog will probably be pretty rough in the early going (i.e. ugly and confusing), but I hope to learn quickly.

Anyway, here are the Betting Market Power Rankings for the Divisional Round of the playoffs. I had to play things by ear with regard to weighting each week, given that each new playoff week only adds a handful of games, rather than the full 16 games. So rather than dropping the oldest week and adding the newest like I do during the regular season, I’m going to keep the old weeks frozen, and just add in the new weeks at progressively higher weights. Here are the weights I am using:

Week 13 – 1
Week 14 – 2
Week 15 – 3
Week 16 – 4
Week 17 – 0 <- final week, too many garbage games Week 18 – 6 <- Wildcard Round Week 19 – 7 <- Divisional Round Week 20 - 8 <- Conference Finals

Here is a glossary of terms (I had to drop the comparisons to the ANS model since the rankings aren’t updated during the playoffs):

LSTWK - The betting market rank as of the prior week (what I would have published for the Wildcard round if I had had the time)
GPF - Stands for Generic Points Favored. It’s what you would expect a team to be favored by against a league average opponent at a neutral site.
oGPF – Offensive Generic Points Favored. The component of a team’s total GPF attributable to its ability to score points.
dGPF – Defensive Generic Points Favored. The component of a team’s total GPF attributable to its ability to prevent the other team from scoring points
O RANK – The team’s oGPF ranking.
D RANK – The team’s dGPF ranking.
GWP - Stands for Generic Win Probability. I converted the GPF into a generic win probability using the following formula: GWP = 1/(1+exp(-GPF/7)).

And here is the ranking table (the Rank column is relative to all 32 teams, but I’m only showing the 12 playoff teams):

Rank	Team	LSTWK	GPF	oGPF	dGPF	GWP	ORank	DRank
1	NO	1	10.0	10.0	0.0	0.81	1	15
2	GB	2	8.5	7.5	1.0	0.78	3	10
3	NE	3	8.0	8.0	0.0	0.76	2	19
5	SF	4	4.5	0.0	4.5	0.65	15	1
6	PIT	6	4.5	0.0	4.5	0.65	14	2
7	BAL	7	4.0	0.5	3.5	0.64	12	3
8	NYG	9	3.5	3.0	0.5	0.62	6	13
9	DET	10	3.0	4.0	-1.0	0.60	4	24
11	ATL	8	2.5	0.5	2.0	0.60	11	7
16	TEX	16	0.0	-2.5	2.5	0.50	24	4
19	CIN	17	-1.0	-1.0	0.0	0.46	21	18
24	DEN	26	-3.0	-2.5	-0.5	0.39	25	22

• New Orleans has taken over the top spot, bypassing both Green Bay and New England.
• According to the betting market the 8 team playoff field breaks down as follows:
o 3 “elite” teams – New Orleans, New England, and Green Bay, all offensive powerhouses according to oGPF.
o 3 “good” teams – San Francisco, Baltimore, and New York (two defensive powerhouses and one good offense – which should tell you something about the relative importance of offenses and defenses)
o 1 “mediocre” team – Houston (with offsetting oGPF and dGPF)
o 1 “bad” team – Denver (negative on both oGPF and dGPF)

Here is how the model predicted the point spreads for each Divisional Round matchup. Thanks to the addition of oGPF and dGPF, I can also generate a prediction of the over/unders as well. “PRED LINE”, “ACT LINE”, and “LINE DIFF” show the line the model predicted, the actual line, and the difference. The next three columns do the same for the over/under.

Game	Pred Line	Act Line	Line Diff	Pred OU	Act OU	OU Diff
DEN @ NE	13.5	13.5	0.0	49	51	2.0
NO @ SF	-2.0	-3.5	-1.5	50.5	47.5	-3.0
NYG @ GB	7.5	8.5	1.0	53.5	52	-1.5
Tex @ Bal	5.5	7.5	2.0	37.5	36	-1.5

The model actually did a pretty good job (in my opinion) at predicting this week, which is unfortunate in a way. Assuming my model is a reasonable baseline for how the betting market normally reacts, a big miss is a reliable indicator that something unusual has happened, like a key injury, or a particularly illuminating on-field performance (there was a severe market correction prior to the Wild Card round in regards to Denver – the point spread was 4 additional points in favor of Pittsburgh than the baseline prediction, and it all came out of Denver’s point total – after that 7-3 final against KC, nobody was putting much confidence in Tebow’s ability to score points).

Here’s another view of the table above, but this time broken down by predicted score for each team (it’s a useful way to understand what’s driving a miss in the line prediction).

Game	Away Pred	Away Act	Away Diff	Home Pred	Home Act	Home Diff
DEN @ NE	17.75	18.75	1.0	31.25	32.25	1.0
NO @ SF	26.25	25.5	-0.75	24.25	22	-2.3
NYG @ GB	23.0	21.75	-1.25	30.5	30.25	-0.3
Tex @ Bal	16.0	14.25	-1.75	21.5	21.75	0.3

What surprised me most is the source of the miss on the NO @ SF line. New Orleans is favored by 1.5 points more than the model indicates. But the source of the miss is that SF is assumed to score fewer points, not that New Orleans is expected to score more.

Conference Finals and Superbowl Predictions

Here are predicted lines and over/unders for each possible Conference Finals matchup and Superbowl matchup (I’ll check back on these to see how I did).

Conference Finals:

Away	Home	Line	Over/Under
BAL	NE	6.5	49
TEX	NE	10.5	47
DEN	TEX	5.5	37
DEN	BAL	9.5	39
SF	GB	6.5	46
NO	GB	1	60.5
NYG	NO	9	56.5
NYG	SF	3.5	42

Superbowl (positive line indicates NFC team is favored):

Away	Home	Line	Over/Under
NE	GB	0.5	58.5
NE	SF	-3.5	47.5
NE	NO	2	62
NE	NYG	-4.5	54.5
BAL	GB	4.5	47.5
BAL	SF	0.5	36.5
BAL	NO	6	51
BAL	NYG	-0.5	43.5
TEX	GB	8.5	45.5
TEX	SF	4.5	34.5
TEX	NO	10	49
TEX	NYG	3.5	41.5
DEN	GB	11.5	48.5
DEN	SF	7.5	37.5
DEN	NO	13	52
DEN	NYG	6.5	44.5

And finally, here is a brief tutorial on how to create point spreads and over/unders for any hypothetical matchup, using GPF, oGPF, and dGPF from the rankings:

How to Build a Point Spread:

Point Spread (in favor of home team) = 2.5 + GPF_home - GPF_away

How to Build a Over/Under

Over/Under = 2*22.0 + oGPF_home + oGPF_away - dGPF_home - dGPF_away

The 22.0 represents league average scoring and is determined dynamically each week with the ratings (but it tends to stay pretty consistent at 22).

How to Build Predicted Scores

Home Team Score = (22.0 + 1.25) + oGPF_home - dGPF_away
Away Team Score = (22.0 - 1.25) + oGPF_away - dGPF_home

NFL Coach Quality: A Bayesian Approach To Approximating the Value of Coaches - UPDATED

2012-01-06T20:15:00.013-05:00

by David Durschlag

You are currently viewing version 1 of this article. To view version two, please click here.

Summary

Evaluating NFL coaches is a difficult task, popular among fans and vitally important to franchises. This is a brief attempt at the task, using purely quantitative data.

Data

The numbers of regular season games each team won each year are treated as data points. No information beyond number of regular season wins was used.

While the "metagame" of the NFL continues to evolve, the data used herein is from 1993 onward, when the last Collective Bargaining Agreement was signed. While victories now come in different environments, they are all under (roughly) the same rules. Data from before this period could be skewed based on the different rules for control of players, so it was excluded.

Also excluded was the performance of any team in a year in which it had multiple head coaches. This was done to ensure that credit for a season was easy to assign.

In total, 107 coaches and 565 team-years of data were used.

Assumptions

Each coach has a hidden "value". Better coaches have higher value.
The number of games a team wins can be modeled as a draw from a normal distribution with a mean of the value of their coach, and an unknown variance dubbed "Season Variance". This variance is constant across all seasons for all coaches.
The value of coaches is normally distributed across the population, with unknown mean and variance.

Process

The above assumptions were encoded as a model for BUGS, which was run for 10,000 iterations, then another 10,000 iterations.

Results

Coach quality had converged after 10,000 iterations.

The posterior distribution for system constants were as follows:

Constant	Mean	Standard Deviation
Season Variance	0.137	0.009
Coach Value Population Mean	7.698	0.191
Coach Value Population Variance	0.626	0.207

The posterior distributions for coach values were as follows:

Coach	Mean Value	Standard Deviation Value
Bill Belichick	10.100	0.633
Tony Dungy	9.948	0.671
Mike Tomlin	9.490	0.920
Bill Cowher	9.350	0.636
Mike McCarthy	9.344	0.865
John Harbaugh	9.303	0.972
Sean Payton	9.245	0.852
Marty Schottenheimer	9.209	0.686
Mike Smith	9.197	0.970
Andy Reid	9.180	0.656
Mike Holmgren	9.107	0.606
Wade Phillips	9.051	0.792
Mike Shanahan	8.970	0.606
Barry Switzer	8.833	0.957
Mike Martz	8.763	0.863
Jimmy Johnson	8.751	0.892
Mike Sherman	8.746	0.856
Tom Coughlin	8.626	0.608
Jeff Fisher	8.578	0.604
Jack Pardee	8.549	1.221
Dennis Green	8.507	0.684
Brian Billick	8.505	0.738
Lovie Smith	8.466	0.777
George Seifert	8.412	0.812
Marv Levy	8.397	0.905
Rex Ryan	8.380	1.020
Don Shula	8.375	1.017
Bill Parcells	8.372	0.694
Jon Gruden	8.370	0.692
Steve Mariucci	8.216	0.778
Bobby Ross	8.148	0.772
Jim Caldwell	8.105	1.009
Wayne Fontes	8.094	0.945
Jim Fassel	8.077	0.805
Brad Childress	8.066	0.908
Dick Vermeil	8.058	0.778
John Fox	7.978	0.743
Pete Carroll	7.967	0.935
Al Groh	7.954	1.210
Ken Whisenhunt	7.876	0.897
Mike Tice	7.845	0.944
Jim Mora	7.833	0.956
Gunther Cunningham	7.801	1.104
Gary Kubiak	7.768	0.849
Jason Garrett	7.766	1.203
Jack Del Rio	7.759	0.746
Hue Jackson	7.745	1.201
Tony Sparano	7.734	0.943
Jim L. Mora	7.731	0.960
Dave Wannstedt	7.722	0.698
Dan Reeves	7.705	0.707
Norv Turner	7.704	0.634
Marvin Lewis	7.695	0.748
Nick Saban	7.631	1.094
Bill Callahan	7.629	1.099
Joe Gibbs	7.616	0.946
Mike White	7.607	1.102
Jim Haslett	7.584	0.855
Ray Rhodes	7.546	0.887
Mike Singletary	7.479	1.092
Mike Mularkey	7.467	1.103
Art Shell	7.423	1.016
Todd Haley	7.403	1.022
Jerry Glanville	7.373	1.210
Chan Gailey	7.358	0.968
Tom Cable	7.311	1.119
Rich Brooks	7.307	1.100
Josh McDaniels	7.155	1.102
Dick Jauron	7.151	0.752
Tom Flores	7.143	1.092
Buddy Ryan	7.142	1.096
Steve Spurrier	7.141	1.099
Lindy Infante	7.139	1.119
Jim Zorn	7.135	1.094
Eric Mangini	7.124	0.906
Vince Tobin	7.107	0.957
June Jones	7.104	1.022
Dennis Erickson	7.098	0.864
Herman Edwards	7.090	0.787
Butch Davis	7.002	0.947
Sam Wyche	6.997	1.030
Scott Linehan	6.983	1.104
Kevin Gilbride	6.977	1.232
Jim E. Mora	6.975	0.958
Richie Petitbon	6.975	1.231
Joe Bugel	6.967	1.113
Lane Kiffin	6.962	1.231
Romeo Crennel	6.870	0.957
Gregg Williams	6.867	1.033
Raheem Morris	6.864	1.035
Ted Marchibroda	6.793	0.861
Mike Nolan	6.722	1.025
Dave McGinnis	6.717	1.030
Chuck Knox	6.654	1.123
Bruce Coslet	6.617	0.972
Dom Capers	6.597	0.789
Mike Ditka	6.573	1.050
Dave Campo	6.569	1.032
Dick LeBeau	6.496	1.124
Mike Riley	6.443	1.052
Cam Cameron	6.366	1.263
Dave Shula	6.311	1.041
Rich Kotite	6.263	0.995
Chris Palmer	6.011	1.162
Marty Mornhinweg	6.009	1.164
Steve Spagnuolo	5.877	1.072
Rod Marinelli	5.864	1.071

Conclusions and Analysis

Despite having a small sample size and extremely limited data, the estimated value of coaches agrees closely with conventional wisdom. Value estimates are relatively narrow, ranging from a 66% chance that Jeff Fisher's value is between 7.974 and 9.182 to a 66% chance Cam Cameron's value is between 5.103 and 7.629. Applying Microsoft's ? - 3 * ? method of combining the parameters of a normal distribution for TrueSkill, then renormalizing (so that the unit of value is approximately the win), the following list is obtained:

Coach	Normalized Combined Rating
Bill Belichick	10.060
Tony Dungy	9.870
Bill Cowher	9.520
Mike Holmgren	9.410
Andy Reid	9.360
Mike Shanahan	9.310
Marty Schottenheimer	9.310
Tom Coughlin	9.070
Jeff Fisher	9.040
Mike McCarthy	9.030
Mike Tomlin	9.010
Sean Payton	8.980
Wade Phillips	8.970
Dennis Green	8.820
John Harbaugh	8.770
Jon Gruden	8.700
Bill Parcells	8.700
Brian Billick	8.700
Mike Smith	8.700
Mike Sherman	8.620
Mike Martz	8.620
Lovie Smith	8.590
Jimmy Johnson	8.550
George Seifert	8.480
Barry Switzer	8.470
Steve Mariucci	8.410
Bobby Ross	8.380
Norv Turner	8.350
John Fox	8.320
Dick Vermeil	8.300
Marv Levy	8.270
Jim Fassel	8.260
Dave Wannstedt	8.230
Dan Reeves	8.200
Jack Del Rio	8.150
Marvin Lewis	8.110
Brad Childress	8.030
Don Shula	8.010
Rex Ryan	8.010
Wayne Fontes	7.970
Gary Kubiak	7.940
Ken Whisenhunt	7.920
Pete Carroll	7.900
Jim Caldwell	7.840
Jim Haslett	7.800
Mike Tice	7.790
Jim Mora	7.760
Tony Sparano	7.720
Dick Jauron	7.710
Ray Rhodes	7.700
Jack Pardee	7.700
Jim L. Mora	7.680
Joe Gibbs	7.630
Herman Edwards	7.590
Dennis Erickson	7.430
Gunther Cunningham	7.420
Chan Gailey	7.390
Eric Mangini	7.360
Art Shell	7.340
Nick Saban	7.320
Todd Haley	7.310
Bill Callahan	7.310
Al Groh	7.300
Mike White	7.290
Vince Tobin	7.240
Dom Capers	7.240
Ted Marchibroda	7.220
Mike Singletary	7.220
Butch Davis	7.190
Mike Mularkey	7.190
Jason Garrett	7.180
Hue Jackson	7.170
Jim E. Mora	7.150
June Jones	7.100
Rich Brooks	7.080
Romeo Crennel	7.070
Tom Cable	7.040
Sam Wyche	7.010
Tom Flores	6.980
Buddy Ryan	6.970
Jim Zorn	6.970
Josh McDaniels	6.970
Steve Spurrier	6.960
Lindy Infante	6.920
Gregg Williams	6.910
Raheem Morris	6.900
Jerry Glanville	6.890
Bruce Coslet	6.860
Scott Linehan	6.840
Mike Nolan	6.820
Joe Bugel	6.810
Dave McGinnis	6.810
Dave Campo	6.700
Mike Ditka	6.660
Mike Riley	6.570
Chuck Knox	6.560
Richie Petitbon	6.560
Kevin Gilbride	6.560
Rich Kotite	6.560
Lane Kiffin	6.550
Dave Shula	6.500
Dick LeBeau	6.450
Steve Spagnuolo	6.120
Rod Marinelli	6.110
Cam Cameron	6.060
Chris Palmer	6.020
Marty Mornhinweg	6.020

The top two coaches both spent a lot of their career with transcendent quarterbacks. With the firing of Steve Spagnuolo and Raheem Morris, Romeo Crennel is the lowest ranking active head coach. If Bill Cowher says he'd like to get back into coaching, and inquires as to whether your organization is hiring, you say "yes." Using a similar model based on points for/against might not only produce slightly more accurate information, but could also reveal whether head coaches can be "defense-oriented" or "offence-oriented" and, if so, which ones are which.

Summary

Evaluating NFL coaches is a difficult task, popular among fans and vitally important to franchises. This is a brief attempt at the task, using purely quantitative data. The goal here is dual -- both to increase our understanding of how (and how much) NFL teams are reflective of their coaches, as well as to introduce the dichotomy of frequentist and Bayesian analysis to the NFL statistics community, from which it is largely absent.

Data

The numbers of regular season games each team won each year are treated as data points. No information beyond number of regular season wins was used.

Also excluded was the performance of any team in a year in which it had multiple head coaches. This was done to ensure that credit for a season was easy to assign.

In total, 107 coaches and 565 team-years of data were used.

Assumptions

Each coach has a hidden "value". Better coaches have higher value.
The number of games a team wins can be modeled as a draw from a normal distribution with a mean of the value of their coach, and an unknown standard deviation which is constant across all seasons for all coaches. This will be refered to as "Season Standard Deviation."
The value of coaches is normally distributed across the population, with unknown mean and standard deviation. These will be refered to as "Population Mean" and "Population Standard Deviation".

Process

The above assumptions were encoded as a model for BUGS, which was run for 10,000 iterations, then another 10,000 iterations.

Results

Coach quality had converged after 10,000 iterations.

The posterior distribution for system constants were as follows. Posterior information for individual coaches is included in the large table in the next section.

Constant	Mean	Standard Deviation
Season Standard Deviation	2.70	0.09
Population Mean	7.69	0.19
Population Standard Deviation	1.33	0.18

Conclusions and Analysis

Below is a table with a variety of data about each coach.

Value Posterior Mean: The mean of the posterior distribution for the coach's value.
Value Posterior StdDev: The standard deviation of the posterior distribution for the coach's value.
Triple-Conservative Rating: μ - 3 * σ -- a conservative single-number rating. Microsoft uses this to collapse TrueSkill distributions to single ratings.
Normalized Triple-Conservative Rating: The triple-conservative rating re-normalized to the same scale as posterior mean coach value.
Raw Average Wins: The coach's raw number of average wins over the data set. Provided for comparison to the posterior means -- this is one way to gauge the benefit of the Bayesian model over a standard frequentist approach. Because the Bayesian model incorporates the idea of uncertainty, a coach with one season of 14 wins is not considered a 14 win coach. Alternately sorting between this column and that of posterior mean, then judging which list looks better, is a reasonable shortcut for juding the modeling approach taken here.
80% Confidence Range: The range of win values the model expects with 80% confidence. In other words, this coach would be expected to win fewer games than the minimum 10% of the time, and more than the maximum 10% of the time. This can be used to gauge the amount of information added by the model -- the narrower these ranges are, the more information was available for judging that coach. The fact that these tend to be very wide indicates that the model cannot make strong predictions -- a result of both the minimal amount of data available and the unpredictability of the NFL. Taking all coaches as a data set together yields an 80% confidence range of 4.27-11.91. Comparing this to the ranges for invidual coaches is a good way to see how much information the model was able to add. In general, you'll find that the range has narrowed only very slightly, but has shifted a win or two. This can be translated roughly as "the uncertainty created by minimal data and the general difficulty in predicting the NFL means it is hard to predict how many games an individual coach's team will win, but we have a pretty good idea who the 'better' coaches are."

Coach	Value Posterior Mean	Value Posterior StdDev	Triple-Conservative Rating	Normalized Triple-Conservative Rating	Raw Average Wins	80% Confidence Range
Al Groh	7.95	1.21	4.32	7.30	9	4.03-11.87
Andy Reid	9.18	0.65	7.21	9.36	9.69	5.81-12.54
Art Shell	7.42	1.01	4.37	7.34	7	3.70-11.14
Barry Switzer	8.83	0.95	5.96	8.47	10	5.17-12.49
Bill Belichick	10.1	0.63	8.20	10.06	10.8	6.76-13.43
Bill Callahan	7.62	1.09	4.33	7.31	7.5	3.82-11.43
Bill Cowher	9.35	0.63	7.44	9.52	9.85	6.00-12.69
Bill Parcells	8.37	0.69	6.29	8.70	8.63	4.97-11.77
Bobby Ross	8.14	0.77	5.83	8.38	8.37	4.67-11.62
Brad Childress	8.06	0.90	5.34	8.03	8.4	4.45-11.67
Brian Billick	8.50	0.73	6.29	8.70	8.88	5.06-11.94
Bruce Coslet	6.61	0.97	3.70	6.86	5.5	2.93-10.29
Buddy Ryan	7.14	1.09	3.85	6.97	6	3.34-10.94
Butch Davis	7.00	0.94	4.16	7.19	6.25	3.34-10.65
Cam Cameron	6.36	1.26	2.57	6.06	1	2.39-10.33
Chan Gailey	7.35	0.96	4.45	7.39	7	3.68-11.03
Chris Palmer	6.01	1.16	2.52	6.02	2.5	2.14-9.87
Chuck Knox	6.65	1.12	3.28	6.56	4.5	2.82-10.48
Dan Reeves	7.70	0.70	5.58	8.20	7.7	4.29-11.11
Dave Campo	6.56	1.03	3.47	6.70	5	2.83-10.30
Dave McGinnis	6.71	1.03	3.62	6.81	5.33	2.98-10.45
Dave Shula	6.31	1.04	3.18	6.50	4.33	2.56-10.05
Dave Wannstedt	7.72	0.69	5.62	8.23	7.72	4.31-11.12
Dennis Erickson	7.09	0.86	4.50	7.43	6.66	3.52-10.66
Dennis Green	8.50	0.68	6.45	8.82	8.81	5.11-11.89
Dick Jauron	7.15	0.75	4.89	7.71	6.88	3.69-10.60
Dick LeBeau	6.49	1.12	3.12	6.45	4	2.66-10.32
Dick Vermeil	8.05	0.77	5.72	8.30	8.25	4.57-11.54
Dom Capers	6.59	0.78	4.23	7.24	6	3.10-10.09
Don Shula	8.37	1.01	5.32	8.01	9.33	4.65-12.09
Eric Mangini	7.12	0.90	4.40	7.36	6.6	3.51-10.73
Gary Kubiak	7.76	0.84	5.22	7.94	7.83	4.21-11.32
George Seifert	8.41	0.81	5.97	8.48	8.85	4.89-11.93
Gregg Williams	6.86	1.03	3.76	6.91	5.66	3.12-10.60
Gunther Cunningham	7.80	1.10	4.48	7.42	8	3.99-11.61
Herman Edwards	7.09	0.78	4.72	7.59	6.75	3.59-10.58
Hue Jackson	7.74	1.20	4.14	7.17	8	3.83-11.65
Jack Del Rio	7.75	0.74	5.52	8.15	7.77	4.30-11.21
Jack Pardee	8.54	1.22	4.88	7.70	12	4.62-12.47
Jason Garrett	7.76	1.20	4.15	7.18	8	3.85-11.67
Jeff Fisher	8.57	0.60	6.76	9.04	8.81	5.26-11.88
Jerry Glanville	7.37	1.21	3.74	6.89	6	3.45-11.28
Jim Caldwell	8.10	1.00	5.07	7.84	8.66	4.39-11.82
Jim E. Mora	6.97	0.95	4.10	7.15	6.25	3.31-10.63
Jim Fassel	8.07	0.80	5.66	8.26	8.28	4.56-11.58
Jim Haslett	7.58	0.85	5.01	7.80	7.5	4.02-11.14
Jim L. Mora	7.73	0.96	4.85	7.68	7.75	4.06-11.39
Jim Mora	7.83	0.95	4.96	7.76	8	4.17-11.49
Jim Zorn	7.13	1.09	3.85	6.97	6	3.33-10.93
Jimmy Johnson	8.75	0.89	6.07	8.55	9.6	5.15-12.34
Joe Bugel	6.96	1.11	3.62	6.81	5.5	3.14-10.78
Joe Gibbs	7.61	0.94	4.77	7.63	7.5	3.96-11.26
John Fox	7.97	0.74	5.74	8.32	8.11	4.52-11.42
John Harbaugh	9.30	0.97	6.38	8.77	11	5.62-12.98
Jon Gruden	8.37	0.69	6.29	8.70	8.63	4.97-11.76
Josh McDaniels	7.15	1.10	3.84	6.97	6	3.34-10.96
June Jones	7.10	1.02	4.03	7.10	6.33	3.37-10.83
Ken Whisenhunt	7.87	0.89	5.18	7.92	8	4.27-11.47
Kevin Gilbride	6.97	1.23	3.28	6.56	4	3.03-10.91
Lane Kiffin	6.96	1.23	3.26	6.55	4	3.02-10.89
Lindy Infante	7.13	1.11	3.78	6.92	6	3.31-10.96
Lovie Smith	8.46	0.77	6.13	8.59	8.87	4.98-11.94
Marty Mornhinweg	6.00	1.16	2.51	6.02	2.5	2.13-9.87
Marty Schottenheimer	9.20	0.68	7.15	9.31	9.75	5.81-12.60
Marv Levy	8.39	0.90	5.68	8.27	9	4.78-12.00
Marvin Lewis	7.69	0.74	5.45	8.11	7.66	4.24-11.14
Mike Ditka	6.57	1.05	3.42	6.66	5	2.81-10.32
Mike Holmgren	9.10	0.60	7.29	9.41	9.5	5.79-12.41
Mike Martz	8.76	0.86	6.17	8.62	9.5	5.19-12.33
Mike McCarthy	9.34	0.86	6.74	9.03	10.5	5.77-12.91
Mike Mularkey	7.46	1.10	4.15	7.19	7	3.65-11.27
Mike Nolan	6.72	1.02	3.64	6.82	5.33	2.99-10.45
Mike Riley	6.44	1.05	3.28	6.57	4.66	2.68-10.20
Mike Shanahan	8.97	0.60	7.15	9.31	9.31	5.65-12.28
Mike Sherman	8.74	0.85	6.17	8.62	9.5	5.18-12.30
Mike Singletary	7.47	1.09	4.20	7.22	7	3.68-11.27
Mike Smith	9.19	0.96	6.28	8.70	10.75	5.52-12.87
Mike Tice	7.84	0.94	5.01	7.79	8	4.19-11.49
Mike Tomlin	9.49	0.92	6.72	9.01	11	5.86-13.11
Mike White	7.60	1.10	4.30	7.29	7.5	3.79-11.41
Nick Saban	7.63	1.09	4.34	7.32	7.5	3.83-11.43
Norv Turner	7.70	0.63	5.80	8.35	7.71	4.36-11.04
Pete Carroll	7.96	0.93	5.16	7.90	8.25	4.32-11.60
Raheem Morris	6.86	1.03	3.75	6.90	5.66	3.12-10.60
Ray Rhodes	7.54	0.88	4.88	7.70	7.4	3.95-11.13
Rex Ryan	8.38	1.02	5.32	8.01	9.33	4.65-12.10
Rich Brooks	7.30	1.1	4.00	7.08	6.5	3.50-11.11
Rich Kotite	6.26	0.99	3.27	6.56	4.75	2.56-9.96
Richie Petitbon	6.97	1.23	3.28	6.56	4	3.03-10.91
Rod Marinelli	5.86	1.07	2.65	6.11	3.33	2.08-9.64
Romeo Crennel	6.87	0.95	3.99	7.07	6	3.20-10.53
Sam Wyche	6.99	1.03	3.90	7.01	6	3.26-10.73
Scott Linehan	6.98	1.10	3.67	6.84	5.5	3.17-10.79
Sean Payton	9.24	0.85	6.68	8.98	10.33	5.68-12.80
Steve Mariucci	8.21	0.77	5.88	8.41	8.5	4.73-11.69
Steve Spagnuolo	5.87	1.07	2.66	6.12	3.33	2.09-9.65
Steve Spurrier	7.14	1.09	3.84	6.96	6	3.33-10.94
Ted Marchibroda	6.79	0.86	4.21	7.22	6.16	3.22-10.35
Todd Haley	7.40	1.02	4.33	7.31	7	3.67-11.13
Tom Cable	7.31	1.11	3.95	7.04	6.5	3.48-11.13
Tom Coughlin	8.62	0.60	6.80	9.07	8.87	5.31-11.93
Tom Flores	7.14	1.09	3.86	6.98	6	3.34-10.94
Tony Dungy	9.94	0.67	7.93	9.87	10.69	6.57-13.32
Tony Sparano	7.73	0.94	4.90	7.72	7.75	4.08-11.38
Vince Tobin	7.10	0.95	4.23	7.24	6.5	3.44-10.77
Wade Phillips	9.05	0.79	6.67	8.97	9.75	5.55-12.54
Wayne Fontes	8.09	0.94	5.25	7.97	8.5	4.44-11.74

One thing to note about this information is that some of it points to possible violations of the model's assumptions. The top two coaches both spent a lot of their career with transcendent quarterbacks, for example. That's ok -- the model will simply be off on coaches for whom the assumptions don't hold as well. This is not about finding an exact cause-and-effect relationship, it's about finding general corrolative information, which means that some coaches will be easier to predict than others.

Betting Market Power Rankings – Offense and Defense Rankings

2012-01-06T01:20:00.014-05:00

by Michael Beuoy

The purpose of this post is to show how the Betting Market Power Rankings can be decomposed into Offensive and Defensive strength by looking at the over/under betting lines in conjunction with the point spreads.

One of the best features of the Advanced NFL Stats efficiency model is that it not only tells you who the best teams are, it also tells you why those teams are the best (passing efficiency, rushing success rate, penalty rate, etc.). Unfortunately, the betting markets don’t tell us why they favor one team over the other; all we get is the final point spread. However, by looking at the betting over/under for each game, and combining it with the point spread, we can at least get a sense as to whether it is offense or defense (or both) that is driving the market’s evaluation of each team.

First, a caveat. For the purpose of these rankings, Offense is defined strictly as “Points Scored per Game” and Defense as “Points Allowed per Game”. While this may align with the general public sentiment as to what makes a good offense or a good defense, the definition is not perfect. The points a team scores is not solely a product of offensive skill and/or the defensive skill of their opponent. It can also be affected by the following:

• Their defense – A defense can provide favorable field position to its offense by forcing short drives or turnovers.
• Special Teams play
• Pace – Not sure if this is much of a factor in the NFL (I know it is in basketball), but teams that play a faster paced game that runs less clock (no huddle, few running plays) will result in games with more scoring opportunities for both teams for a given 60 minutes of playing time.

The ANS efficiency model avoids these pitfalls by focusing on per-play statistics. But I have no choice but to work with per-game estimates.

Methodology
The methodology ended up being very similar to the original power ranking methodology. I just had to apply some simple algebra in order to arrive at a new target. I’ll take Week 16’s Arizona @ Cincinnati game as an example. Cincinnati was favored by 4.5 points and the over/under on total points was 40.5. So, if the difference of the scores was expected to be 4.5 and the sum of the scores was expected to be 40.5, then that means that the implied predicted score was Cincinnati 22.5 and Arizona 18 (simple algebra).

We know that average points scored in the NFL is around 22 points per team. So, the fact that the market expected Arizona to score only 18 points says either that Cincinnati’s defense is good, or that Arizona’s offense is bad (or a combination of both). Much in the same way that a high point spread tells you either the favored team is good or that the underdog is bad (or a combination of both).

Here is how I built the original model that was based solely on point spreads (GPF = Generic Points Favored):

Point Spread = Home Team GPF - Visiting Team GPF + 2.5

With the team GPFs determined such that they best predicted the point spreads.

The new model is built in a very similar fashion as follows:

Implied Home Score = League Average Scoring + Home Team Offense GPF (oGPF) – Away Team Defense GPF (dGPF) + 1.25
Implied Away Score = League Average Scoring + Away Team Offense GPF (oGPF) – Home Team Defense GPF (dGPF) - 1.25

Where I now determine two separate numbers for each team, an “oGPF” and a “dGPF”, which sum to the total team GPF (the League Average Scoring term works just like an intercept). Also note that I split the 2.5 point home field advantage evenly between offense and defense.

See below for an updated week 16 ranking that includes O RANK and D RANK (I continue to blatantly plagiarize the ANS format):

Rank	Team	GPF	GWP	O Rank	D Rank	ANS Rank
1	NE	9	0.78	1	16	4
2	GB	8.5	0.77	3	9	5
3	NO	7.5	0.74	2	17	3
4	SF	5	0.68	13	1	13
5	PHI	5	0.67	4	13	6
6	BAL	4.5	0.66	11	3	9
7	PIT	4	0.64	14	2	2
8	ATL	4	0.64	8	8	12
9	DAL	3	0.60	5	21	7
10	SD	2.5	0.60	6	20	11
11	NYJ	2.5	0.59	12	7	16
12	NYG	1.5	0.55	7	25	8
13	MIA	1.5	0.55	18	5	18
14	DET	1	0.54	9	23	10
15	SEA	1	0.53	16	10	24
16	TEX	0	0.50	24	4	1
17	CIN	0	0.50	17	14	15
18	WAS	-0.5	0.48	21	12	19
19	DEN	-1	0.47	25	11	25
20	CAR	-1	0.47	10	26	23
21	TEN	-1.5	0.44	23	15	21
22	ARZ	-2	0.43	22	19	22
23	CHI	-2	0.42	27	6	17
24	RAI	-3.5	0.38	15	29	14
25	BUF	-4.5	0.35	20	28	20
26	MIN	-4.5	0.35	19	30	32
27	KC	-5	0.33	31	18	27
28	CLE	-5.5	0.31	30	22	26
29	TB	-7	0.27	26	31	30
30	STL	-7	0.27	32	24	29
31	JAC	-7.5	0.26	29	27	28
32	IND	-8	0.24	28	32	31

A couple things to note:

• These should match the previous Week 16 rankings, but they don’t. I think there were line movements prior to Sunday which shuffled the rankings a bit.
• Both the top 3 offenses (NE, NO, GB) and the top 3 defenses (SF, PIT, BAL) pass the sniff test.

Here’s another view which shows the oGPF and the dGPF explicitly (the baseline League Average scoring is 22.0 points).

Rank	Team	GPF	oGPF	dGPF
1	NE	9	8.5	0
2	GB	8.5	7.0	1.5
3	NO	7.5	7.5	0
4	SF	5	0.5	4.5
5	PHI	5	3.5	1
6	BAL	4.5	1.0	3.5
7	PIT	4	0.5	4
8	ATL	4	2.5	2
9	DAL	3	3.5	-0.5
10	SD	2.5	3.0	0
11	NYJ	2.5	1.0	2
12	NYG	1.5	2.5	-1.5
13	MIA	1.5	-0.5	2
14	DET	1	2.5	-1
15	SEA	1	-0.5	1
16	TEX	0	-2.0	2
17	CIN	0	-0.5	0.5
18	WAS	-0.5	-2.0	1
19	DEN	-1	-2.0	1
20	CAR	-1	1.5	-2.5
21	TEN	-1.5	-2.0	0.5
22	ARZ	-2	-2.0	0
23	CHI	-2	-4.0	2
24	RAI	-3.5	0.0	-3
25	BUF	-4.5	-1.0	-3
26	MIN	-4.5	-1.0	-3.5
27	KC	-5	-5.0	0
28	CLE	-5.5	-4.5	-1
29	TB	-7	-3.5	-3.5
30	STL	-7	-6.0	-1.5
31	JAC	-7.5	-4.5	-3
32	IND	-8	-4.5	-3.5

What jumped out at me most here was how much wider the variation was in the oGPF than in the dGPF. The standard deviation of the oGPF is 3.6 points, while it is 2.2 points for dGPF. In the comments on the ANS Week 17 Efficiency Rankings, there was a discussion with respect to the variability of offensive and defensive stats, with the conclusion that team defensive stats are more variable week to week because the defenses are at the mercy somewhat of what the offenses can do. I think the data above supports that conclusion, but I may not have thought it through entirely.

Also, there is a correlation between the oGPF and dGPF, which probably goes beyond bad teams just being bad on both sides of the ball. The correlation coefficient is 0.24 (it varies from 0.05 to 0.50 when looking at past seasons, but it’s always positive)

I’m hoping to do an updated ranking (including the oGPF and dGPF split) featuring just the 12 playoff teams and the latest lines, but I may not have time to get it out before the Wildcard round starts.

Also, you can use the chart above to build point spreads and over/unders for any matchup.

Respect Randomness, K.I.S.S., Beat Vegas.

2012-01-05T22:37:00.008-05:00

by Jim Glass

The 2011 end-of-season result is in for BigWin% - the team rating system that treats games decided by one score, 8 points or less, as ties in computing each team's W-L%, then adds a strength-of-schedule adjustment, that is all. (Rationale and background explained previously.)

Here are game prediction and efficiency results for the final eight weeks of the season. ("Efficiency" = correct game predictions divided by expected correct predictions. E.g., if among a week's 16 predictions the average predicted winner is a .750 favorite then 12 correct predictions would be expected. If the actual number is 10 then efficiency is .833, if 11 then efficiency is .917, etc.)

	Won-Lost	PCT	Efficiency
Big Win Index	82-40	.672	1.003
Las Vegas	81-43	.653	.985

(Game counts don't match because of no-favorite predictions and "push" results.)

OK, this isn't really a method to "beat Vegas", that was just a bit of hyperbole.

But it's remarkable that such a simple, bare bones rating-and-picking system can so equally match Vegas while dismissing 51% of all game outcomes as being 50-50, split-the-difference, random chance. And while being applied purely mechanically, with no knowledge of teams being down to their third-string QBs, special match-ups, teams resting starters, or any of the other game-specific information known to Vegas.

Of the 126 games played during these eight weeks, 64 were decided by less than 9 points. That is 50.8%, or slightly more than the 42% of game outcomes that are determined by random chance according to Brian Burke. These game outcomes were dismissed, treated as "ties" by BigWin%.

Disregarding more than half of all game decisions may seem like the loss of a lot of information when evaluating teams, but sometimes less is more. Or, more may be less when what is considered more information really is just random noise.

The idea behind BigWin% simply was to filter out the 42% of game decisions that Brian says are decided by chance to get team W-L records much less distorted by chance. It works!

One can draw much larger lessons from this exercise about sport, life, fate, and the great amounts of work and resources that are spent in our time on parsing noise, but I shall resist.

For the record, here are the season-end BigWin% ratings of all the teams to make the playoffs:

RANK	Team	Big Win%
1	GB	0.776
2	NE	0.743
3	NO	0.710
4	BAL	0.647
5	SF	0.639
6	PIT	0.623
7	HOU	0.600
8	DET	0.581
9	CIN	0.580
...	...	...
12	ATL	0.544
...	...	...
17	NYG	0.507
...	...	...
25	DEN	0.399

Yes, Denver is down at #25. BigWin% considers Denver's record during the 11 games with Tebow starting to be 4.5-6.5 (1-3 in two-score games plus seven close games divided 3.5-3.5) against .476 strength opposition, or .385 overall.

One of the life lessons exercises like this teach is to not confuse luck with a repeatable skill, but I've beaten that drum before.

Towards a Better Pythagorean: Should Football Outsiders "hold the update"?

2011-12-23T20:10:00.007-05:00

by Jim Glass

The good people at Football Outsiders say they are changing the formula for Pythagorean Expectation that they use to gauge team strength, and intend to update all the Pythagorean data on their website via their new formula during the offseason.

The "traditional" Pythagorean formula they've used until now produces a win expectation with about a 91% correlation to actual team wins. They say the new, improved formula increases the correlation to .9134 from .9120.

That's something - but a much simpler adjustment to applying the standard Pythagorean formula that I've been using increases the correlation to 95%. Also, while FO's new methodology uses a log function applied to year-to-date data that will be opaque to the average fan, the method I've been using gives a clear game-by-game result that anybody can easily grasp.

So I submit, for their consideration and yours, the formula adjustment below as being more accurate, simpler to apply, and easier for fans to refer to, understand, and play with.

Take it for what it's worth.

Regular Pythagorean
For those who may be unfamiliar with it, "Pythagorean win expectation" or "projection" is an expected winning percentage derived for a team from its points for-against totals using the formula PF^X/(PF^X+PA^X). It was created by Bill James in the 1980s for baseball, and the exponent "X" he used was 2. Its form reminded him of the Pythagorean Theorem in geometry, hence the name.

The idea quickly was applied to other sports, with modest changes in the exponent found to provide "best fit" for each. The exponent derived for the NFL in the 1980s was 2.37, and it has been the most commonly used ever since - for instance, in determining the "expected W-L" numbers on the team pages at PFR.com. I find that for the years 2001-10 the exponent producing the best fit is 2.67, but the difference this change makes is very minor and not the point here.

Pythagorean expectation is derived not from the difference between points "for" and "against" but from their ratio. NFL teams score an average of about 22 points per game. A team that outscores its opponents by an average of 10 points using offense, by 32-22, has a Pythagorean expectation of 72%. Another that outscores its opponents by the same average of 10 points using defense, by 22-12, has a win expectation of 83%. (This makes sense since if in ten games played to a decision a team outscored its opponents by 50-0 then it must have gone 10-0, while if it outscored them by 450-400 it's likely to have lost several of those shoot-outs, possibly most of them.)

Plenty of data from all the major sports show that when a team's W-L record is a lot better or worse than its Pythagorean expectation there is a strong tendency for its future WL% to regress to its Pythagorean. WL% diverging from Pythagorean expectation is commonly deeemed the result of luck, good or bad, with the Pythagorean being a measure of the team's true strength. This is supported by that fact that going forward, Pythagorean expectation is demonstrably better than past WL% as a predictor of future WL%.

"Unit Pythagorean"
Pythagorean expectation has always been figured using total points for and against for the entire season. A while back I wondered what the result would be if it was calculated on a game-by-game basis, computing the expectation for each individual game score and then averaging them. No more than that. Simple.

Applying both regular Pythagorean and what I think of as "unit Pythagorean" - treating each game as an individual unit, rather than all games in the aggregate - to all 319 teams during the ten seasons 2001-10, using the 2.67 exponent, and comparing the difference between actual and expected winning percentage, produced these results:

* Correlation between expected and actual wins increased to .952 from .914.

* Standard deviation of the difference between actual and expected winning percentage fell to .130 from .180.

A significant improvement. The original 8.6 points of "non correlation" are reduced by 44% while the standard deviation of the difference between expected and actual wins is reduced by 28%.

The reason behind this improvement, I believe, is that figuring the Pythagorean for each game as an individual unit increases the number of observations. Football (unlike baseball) is always cursed by small sample size in statistical analysis. "Per play" analysis systems (such as EPA and DVOA) work by counting each play as an observation, greatly increasing the number of observations about a team compared to the few outcomes observed in its won-lost record. This is especially so early in the season when W-L totals are so low as to prove nothing, but hundreds of plays per team can be evaluated to provide credible estimates of team strength.

Increasing the number of Pythagorean observations from one to as many as 16 or more should provide similar benefits - as one example, in containing the excess effects of extreme, outlier game scores.

For instance, in week 7 the Saints beat the Colts by 62 to 7. The Unit Pythagorean method gives the Saints a .997 score for that week, but only for that week. A Pythagorean expectation of over .969 rounds off to a perfect 16-0 season, so any percentage higher than that is meaningless in practical terms. The Saints exceeded that .969 when the score in that game reached 27-7. The extra 35 points they scored beyond that increased their Unit Pythagorean score for the game by only .028, which divided by 16 games is less than .002, about nothing, just what it should be in practical terms.

But those extra 35 points have a significant impact on regular Pythagorean expectation, as they average 2.2 points a game that one might think of as being "carried over" into other games over the entire season. Over a 16-game season they increase an otherwise average .500-team's winning expectation to over 56%, and the effect is of course larger earlier in the season. At mid-season, after 8-games, after the 62-7 score, a team with a Unit Pythagorean of .500 would have a regular Pythagorean of .620 -- and look like a contender.

Another advantage of Unit Pythagorean is that it is really easy on the eye and the understanding. One can produce a simple table of each team's game-by-game Pythagorean to show just where its Unit Pythagorean came from. The total season-to-date Unit Pythagorean is just the average. If one wants, one can add a column adjusting each game's "rating" by the strength of the opponent, to give a "quality" measure for each game. Then one can rank individual games in order of impressiveness of performance, draw a trend line to see if performance is getting better or worse, lots of things ñ all with no math any more fancy than the Pythagorean formula itself given above.

Pythagenport
Football Outsiders can best explain its own proposed change for itself. Quoting:

We've been writing about the Pythagorean projection since we launched in 2003. We've always used 2.37 as the exponent in the equation ... However, that exponent is based on the offensive environment of the league. We all know the offensive environment is a bit different now. Teams are scoring more points and allowing more points. So the exponent has changed, and 2.37 is not the most accurate way to estimate Pythagorean wins anymore.

Actually, if we want to be as accurate as possible, each team plays in a different offensive environment. Saints games feature lots of points. Jaguars games feature fewer points. The exponent should be different for each team. Baseball Prospectus discovered this a few years ago and started replacing Pythagorean wins with something it called "Pythagenport" (after writer Clay Davenport).

I've figured out a similar method to get better results for the NFL. Pythagenport finds a different exponent for each team based on their offensive environment. The equation that works best in the NFL is 1.5 * log ((PF+PA)/G). The improvement is slight. The correlation between Pythagorean wins and actual wins for 1990-2010 is .9120. The correlation between Pythagenport and actual wins for 1990-2010 is .9134.

However, the improvement from Pythagenport is bigger in recent seasons because scoring has been higher in recent seasons. (In particular, it helps with the Colts, who have continuously outperformed the standard Pythagorean projection all decade.)

Note that I am not criticizing Pythagenport in any way. If it has something interesting to say about the Colts outlier performance regarding regular Pythagorean in recent years, I'm eager to hear it.

All I'm doing is reporting the results I find. Comparing expected-to-actual wins for the 319 team seasons during the years 2001-10, computed using regular Pythagorean, the Pythagenport formula given above, and Unit Pythagorean, I find...

	Correlation	Standard Deviation
Unit Pythagorean	0.952	0.130
FO Pythagenport	0.916	0.167
Reg. Pythagorean	0.914	0.180

Into the public domain Unit Pythagorean is like Big Win% in that it is so simple I have to believe others have used it before, though I have no knowledge of anyone who has. I make no claim to having "invented" it, only to having independently come upon it.

The two are closely related, both use the fact that one-sided victories (and defeats) are much better indicators of team strength than close game outcomes. But while BigWin% treats close games as ties, Unit Pythagorean gives a "strength" rating on a graduated scale to every outcome: Winning a game by 23-22 gives the winner a 53% strength rating for the game (before adjusting for home field advantage and strength of schedule). So one can easily produce a ranking of all teams by strength using Unit Pythagorean and a strength-of-schedule adjustment.

The idea of applying Pythagorean expectation game-by-game came to me when considering the peculiar fact that when applying BigWin% backward to the past 15 years of playoff games, it outperformed not only regular WL% at "predicting" winners (as expected) but also outperformed Pythagorean. That was surprising, because while BigWin% considered only won-lost-tie data, Pythagorean considered all game scores in a theoretically sound manner. It seemed peculiar that the method more crudely using less data would be more successful.

Then it occurred to me that as Pythagorean used only one observation (total points for and against for the season) while BigWin% used 16 (all game outcomes) regular Pythagorean might actually be using less data.

Be that as it may, here are what I tried and the results. Take them for what they are worth and, if you wish, use it all as you will.

Just for fun, below is the Dolphins' game-by-game Pythagorean performance adjusted by strength of opponent. Worst performance: Game 5 against the Jets. Best: Game 10 against the Cowboys.

Trend: Strongly up.

Maybe things are looking up for the next coach.

Betting Market Power Rankings – Week 16

2011-12-22T09:33:00.007-05:00

by Michael Beuoy

Here are the week 16 betting market power rankings. I have provided two versions this time because I think the default methodology is breaking down this late in the season. The default methodology incorporates the following week’s spreads into the rankings, if they’re available. Because week 17 often includes meaningless games for teams trying to stay healthy for the playoffs, the spreads don’t necessarily reflect the true strength differential.

For example, the week 17 line for the Green Bay- Detroit game has Green Bay as a 3 point underdog. At home. It’s not very likely that the market thinks that Detroit is truly 5.5 points better than Green Bay, but it does appear to expect Green Bay to have things wrapped up by week 17 and not be playing at full strength.

So, I have provided two versions of the rankings. The first is the standard approach, which includes week 17 lines (probably not reliable). The second excludes week 17 from the rankings, and appears to make more sense.

Methodology
The goal I had was to generate a set of point-based rankings that would best predict how the betting market would set the point spread for the coming week’s matchups. The better I was able to match the point spread, the better the rankings were a reflection of the market’s estimate of team by team strength. Through trial and error experimentation, I found that using point spreads for the most recent five weeks (with higher weighting given to more recent weeks), combined with an adjustment that accounted for actual game outcomes, generated the best predictive accuracy. More detail here.

Week 16 Rankings – Including Week 17 Lines (probably not reliable)

Glossary:
LSTWK - The betting market rank as of the prior week (using the same methodology).
GPF - Stands for Generic Points Favored. It’s what you would expect a team to be favored by against a league average opponent at a neutral site.
GWP - Stands for Generic Win Probability. I converted the GPF into a generic win probability using the following formula: GWP = 1/(1+exp(-GPF/7)). This gives a more direct comparison to the ANS rankings.
ANS RNK - The Advanced NFL Stats Team Efficiency rankings for the same week.
ANS GWP - The Advanced NFL Stats Generic Win Probability for the same week.

RANK	Team	LSTWK	GPF	GWP	ANS RNK	ANS GWP
1	NE	2	8.0	0.76	4	0.68
2	NO	3	8.0	0.75	3	0.68
3	BAL	4	5.0	0.68	9	0.61
4	GB	1	5.0	0.68	5	0.67
5	DET	10	5.0	0.67	10	0.57
6	ATL	7	5.0	0.66	12	0.56
7	SF	6	4.5	0.66	13	0.52
8	PHI	12	4.5	0.66	6	0.65
9	PIT	5	4.5	0.65	2	0.74
10	SD	11	4.0	0.63	11	0.57
11	DAL	9	3.0	0.60	7	0.63
12	NYJ	8	3.0	0.60	16	0.50
13	NYG	13	1.5	0.56	8	0.63
14	MIA	18	0.5	0.52	18	0.48
15	TEX	14	0.0	0.51	1	0.76
16	CIN	17	-0.5	0.49	15	0.50
17	CAR	23	-0.5	0.49	23	0.42
18	SEA	20	-0.5	0.48	24	0.42
19	WAS	24	-0.5	0.48	19	0.48
20	TEN	16	-1.0	0.46	21	0.45
21	ARZ	22	-1.5	0.45	22	0.43
22	DEN	15	-2.0	0.42	25	0.39
23	RAI	21	-2.5	0.41	14	0.52
24	MIN	25	-3.5	0.37	32	0.28
25	CHI	19	-4.0	0.36	17	0.48
26	BUF	26	-4.5	0.35	20	0.45
27	KC	30	-5.0	0.32	27	0.34
28	CLE	27	-5.5	0.32	26	0.35
29	TB	29	-6.5	0.28	30	0.30
30	JAC	28	-6.5	0.28	28	0.34
31	IND	32	-7.5	0.25	31	0.29
32	STL	31	-9.0	0.22	29	0.32

Week 16 Rankings – Excluding Week 17 Lines

RANK	Team	LSTWK	GPF	GWP	ANS RNK	ANS GWP
1	NE	2	9.0	0.79	4	0.68
2	GB	1	8.5	0.77	5	0.67
3	NO	3	7.5	0.74	3	0.68
4	SF	6	5.0	0.68	13	0.52
5	PIT	5	5.0	0.67	2	0.74
6	BAL	4	5.0	0.67	9	0.61
7	ATL	7	4.5	0.65	12	0.56
8	PHI	12	4.5	0.65	6	0.65
9	DAL	9	3.5	0.62	7	0.63
10	NYJ	8	2.5	0.59	16	0.50
11	SD	11	2.5	0.59	11	0.57
12	DET	10	1.5	0.55	10	0.57
13	NYG	13	1.0	0.54	8	0.63
14	MIA	18	1.0	0.53	18	0.48
15	SEA	20	0.5	0.52	24	0.42
16	TEX	14	0.0	0.51	1	0.76
17	CIN	17	-0.5	0.49	15	0.50
18	WAS	24	-0.5	0.48	19	0.48
19	CAR	23	-1.0	0.47	23	0.42
20	DEN	15	-1.0	0.47	25	0.39
21	TEN	16	-1.5	0.44	21	0.45
22	ARZ	22	-2.0	0.43	22	0.43
23	CHI	19	-2.5	0.42	17	0.48
24	RAI	21	-3.0	0.39	14	0.52
25	MIN	25	-4.5	0.35	32	0.28
26	BUF	26	-4.5	0.35	20	0.45
27	KC	30	-5.0	0.32	27	0.34
28	CLE	27	-5.5	0.31	26	0.35
29	TB	29	-6.5	0.28	30	0.30
30	JAC	28	-7.0	0.27	28	0.34
31	IND	32	-8.0	0.24	31	0.29
32	STL	31	-8.5	0.23	29	0.32

• There’s a new number one, with New England leap-frogging Green Bay for the top spot (but only ahead by a half point)
• Philadelphia was one of the bigger movers this week and is now ranked as the best team in the NFC East.
• The Lord taketh away – After moving up five spots last week from 20 to15, Denver drops back down to 20.
• The Colts were able to crawl out of both the Betting Market Ranking basement as well as the ANS Ranking basement. Yay?

Prediction of This Week’s Point Spreads
See below for how well the ranking methodology predicted this week’s point spreads. Note that the “PRED LINE” column excludes both week 17 lines (because it is unreliable) as well as week 16 (because I want to see how well the model does when it can’t “peek” at the answers)

Game	Pred Line	ActLine	Diff
ARZ @ CIN	4.5	4.0	-0.5
ATL @ NO	5.0	6.5	1.5
CHI @ GB	13.5	13.0	-0.5
CLE @ BAL	13.0	13.0	0.0
DEN @ BUF	0.5	-2.5	-3.0
JAC @ TEN	8.5	7.5	-1.0
MIA @ NE	11.5	9.5	-2.0
MIN @ WAS	5.5	6.5	1.0
NYG @ NYJ	4.5	3.0	-1.5
PHI @ DAL	2.5	1.5	-1.0
RAI @ KC	0.0	1.0	1.0
SD @ DET	1.5	2.0	0.5
SF @ SEA	-2.5	-2.5	0.0
STL @ PIT	15.5	16.0	0.5
TB @ CAR	8.5	7.5	-1.0
TEX @ IND	-5.5	-6.0	-0.5

I probably won’t generate these rankings next week (I will be out of town without access to a computer and the rankings themselves probably won’t have much value, owing to the week 17 issue). However, I am thinking I may try to update these after each playoff week, as a way to see how the market continues to re-evaluate team strength.

Dispatches From the Anti-League: #2

2011-12-21T18:52:00.005-05:00

by James Sinclair

In September I wrote an overview of a fantasy football league some friends and I started this year where the goal is to compile the worst team possible. Here's the long-awaited follow-up—a bit later than intended, but at least I got it in before the end of the season. Barely.

First, a few observations:

1. The draft was considerably less important than in conventional fantasy football, because in the Anti-League it's actually possible for a player to be too "good" (and with that, I'll stop using quotation marks to indicate ironic reversals of good and bad, because it would definitely get out of hand). Case in point: my first round pick, Jacksonville's Luke McCown. He put up a decent score in week 1, and then an outstanding score against the Jets in week two (the fifth-highest single-game point total of the year, as you'll see below). And even as I was watching that game I was thinking "oh crap, he's going to be benched", which is exactly what happened. Fortunately I was able to pick up Blaine Gabbert off waivers, and even more fortunately the Jaguars have stuck with Gabbert all season (presumably because their backup is Luke McCown).

Other first round picks included two rookie quarterbacks widely expected to be awful—Andy Dalton and Cam Newton. Dalton has been kind of middle-of-the-road (several higher-scoring quarterbacks went undrafted), while the Newton pick, beginning with his -10.7 point effort in week 1, was a disaster.

2. There might've been some concerns that it would be too difficult to keep scores in the black, and thus tempting to leave roster spots empty or start inactive players, but for the most part that didn't happen. Although I did win my first game with a score of -8.8 to -18.5 (no comment on whether the team I was facing was full of superstars like Tom Brady and Adrian Peterson because its owner had auto-drafted, and then couldn't change his roster in time, and was somehow on track to beat me anyway until Brady put up a -26.5 in the Monday night game).

3. It's hard to conceive of a scenario where a player could excel under both Anti-League and conventional fantasy scoring in the same game, but it hasn't been uncommon for a player to wind up with modest, but positive point totals in both. A running back who gets 50 yards on 15 carries, for example, would earn 5 points in each scoring system.

The point system (which is detailed at the bottom of the September post) was never intended to scientifically determine the worst (or least effective) players, of course, but our hope was that it would at least be somewhere in the vicinity. There are plenty of areas where some tweaking may be in order—QB scores are probably higher than they should be relative to other positions, WR scores are a little screwy and maybe too QB-dependent, etc.—but overall I'm pretty happy with the results.

Here are the ten highest-scoring quarterbacks who've started at least eight games (averages reflect points scored in starts only):

	Quarterbacks	Team	Starts	Pts/Start
1	Sam Bradford	StL	10	15.3
2	Blaine Gabbert	Jax	12	14.6
3	Colt McCoy	Cle	13	10.5
4	Rex Grossman	Was	11	9.3
5	Christian Ponder	Min	8	8.5
6	Matt Cassel	KC	9	8.2
7	Curtis Painter	Ind	8	8.1
8	Joe Flacco	Bal	14	7.4
9	Tarvaris Jackson	Sea	12	7.3
10	Kevin Kolb	Ari	9	7.3

As you can see, it's been a banner year for the Big 12. Also, honorable mention to Caleb Hanie, who has averaged an incredible 19.0 in his four starts.

Here are the leaders at the other positions (for reasons explained in the September post, we don't have a roster spot for tight ends):

	Running Backs	Team	Games	Pts/Gm
1	Peyton Hillis	Cle	8	6.9
2	Chris Johnson	Ten	14	6.6
3	Montario Hardesty	Cle	8	6.3
4	Dexter McCluster*	KC	14	5.0
5	Daniel Thomas	Mia	11	4.8
6	Deji Karim	Jax	11	4.6
7	Javon Ringer	Ten	12	4.4
8	Tashard Choice	3TM	11	4.4
9	Roy Helu	Was	14	4.0
10	Joseph Addai	Ind	10	3.9

*I'm including McCluster on just the RB list, but in many fantasy leagues he's also eligible at WR.

	Wide Receivers	Team	Games	Pts/Gm
1	Austin Collie	Ind	14	6.3
2	Mike Thomas	Jax	13	6.2
3	Mike Williams	TB	14	5.7
4	Brandon Lloyd	2TM	13	5.4
5	Greg Little	Cle	14	5.2
6	Donald Jones	Buf	8	5.1
7	Jon Baldwin	KC	9	4.7
8	Andre Caldwell	Cin	13	4.5
9	Devin Aromashodu	Min	14	4.4
10	Eddie Royal	Den	10	4.4

	Kickers	Team	Games	Pts/Gm
1	Graham Gano	Was	14	2.3
2	Olindo Mare	Car	14	2.1
3	Shaun Suisham	Pit	14	1.4
4	Neil Rackers	Hou	14	1.4
t5	Billy Cundiff	Bal	14	1.3
t5	Mike Nugent	Cin	14	1.3

	D/ST	Pts/Gm
1	Colts	6.5
2	Buccaneers	5.9
3	Vikings	5.6
4	Raiders	5
5	Panthers	4.9
6	Giants	4.8
7	Bills	4.2
8	Patriots	4
9	Saints	3.8
10	Rams	3.7

Some big names at the top of the running back list, but Peyton Hillis and Chris Johnson have both had rather mediocre seasons—127 carries for 445 yards (3.5 yds/carry) and 3 TDs for Hillis; 232 carries for 930 yards (4.0 yds/carry) and 4 TDs for Johnson.

Drifting further into the realm of morbid curiosity, here are the best single-game point totals. First, the quarterbacks, whose scores were generally higher than the other positions:

	Player	Team	Opp.	Week	Pts
1	Mark Sanchez	NYJ	@Bal	4	34.5
2	Caleb Hanie	Chi	KC	13	32.8
3	John Beck	Was	@Buf	8	30.6
4	Matthew Stafford	Det	@Chi	10	29.4
5	Luke McCown	Jax	@NYJ	2	28.3
6	Kevin Kolb	Ari	@Min	5	27.4
t7	Charlie Whitehurst	Sea	@Cle	7	27.0
t7	Sam Bradford	StL	Sea	11	27.0
9	Sam Bradford	StL	Was	4	26.8
10	Joe Flacco	Bal	NYJ	4	26.5

And everyone else:

	Player	Pos	Team	Opp.	Week	Pts
1	Giants	D/ST	NYG	@NO	12	24.0
2	Calvin Johnson	WR	Det	@Chi	10	23.8
3	Colts	D/ST	Ind	@NO	7	23.0
4	Reggie Wayne	WR	Ind	Pit	3	21.2
5	Chris Johnson	RB	Ten	Bal	2	21.0
t6	Jacoby Jones	WR	Hou	Oak	5	20.2
t6	Arian Foster	RB	Hou	@Ten	7	20.2
8	Dolphins	D/ST	Mia	NE	1	19.5
9	Santonio Holmes	WR	NYJ	@Bal	4	19.4
t10	Greg Little	WR	Cle	@SF	8	19.0
t10	Rams	D/ST	StL	Bal	3	19.0
t10	Vikings	D/ST	Min	NO	15	19.0

Note that three of the top five defensive performances came against the Saints. And with that 24-point game the Giants achieved the highest score a defense can possibly get under our system (46+ points allowed, 550+ yards allowed, and no sacks, turnovers, blocked kicks, safeties, or TDs). The Colts would've pulled off a perfect score too, had they restrained themselves from sacking Brees a couple times.

Scores for kickers tended to be pretty low for the simple reason that kickers rarely miss—the most common single-game score was zero—but Neil Rackers (week 10) and Graham Gano (week 12) each had a 15-point day, which in both cases consisted of a missed field goal of less than 40 yards and the extremely rare 10-point missed PAT bonanza.

Finally, since I'm sure you were wondering, here are the worst single-game scores through week 15:

	Player	Pos	Team	Opp.	Week	Pts
1	Julio Jones	WR	Atl	@Ind	9	-36.8
2	Drew Brees	QB	NO	@Min	15	-34.4
t3	Aaron Rodgers	QB	GB	Den	4	-32.6
t3	DeMarco Murray	RB	Dal	StL	7	-32.6
5	Torrey Smith	WR	Bal	@StL	3	-31.4
6	Drew Brees	QB	NO	Ind	7	-30.3
7	Kevin Smith	RB	Det	Car	11	-30.2
t8	Arian Foster	RB	Hou	@Ten	7	-29.8
t8	Calvin Johnson	WR	Det	@Oak	15	-29.8
10	Pierre Garcon	WR	Ind	@TB	4	-27.2

I was surprised to see Julio Jones at the top, but it makes a certain amount of sense. The point system is designed to reward players who are heavily involved, but ineffective, and against the Colts Julio was just the opposite. He was barely involved (only four targets for three receptions, and he ran the ball twice), and he was extremely effective (164 total yards, including 50- and 80-yard catches for touchdowns). It was everything the Anti-League doesn't stand for.

The Favorite/Long Shot Bias – Analysis of Superbowl Futures

2011-12-18T19:00:00.021-05:00

by Michael Beuoy

In the week14 post, I outlined an approach to test the validity of the rankings by looking at Superbowl futures. At the time, I thought that Chris Cox’s NFL Forecast tool allowed for customization at the team strength level. Unfortunately, it doesn’t, but Chris was nice enough to run a one-off of his model, using the GWP’s from the Week 15 Betting Market Rankings.

Here are the results of the analysis. I took Superbowl futures from footballocks.com (thanks Ed) as of December 14. I then removed the “vig” from the odds under the assumption that each bet had the same (negative) expected value. In this case, the vig turned out to be a whopping 28%.

Glossary:
Futures Odds – The actual odds from footballocks.com
Futures Odds w/o Vig – Those same odds with the vig removed
NFL Forecast Odds – The odds of winning the Superbowl according to Chris Cox’s NFL Forecast simulation, using the week 15 Betting Market GWP’s
Futures Prob – The same as “Futures Odds w/o Vig” but expressed as a probability
NFL Forecast Prob - The same as “NFL Forecast Odds” but expressed as a probability
Exp Val / $ Bet – For you inveterate gamblers, the expected value of a $1 bet, using the “Futures Odds” column as the payout and the “NFL Forecast Prob” column for the probabilities

At 4.5 to 1, the Patriots are the only positive expected value bet, according to the NFL Forecast probabilities. Unfortunately for me, it’s against my religion to side with the Patriots on anything.

Team	Future Odds	Futures Odds w/o Vig	NFL Fcst Odds	Futures Prob	NFL Fcst Prob	Exp Val / $ Bet
ARZ	400	558	9999	0.20%	0.00%	($0.96)
ATL	40	56	70	1.70%	1.40%	($0.43)
BAL	08	12	09	8.00%	10.30%	($0.07)
CHI	50	70	4999	1.40%	0.00%	($0.99)
CIN	100	140	1999	0.70%	0.10%	($0.95)
DAL	20	28	142	3.40%	0.70%	($0.85)
DEN	18	25	173	3.80%	0.60%	($0.89)
DET	40	56	188	1.70%	0.50%	($0.78)
GB	02	03	02	28.70%	37.30%	($0.07)
TEX	15	21	35	4.50%	2.70%	($0.56)
KC	5000	6972	99999	0.00%	0.00%	($0.95)
NE	05	07	04	13.00%	20.80%	$0.14
NO	07	10	08	9.00%	11.70%	($0.06)
NYG	20	28	184	3.40%	0.50%	($0.89)
NYJ	18	25	134	3.80%	0.70%	($0.86)
RAI	100	140	1562	0.70%	0.10%	($0.94)
PHI	80	112	3124	0.90%	0.00%	($0.97)
PIT	09	13	13	7.20%	7.20%	($0.28)
SD	80	112	1999	0.90%	0.10%	($0.96)
SF	10	14	18	6.50%	5.30%	($0.42)
SEA	500	698	7142	0.10%	0.00%	($0.93)
TEN	200	279	908	0.40%	0.10%	($0.78)

My hope going into this was that the probabilities would align fairly closely. As can be seen from the table above, that was not the case. However, the results did follow a pattern that was familiar to me; one very similar to what is found in thoroughbred racing betting markets. The pattern becomes more apparent if you graph the NFL Forecast Odds against the No Vig Odds (shown on a log scale):

The straight line indicates perfect agreement between the two approaches. As the NFL Forecast odds get higher, the actual odds drop further below the line. If we take the NFL Forecast odds as the “real” odds, this means that the bigger the longshot a team is, the worse the value of the bet. Here’s one more view of the same data:

In horse racing, there is what’s known as the Favorite-Long Shot Bias. It’s a remarkably persistent phenomenon in which favorites are consistently underbet and longshots are consistently overbet (see Fig. 1 from the link). There are many theories behind what causes this. I’m partial to the most prevalent explanation, which is that gamblers are willing to pay a higher price for a low probability / high payoff bet than they are for high probability / low payoff bet. If you’re at the track, are you really going to be hi-fiving your friends after making a $5 profit on your $10 bet on a 3 to 2 horse? Similarly, laying down money on the Packers to win the Superbowl, at this point in the season, is not going to impress many people if the Packers happen to win.

This can also explain why lotteries are so popular, despite being one of the worst expected value bets you can make. Or why slots pay out worse than blackjack (jackpots are sexier than the slow and steady progression of blackjack). And, it appears to explain the payout odds of a team winning the Superbowl. That being said, there are alternative explanations:

• My conversion from GPF to GWP could be off. I use the formula GWP = 1/(1+exp(-GPF/7)). If the GWPs should be more “compressed” than what I have them as, then the odds should line up more closely. However, I just did a more thorough check, using NFL games back to 1998, and “GPF/7” generates the lowest mean squared error in terms of predicting win percentage at a given spread (I may share that in a separate post)
• Injuries. The GWPs are calibrated to match the market’s near - term predictions. An injury to a key player can cause a strong team’s performance to regress to the mean. It’s possible that the Superbowl futures have factored that uncertainty into the payouts.

I don’t think these alternatives could explain the magnitude of the discrepancy I’m seeing between the two sets of odds, so I’m sticking by the Favorite-Long Shot bias explanation.

A HUGE thanks to Chris Cox at nfl-forecast.com for running a custom version his model for me and sending the results.

Revisiting the Big Wins Index: the kind of wins today that do predict wins tomorrow

2011-12-16T13:32:00.006-05:00

by Jim Glass

All wins count equally in the standings ñ but they don't count equally as a measure of team strength or indicator of probable future won-loss record.

Brian Burke has written that random chance determines more than 40% of NFL game outcomes. Thirty years ago Bill James showed that baseball teams that win many (or few) close game later consistently see their W-L record regress to their record in decisive games - indicating that close game outcomes are heavily luck, and teams with good W-L records based on luck see their luck run out. At the same time, teams with disappointing W-L records due to having a lot of close losses offsetting decisive wins are primed for a turn to the better. This has since also been well documented for football and across other sports.

Of course, all this goes 100% *against* the great popular belief in the importance of "clutch play" - but that's reality. Last year, I looked at the results of 15 years of NFL playoff games for all teams that had won 11 or more games during the regular season. Sorting them by record in terms of "big wins", by 10 points or more, and "clutch, close wins", by less, produced these numbers...

* Four teams had 10 or more "big" wins in a season. Their playoff record was 11-1 with three Super Bowl wins (the fourth team was the 18-1 Patriots). Twelve teams had 9 or more "big" wins. Their playoff record was 24-7 with five SB winners, plus three SB runners-up - so eight of the 12 teams were in the Super Bowl.

* Nine teams had won nine or more close games during the regular season. Their subsequent record in the playoffs: 8-9.

* The 15 teams with the best close-game records during the regular season were a combined 103-11, 90%, in them. In the playoffs they had a record of 15-14, 52%.

* The seven teams with the worst records in close games during the regular season went only 18-30, 38%, in them. In the playoffs these "very worst" clutch-game teams went 14-4, 78%, and won three Super Bowls. (To have such an 11-5 or better W-L with a losing record in close games, these teams had to dominate in one-sided games ñ they were superior "big win" teams.)

So much for "champions win close games"!

Systematizing Big Wins.
The fact that decisions in one-sided games much better reflect team strength than decisions in close games has been known since the 1980s. But as of last year, as far as I knew, nobody had quantified the effect in a rating system. Hey, the world is full of rating systems, why not another one?

So I whipped up the "Big Win Index", a system that is simplicity itself: "Big" wins and losses are counted as wins and losses, "close games" are counted as ties, these give each team a winning percentage, which is adjusted in light of strength of schedule. Done.

But there is a real point behind it. Teams should not be evaluated on the basis of their luck. Treating close games as ties eliminates the luck factor in them for rating purposes - and so *should* produce a W-L% for each team that more closely reflects its true strength than the regular W-L record does.

As the break point between "big" and "close" I use 9 points - that eliminates just about the closest 40% of all games (corresponding to the percentage of game outcomes determined by luck) and is the border between one-score games, in which just one play may change the outcome up until the very last moment (see any Tebow game this year) and two-plus score games, in which one play can't.

This is not a "beat the Vegas spread" rating system. BWI doesn't know that the Texans are down to their third QB or if a blizzard is going to blow into Buffalo for the Dolphins game. It does not make fine distinctions between teams, or divine strengths and weaknesses. Its purpose is simply to make clear to the naked eye when one may be misjudging a team by putting too much weight on a WL record compiled in close decisions (and when other people may be doing it too). And at this, it has proved pretty effective.

Seen via Big Wins
Last season after 14 games the media and punditry were all hailing the 12-2 Falcons as they marched to the first seed in the NFC, while the Packers were a mediocre 8-6 struggling in the fight for a wildcard spot. But the first version of the BWI tabbed the Packers as #1 in the NFC and the Falcons as fifth. We know how that turned out. When the Falcons fell decisively before the Pack in their playoff game "it was hilarious to watch ESPN's Sports Reporters Sunday and see the likes of Lupica and Albom struggle to comprehend such an upset [BB]", but BWI said simply, "Best team won". The Packers had taken their losses close, the Falcons had taken their victories close.

This season after eight games, when I first ran the BWI numbers for this year, here's how they were sobering for NYC football fans (like me)...

* The Giants were a sterling 6-2, and Giants fans here in NYC were talking "Super Bowl run". But BWI picked them as the team most likely to fall off a cliff. With both their losses big and five-of-six wins small, their BW% was only 46%, with the toughest second-half schedule in the league ahead of them. They've since gone 1-4.

* The Patriots had just lost two straight to fall to 5-3 and were Vegas underdogs in a showdown with the Jets. Us Jets fans here in NYC were thinking "we're finally about to dethrone the Pats!" But all the Pats' losses were small, BWI still had them as the top team in the AFC and the Jets as just a little over .500. The Pats won by 21, and have been putting air between themselves and the competition ever since.

As to the hot topic of the moment, BWI is not impressed by the Tebow Broncos. It has the five-game Orton Broncos as a .475 team, the eight-game Tebow Broncos as a .468 team.

Perhaps this explains the mystery of Tebow's "missing stats", the Tebow "intangibles" that must exist in great amount to lift a 1-4 team up to being a 7-1 team, yet somehow can't be captured by any statistical system.

Broncos/Tebow fans treat close games as big ones, and so think Tebow has lifted the Broncos an immense distance, from being a .200 team to a .875 team, which would indeed be a tremendous accomplishment! If Tebow's huge contribution driving that immense improvement can't be seen in his numbers, then mere numbers simply must miss many very important things that go into winning football games.

But BWI says the Broncos with Orton were a 47% team, and with Tebow are still 47% team. There's no "magic" at all to explain in that. One doesn't have to work miracles to get a 47% team to a 47% level. How will this turn out in the end? We shall see.

Now I'll add that while BWI is in no way meant to serve as a "beat Vegas" metric, of course I do track it against the Vegas line (and other prediction systems) ñ and it has done surprisingly well.

The point spreads of the Vegas line and percentage win prediction of BWI are convertible into each other using Pythagorean and Log5. So in addition to tallying winning/losing picks, I also tally "efficiency", the number of favorites that win relative to the number that should win by the probabilities generated by the system. (For instance, say 10 of 16 picks win, .625. If the average pick was a 75% favorite then spreads are too high, efficiency is .625/.75 = .833, as 12 picks should have been winners and 10/12 =.833. The desired number is of course 1.00.)

Results for the five weeks of games 9 through 13.

Favorites	Won-Lost	PCT	Efficiency
Vegas	50-26	.658	99%
BWI	52-25	.675	102%

(Numbers don't match exactly because of "pick 'ems" and pushes.)

Pretty good! BWI is 1.5 games ahead of Vegas without even trying to be. Well, that's only by a hair, and this is a quite small sample size, so I don't expect it to last.

But I find it very interesting that a system that uses such extremely minimal information and calculations can be competitive with the most data-loaded and sophisticated of all. More on that another time, perhaps

Now, for any who've read this far and so may be interested, the current BWI.

2011 Big Win Ratings after Game 13
This table gives each team's BigW% (its expected winning percentage against average opposition), the corresponding number of games expected to have won currently out of 13, the average strength of its full-season opposition (including the final three games of the season) and its projected final result starting from today's actual record.

RANK	Team	Big Win%	Expected Wins	S-O-S	Projected Final
1	GB	0.78	10.19	0.466	15.4
2	NE	0.74	9.64	0.46	12.3
3	BAL	0.73	9.47	0.493	12.2
4	HOU	0.68	8.87	0.478	12.2
5	PIT	0.68	8.84	0.50	12.3
6	NO	0.67	8.72	0.476	12.1
7	CIN	0.62	8.09	0.496	9.0
8	SF	0.61	7.89	0.452	11.9
9	TEN	0.58	7.58	0.497	8.9
10	ATL	0.55	7.19	0.506	9.7
11	DET	0.55	7.19	0.522	9.5
12	DAL	0.55	7.12	0.461	8.9
13	NYJ	0.54	7.06	0.497	9.7
14	CHI	0.54	7.0	0.512	8.4
15	SD	0.53	6.83	0.498	7.4
16	PHI	0.48	6.27	0.483	6.5
17	SEA	0.48	6.2	0.482	9.4
18	NYG	0.47	6.15	0.507	8.5
19	DEN	0.47	6.11	0.508	9.4
20	CAR	0.46	5.92	0.505	5.2
21	MIA	0.44	5.76	0.498	5.1
22	MIN	0.43	5.61	0.512	3.2
23	BUF	0.43	5.58	0.515	6.1
24	JAC	0.42	5.52	0.527	5.4
25	WAS	0.37	4.87	0.484	5.2
26	ARI	0.37	4.85	0.483	7.2
27	OAK	0.36	4.67	0.507	8.1
28	KC	0.35	4.5	0.507	5.9
29	TB	0.31	4.09	0.548	4.9
30	CLE	0.28	3.69	0.532	4.6
31	IND	0.26	3.44	0.548	0.7
32	STL	0.24	3.11	0.535	2.5

There are no dramatic contrasts like last year's Green Bay-Atlanta. But for the record, measuring by the difference between actual WL% and BW%, the most overrated teams by regular WL% currently are:

* 0.217 Green Bay

* 0.179 Oakland

* 0.163 San Francisco

* 0.145 Denver

The Packers of course also are the best team by BW%, proving once more that being very good *and* lucky is the unbeatable combination.

The most underrated teams are ...

* -0.117 Jacksonville

* -0.135 Miami

* -0.148 Carolina

* -0.264 Indianapolis

* -0.277 Minnesota

There's always next year!

Betting Market Power Rankings – Week 15

2011-12-14T23:33:00.011-05:00

by Michael Beuoy

Here are the week 15 betting market power rankings. As noted last week (link), I have modified the methodology to now incorporate the point spreads for the upcoming week, if they’re available (week 16, in this case).

Methodology
The goal I had was to generate a set of point-based rankings that would best predict how the betting market would set the point spread for the coming week’s matchups. The better I was able to match the point spread, the better the rankings were a reflection of the market’s estimate of team by team strength. Through trial and error experimentation, I found that using point spreads for the most recent five weeks (with higher weighting given to more recent weeks), combined with an adjustment that accounted for actual game outcomes, generated the best predictive accuracy. More detail here

The Rankings
Here are the Betting Market Power Rankings for Week 15:

Glossary:
LSTWK - The betting market rank as of the prior week (using the same methodology).
GPF - Stands for Generic Points Favored. It’s what you would expect a team to be favored by against a league average opponent at a neutral site.
GWP - Stands for Generic Win Probability. I converted the GPF into a generic win probability using the following formula: GWP = 1/(1+exp(-GPF/7)). This gives a more direct comparison to the ANS rankings.
ANS RNK - The Advanced NFL Stats Team Efficiency rankings for the same week.
ANS GWP - The Advanced NFL Stats Generic Win Probability for the same week.

RANK	Team	LSTWK	GPF	GWP	ANS RNK	ANS GWP
1	GB	1.0	10.0	0.81	3	0.73
2	NE	2.0	8.0	0.76	4	0.67
3	NO	3.0	7.5	0.74	5	0.65
4	BAL	5.0	5.5	0.69	7	0.64
5	PIT	4.0	5.5	0.69	2	0.76
6	SF	6.0	4.5	0.65	17	0.50
7	ATL	7.0	3.5	0.62	11	0.55
8	NYJ	9.0	3.0	0.61	12	0.54
9	DAL	8.0	3.0	0.60	8	0.62
10	DET	12.0	2.0	0.58	10	0.61
11	SD	14.0	2.0	0.58	14	0.52
12	PHI	16.0	2.0	0.57	9	0.61
13	NYG	10.0	1.5	0.56	6	0.64
14	TEX	13.0	1.5	0.55	1	0.77
15	DEN	20.0	0.0	0.50	24	0.39
16	TEN	17.0	-0.5	0.49	18	0.48
17	CIN	15.0	-0.5	0.48	13	0.52
18	MIA	11.0	-0.5	0.48	20	0.45
19	CHI	21.0	-0.5	0.47	15	0.51
20	SEA	23.0	-1.0	0.46	25	0.38
21	RAI	18.0	-1.5	0.44	16	0.50
22	ARZ	22.0	-2.0	0.43	22	0.43
23	CAR	19.0	-2.5	0.41	23	0.40
24	WAS	26.0	-2.5	0.41	21	0.44
25	MIN	25.0	-3.0	0.40	28	0.33
26	BUF	24.0	-3.5	0.37	19	0.48
27	CLE	29.0	-5.5	0.31	27	0.34
28	JAC	30.0	-6.0	0.30	26	0.36
29	TB	28.0	-6.0	0.30	30	0.30
30	KC	27.0	-6.5	0.29	31	0.28
31	STL	31.0	-8.5	0.23	29	0.32
32	IND	32.0	-9.0	0.21	32	0.26

• Obligatory Tebow-Watch – Denver moved up 5 spots to number 15, and a GWP of 0.50.
• The ANS model still disagrees pretty significantly with the Betting Market on San Francisco.
• I’m surprised the Giants are ranked as low as they are.

Prediction of This Week’s Point Spreads

See below for how well the ranking methodology predicted this week’s point spreads:

Game	Pred Line	ActLine	Diff
BAL @ SD	-0.5	-2.0	-1.5
CAR @ TEX	6.0	6.5	0.5
CIN @ STL	-5.5	-6.0	-0.5
CLE @ ARZ	5.0	6.5	1.5
DAL @ TB	-5.5	-6.5	-1.0
DET @ RAI	-1.5	-1.0	0.5
GB @ KC	-13.5	-14.0	-0.5
JAC @ ATL	12.0	11.5	-0.5
MIA @ BUF	-1.5	1.0	2.5
NE @ DEN	-5.0	-6.0	-1.0
NO @ MIN	-8.5	-7.0	1.5
NYJ @ PHI	0.5	3.0	2.5
PIT @ SF	0.0	2.5	2.5
SEA @ CHI	2.5	4.0	1.5
TEN @ IND	-6.0	-6.5	-0.5
WAS @ NYG	7.0	7.0	0.0

Will Tim Tebow be Denver's Dick Jauron? Or: The Meaning of Clutch Victories

2011-12-09T09:13:00.006-05:00

by Jim Glass

Is the Tim Tebow story real? I enjoy Tebow, for years have wanted to see somebody try the option in the NFL, am entertained by watching the challenges it throws up for opposing teams, and am rooting for Tebow football to work. But is the Tim Tebow story as heard everywhere from his fans and admirers (and worshipers) real?

Tebow is a type of QB unique in the modern game. But the Tebow story is very old and familiar: the tale of "clutch winning". It's the story of *not* having the stats that go with winning, but winning anyhow. Thus, credit for winning goes to character, leadership, inspiring teammates, making others better, and - most of all - coming through with big plays in the last minutes to win close games in the clutch.

Tebowmania is based on the Broncos pulling out five close, clutch, one-score victories in the last moments (by 7, 4, and 3 points, and in OT twice) after he became the starting QB. These plus one decisive win and one decisive loss make the Broncos 6-1 with him at the helm, after a miserable 1-4 start with him on the bench. What a difference!

No, Tebow doesn't have the "stats" that usually go along with a QB who wins games. His EPA and WPA numbers are both negative, with his EPA-per-play rank 35th and WPA-per-play rank 27th. Other rating systems agree, by DVOA he is 27th. Tebow passes for only about 130 yards per game, 34th among QBs in a league of 32 teams. These normally are the stats of QBs about to get cut for losing games.

But he wins! The clutch winner like Tebow has "intangibles" that can't be measured in stats, but which *win* and so are more important than skills measured in mere stats, because winning is what it is all about. QED.

And who can deny that this guy has these intangibles that give him a special ability to win close games? The record speaks for itself. So the story goes.

Reality
It's a great story - but does an ability to win close games like this in the NFL actually exist?

To see, I looked at a larger record, that of all teams that (like the Broncos with Tebow) have been +5 net or better in one-score games (decided by 7 points or less) during the era of the 16-game season, from 1978 through 2009. I compared each team's record in its season of close-game success and clutch victories to its record in the following season (1979 through 2010). If there really is some ability, some skill, that enables a team to win close games in the NFL, it should carry over from one season to the next at least in some degree.

Altogether, 47 teams were a net +5 or better in close games, 5% of the 945 team of the 32 seasons. So the Broncos with Tebow at the helm are on course to a top 5%-or-better performance in clutch games. If you're a Broncos fan, what's not to be thrilled about?

But in the subsequent year, only the barest majority of the 47 teams were even +1 in close games, just 24 of the 47.

The 47 "best in the clutch" teams of the last 32 years were +263 net in close games - but only +15 in the subsequent season. Their won-lost record in one-score games fell in one year from 328-65 (83.5%) to 189-174 (52%). The correlation between their numbers of net close wins over the two seasons was an almost invisible 3%.

Comprehensively, for all 945 teams over the full 32 seasons, the correlation in year-to-year net close wins is 8%. In realistic terms: next to nothing.

Well, OK, that's everybody, the masses, but are the greats different? We've all heard that "Great teams, great players, win close games". Just because the masses don't win close games doesn't mean Tebow can't do it as the other greats have done!

But have the greats done it? A quick look at career records in 3-point games of various greats finds:

• Vince Lombardi's Packers: 12-11, 52%, while winning five NFL titles and the first two Super Bowls.

• Bill Walsh's 49ers: 17-22, 44%, winning three Super Bowls.

• Chuck Noll's Steelers: 13-23, 36%, during the Terry Bradshaw years with four Super Bowl titles.

Those greats sure didn't do it. Who actually was the greatest at winning close games?

Well, during the last 32 years it was Dick Jauron and his Bears team, quarterbacked by Jim Miller, that pulled out one "miracle" win after another, just like the Tebow Broncos and even more so! They went +8 in one-score games amid piling up a 13-3 record and earning Jauron the "Coach of the Year" award plus a three-year contract extension.

The next year the Bears went 4-12, and -2 in close games. In Jauron's ten-year coaching career he never had another winning season, going 47-79 in nine other losing years. Miller lasted at QB one more year.

The other story
Another story becomes visible in the above: Close-game outcomes are overwhelmingly determined by luck, random chance.

There is no skill, no ability, to consistently win close games in the NFL. It doesn't exist.

Vince Lombardi and Bart Starr couldn't do it. Bill Walsh and Joe Montana couldn't do it. Chuck Noll and Terry Bradshaw couldn't do it.

So when the fans of Tim Tebow say he does it - "he wins close games, he just does what it takes to win" - they really are making quite an ambitious claim!

Now consider the alternative. If Tebow doesn't win close games any more than Starr, Montana, and Bradshaw did, then what's left of the Tebow story? The entire Tim Tebow tale is "he makes the team win, he just does what it takes". But if he doesn't, the whole story evaporates and there's nothing left - he's just another young project at QB with very bad numbers so far. Starr, Montana, and Bradshaw put up great numbers. That's how they won.

In this story Tebow is winning like Dick Jauron did. The Broncos - all 53 players, not just Tebow - have played five generally weak teams (combined record of 23-37, 38%) evenly ... and won five coin flips.

If three of those coin flips had gone the other way - say, Miami QB Matt Moore hadn't fumbled in OT in field goal range for Denver, San Diego hadn't missed that field goal in OT, and Ponder this week didn't throw a last-minute interception again in Denver field goal range - then nobody is telling the "he just wins" story about Tebow today, because he isn't winning. The support for Tebow Idolatry is that tissue-thin.

One of the bad mistakes you can make in life is confusing good luck with superior ability, then doubling down on your confidence in that superior ability - and losing your house when the luck runs out.

In 2001 Dick Jauron was voted Coach of the Year over runner-up Bill Belichick. He was hailed for being the only other Bears coach ever to match the top season win totals of George Halas and Dick Butkus. He got a raise and a three-year contract extension ñ and after he was fired, on the strength of his "success" with the Bears, he got *another* head coaching job ... until his bosses had paid for nine years of losing records. That cost them plenty.

Broncos fans and Tebowmaniacs are investing a heck of a lot in their belief that Tebow won those five close games. It will be interesting to see how much Elway and Fox are willing to invest.

Betting Market Power Rankings – Week 14

2011-12-07T21:23:00.027-05:00

by Michael Beuoy

Here are the week 14 betting market power rankings. Here is a link to the first set of rankings I generated last week.

First off, thanks to Brian for making the Community site available as well as calling out last week’s post on the main blog. There was a lot of good feedback in the comments section. Most of it I’m still chewing over, but I have decided to incorporate a suggestion from Jim A, who has been creating a very similar set of rankings over at Nutshellsports.com. More on that later.

Methodology

The original post has more detail, but here’s an overview:

The goal I had was to generate a set of point-based rankings that would best predict how the betting market would set the point spread for the coming week’s matchups. The better I was able to match the point spread, the better the rankings were a reflection of the market’s estimate of team by team strength. Through trial and error experimentation, I found that using point spreads for the most recent five weeks (with higher weighting given to more recent weeks), combined with an adjustment that accounted for actual game outcomes, generated the best predictive accuracy. More detail here.

The Rankings

Here are the Betting Market Power Rankings for Week 14:

Glossary:

LSTWK - The betting market rank as of the prior week (using the same methodology). It’s interesting to see who the big movers are.
GPF - Stands for Generic Points Favored. It’s what you would expect a team to be favored by against a league average opponent at a neutral site.
GWP - Stands for Generic Win Probability. I converted the GPF into a generic win probability using the following formula: GWP = 1/(1+exp(-GPF/7)). This gives a more direct comparison to the ANS rankings.
ANS RNK - The Advanced NFL Stats Team Efficiency rankings for the same week.
ANS GWP - The Advanced NFL Stats Generic Win Probability for the same week.

RANK	Team	LSTWK	GPF	GWP	ANS RNK	ANS GWP
1	GB	1	8.5	0.77	3	0.71
2	NE	2	8.5	0.77	5	0.67
3	PIT	4	7.5	0.75	2	0.74
4	NO	3	7	0.73	4	0.69
5	BAL	5	5.5	0.69	7	0.62
6	SF	8	4	0.64	11	0.54
7	ATL	6	3.5	0.62	12	0.54
8	NYJ	9	3.5	0.62	13	0.54
9	DAL	7	3	0.61	8	0.61
10	TEX	10	1	0.54	1	0.8
11	NYG	12	1	0.53	6	0.65
12	MIA	15	1	0.53	17	0.5
13	SD	18	0.5	0.53	16	0.5
14	CIN	16	0.5	0.52	18	0.48
15	DET	13	0.5	0.52	9	0.61
16	PHI	11	0.5	0.51	10	0.59
17	TEN	19	-0.5	0.49	20	0.44
18	RAI	17	-0.5	0.48	14	0.53
19	CHI	14	-1	0.47	15	0.52
20	CAR	20	-1.5	0.45	22	0.39
21	DEN	22	-1.5	0.45	23	0.39
22	SEA	25	-2.5	0.41	25	0.37
23	WAS	23	-3	0.39	21	0.44
24	BUF	21	-3	0.39	19	0.48
25	ARZ	27	-3.5	0.38	24	0.37
26	MIN	24	-4	0.36	28	0.33
27	KC	30	-4	0.36	31	0.3
28	TB	26	-4.5	0.34	29	0.33
29	CLE	29	-5	0.33	26	0.36
30	JAC	28	-6.5	0.28	27	0.36
31	STL	31	-6.5	0.28	30	0.32
32	IND	32	-8.5	0.23	32	0.27

Some observations:

• San Francisco moved up a couple spots on the strength of their convincing victory over St. Louis.
• Philadelphia continued their nosedive, dropping from 11th to 16th.
• San Diego moved in the opposite direction, climbing 5 spots to 13th.
• If you throw out Houston (the ANS model doesn’t know Matt Schaub is injured), the ANS top 4 are in line with the betting market top 4: Green Bay, New England, Pittsburgh, and New Orleans.
• Count the nation’s gamblers among the Doubting Thomases to the miracles of Tebow. Denver only moved up one spot to 21.
• My Colts are now only buried under 25 feet of crap (2 points instead of last week’s 4). Progress!

Predicted of This Week’s Point Spreads

See below for how well the ranking methodology predicted this week’s point spreads (that SF/ARZ spread puzzles me):

Game	Pred Line	ActLine	Diff
ATL @ CAR	-1	-2.5	-1.5
BUF @ SD	5.5	7	1.5
CHI @ DEN	2.5	3.5	1
CLE @ PIT	15	14	-1
IND @ BAL	17	16.5	-0.5
KC @ NYJ	10.5	9	-1.5
MIN @ DET	7	7.5	0.5
NE @ WAS	-10	-8	2
NO @ TEN	-6	-3.5	2.5
NYG @ DAL	5	3.5	-1.5
PHI @ MIA	4	3	-1
RAI @ GB	12.5	11	-1.5
SF @ ARZ	-6.5	-3.5	3
STL @ SEA	5	7	2
TB @ JAC	0	0	0
TEX @ CIN	1.5	3	1.5

Proposed Methodology Change

In the comments, Jim A mentioned that he uses point spreads for future weeks as well (since these are available more than a week in advance in a lot of cases). I think this makes sense and have recalculated the rankings using this approach. Under the new approach, I gave both this week and the next a weight of 4, and prior weeks descending weights of 3, 2, and 1. The model seemed to work best with 5 weeks of “interconnectedness”, so the new approach keeps 5 weeks of data, but now has the advantage of being able to give more weight to the latest betting market information, as opposed to stale information from prior weeks. Here is how the new rankings compare to the rankings above:

Rank	Team	GPF	GPF New	Diff
1	GB	8.5	9	0.5
2	NE	8.5	7.5	-1
3	PIT	7.5	7	-0.5
4	NO	7	7.5	0.5
5	BAL	5.5	6	0.5
6	SF	4	5	1
7	ATL	3.5	3.5	0
8	NYJ	3.5	2.5	-1
9	DAL	3	3	0
10	TEX	1	0.5	-0.5
11	NYG	1	1.5	0.5
12	MIA	1	1	0
13	SD	0.5	0.5	0
14	CIN	0.5	0	-0.5
15	DET	0.5	1	0.5
16	PHI	0.5	0	-0.5
17	TEN	-0.5	0	0.5
18	RAI	-0.5	-0.5	0
19	CHI	-1	-1.5	-0.5
20	CAR	-1.5	-1	0.5
21	DEN	-1.5	-1	0.5
22	SEA	-2.5	-3	-0.5
23	WAS	-3	-4	-1
24	BUF	-3	-3	0
25	ARZ	-3.5	-2.5	1
26	MIN	-4	-3.5	0.5
27	KC	-4	-4.5	-0.5
28	TB	-4.5	-4.5	0
29	CLE	-5	-5	0
30	JAC	-6.5	-7	-0.5
31	STL	-6.5	-7	-0.5
32	IND	-8.5	-8.5	0

The biggest change is clear separation of Green Bay and New England, although the ranks remain the same at 1 and 2. For future weeks, I plan on using this approach, so the “Last Week” column for next week’s rankings will reflect this new approach, rather than the ranks in the first table above.

Future Investigations

Another source of insight into the betting market is the Superbowl futures (also pointed out by Jim A). Unfortunately, these are not only just a function of inherent team strength, but also a reflection of how difficult a team’s path may be to get to the Superbowl. If they’re in a strong conference, or if they’ve underachieved thus far in regards to wins and losses, this will reflect poorly on their Superbowl odds.

To get around this difficulty, I was thinking I could use Chris Cox's ridiculously awesome NFL Forecast tool. I could plug in the betting market GWP’s into the tool (I believe it allows for that type of customization), and then use those to generate Superbowl probabilities for each team. These could then be compared to the probabilities implied by the Superbowl futures odds.

Betting Market Power Rankings

2011-12-02T17:35:00.019-05:00

by Michael Beuoy

The purpose of this post is to use the point spreads from recent weeks of the season to derive an implied power ranking. Basically, the point is to try to figure out what the betting market thinks are the best and worst teams in the NFL. From a broader perspective, I hope to provide insight into how the betting market “thinks” in general. One result that emerged from this analysis was a measure of how much the betting market reacts to the result of a particular game.

The challenge in deriving a power ranking from the point spreads is that the point spread only tells you the relative strength of the two teams. For example, Green Bay is favored by 7.0 points on the road against the NY Giants this week. We know that home teams are favored on average by 2.5 points, so after removing the home team bias, the betting market appears to think that Green Bay is 9.5 points better than the Giants. New England is favored by 21(!) points at home against Indianapolis So the betting market thinks that New England is 18.5 points better than Indianapolis.

The question is, does the betting market think New England or Green Bay is the better team? It’s impossible to answer just using the spreads from this week (you have 32 unknowns and only 16 equations). My approach below is to look back over the past five weeks of point spreads and results to come up with a best fit ranking, where the ranking is calibrated such that it best predicts the point spread according to the following formula:

Point Spread = Home Team Rank - Visiting Team Rank + 2.5

I figured I would cut to the chase and provide the rankings themselves, and save the methodology explanation for the end. I followed the format of the Advanced NFL Stats (ANS) Team Efficiency rankings, and also provided the actual ANS rankings as a point of comparison.

Here is a glossary of terms:

LSTWK - The betting market rank as of the prior week (using the same methodology). It’s interesting to see who the big movers are.
GPF - Stands for Generic Points Favored. It’s what you would expect a team to be favored by against a league average opponent at a neutral site.
GWP - Stands for Generic Win Probability. I converted the GPF into a generic win probability using the following formula: GWP = 1/(1+exp(-GPF/7)). This gives a more direct comparison to the ANS rankings.
ANS RNK - The Advanced NFL Stats Team Efficiency rankings for the same week (week 12 in this case)
ANS GWP - The Advanced NFL Stats Generic Win Probability for the same week.

Here are the rankings:

RANK	TEAM	LSTWK	GPF	GWP	ANS RNK	ANS GWP
1	GB	2	9.5	0.80	2	0.74
2	NE	1	9.0	0.78	4	0.69
3	NO	3	7.0	0.73	5	0.69
4	PIT	4	5.5	0.69	3	0.72
5	BAL	6	5.0	0.66	10	0.59
6	ATL	12	4.5	0.66	14	0.53
7	DAL	7	4.0	0.64	6	0.65
8	SF	8	3.5	0.63	13	0.53
9	NYJ	10	3.5	0.62	15	0.52
10	TEX	5	3.0	0.61	1	0.82
11	PHI	9	1.5	0.55	7	0.62
12	NYG	11	1.0	0.54	8	0.62
13	CHI	13	0.5	0.52	11	0.57
14	DET	15	0.5	0.51	9	0.61
15	MIA	19	0.5	0.51	18	0.48
16	CIN	14	0.0	0.51	16	0.50
17	RAI	17	0.0	0.50	12	0.55
18	SD	16	0.0	0.50	19	0.45
19	TEN	18	-0.5	0.47	21	0.44
20	DEN	25	-2.5	0.42	23	0.38
21	BUF	22	-2.5	0.42	17	0.48
22	TB	20	-2.5	0.40	26	0.36
23	WAS	28	-3.0	0.39	20	0.44
24	SEA	23	-3.5	0.37	28	0.34
25	MIN	26	-3.5	0.37	29	0.34
26	CAR	27	-4.0	0.36	25	0.38
27	ARZ	29	-4.5	0.34	30	0.33
28	JAC	21	-4.5	0.34	22	0.40
29	CLE	24	-5.0	0.33	24	0.38
30	KC	31	-5.5	0.31	31	0.27
31	STL	30	-6.0	0.30	27	0.35
32	IND	32	-10.0	0.19	32	0.23

Some observations:
The top team and bottom team shouldn’t come as any surprise. In addition, there is the proverbial “50 feet of crap” (or 4 points) between the Colts and the next worse team.
Despite San Francisco’s place near the top of the “conventional” power rankings (ESPN, CBS, etc.), the market has them ranked much lower at number 8; not as low as the ANS rank of 13, but in the ballpark.
I was surprised to see New England ranked so closely to Green Bay (they were actually a half point ahead of them last week).

Methodology

The first step was to see how many prior weeks of point spreads I had to feed into the model in order to get an optimized estimate of the point spreads for future games. The drawback of using prior weeks is that you’re using stale information. The point spread from a few weeks ago will not accurately reflect the market’s latest assessment of their strength. I attempted to address this somewhat by using a recency weighted average. If I was using 7 weeks of spreads, the most recent week would get a weight of 7, the week before a weight of 6, and so on. This allowed me to arrive at an answer while still giving preferential treatment to the more recent market estimates. Through trial and error optimization, I found that using the most recent five weeks of point spreads produced the lowest mean squared estimate error of the point spread for the coming week. The calculation itself is equivalent to a weighted linear regression with 32 dummy variables, 1 for each team.

How the Betting Market Reacts to Game Results

Although the approach above generated a set of rankings, it ignores some potentially useful information that could be used to better match the coming week’s point spreads. For example, the week 13 rankings used the point spreads from weeks 9 through 13. In week 9, New England was favored by 9.5 points over the New York Giants. However, the Giants ended up winning by 4 in that game. So, the outcome of the game deviated from the market’s expectation by 13.5 points. One would expect that the market would factor that result into future estimates of both New England’s and New York’s strength. I assumed that the betting market would recallibrate itself according to the following formula:

revised “best estimate” spread = original spread + (credibility coefficient) x (deviation from expected)

I then determined what that credibility coefficient (CC) was by trial and error optimization. I found that a coefficient of 15% generated the most accurate prediction of the coming week’s spreads. In other words, the betting market appears to treat the outcome of each game with 15% credibility when revising its estimates of each team’s strength. So, in the New England/ New York example above, if those two teams had been scheduled to play each other at New England again, the new spread would have been revised down from 9.5 points to 7.5 points ( = 9.5 + 0.15 * (-9.5 - 4).

Prediction of This Week’s Point Spreads

See below for a comparison if how well the ranking methodology predicted this week’s point spreads. Note that this uses rankings that factor in the results from last week’s games, but does not factor in the spreads of this week’s games into the rolling 5 week average (this keeps the estimate independent):

GAME	PRED LINE	ACT LINE	DIFF
ATL @ TEX	6.0	-2.0	-8.0
BAL @ CLE	-6.0	-6.5	-0.5
CAR @ TB	5.0	3.5	-1.5
CIN @ PIT	8.5	6.5	-2.0
DAL @ ARZ	-6.5	-4.5	2.0
DEN @ MIN	2.0	0.0	-2.0
DET @ NO	10.0	8.5	-1.5
GB @ NYG	-4.5	-7.0	-2.5
IND @ NE	21.5	21.0	-0.5
KC @ CHI	8.5	8.0	-0.5
NYJ @ WAS	-5.0	-3.0	2.0
PHI @ SEA	-4.0	-3.0	1.0
RAI @ MIA	2.5	3.0	0.5
SD @ JAC	1.0	-2.5	-3.5
STL @ SF	11.0	13.5	2.5
TEN @ BUF	0.5	1.5	1.0

The biggest miss in the line prediction is on the ATL/TEX game where it appears that the market values Matt Schaub’s talents over his replacement by a significant margin. I think this may also be inflating ATL’s overall ranking somewhat. Its favorable point spread over Houston is being compared (on a recency weighted basis) against point spreads when Matt Schaub was playing.

If there’s interest, I can produce these weekly. I’ve got this boiled down to a quick piece of R code (which anyone is welcome to if they’re curious about the details of the methodology).

Adjusting Strength of Schedule

2011-11-09T19:15:00.003-05:00

by Michael Beuoy

One of the more interesting components (to me) of Brian Burke's efficiency model is the strength of schedule adjustment. I found it interesting the way you could bootstrap yourself into a self-consistent opponent adjustment. Here is the description (link):

"To adjust for opponent strength, I could adjust each team efficiency stat according to the average opponents’ corresponding stat. In other words, I could adjust the Cardinals’ passing efficiency according to their opponents’ average defensive efficiency. I’d have to do that for all the stats in the model, which would be insanely complex. But I have a simpler method that produces the same results.

For each team, I average its to-date opponents’ GWP to measure strength of schedule. This season Arizona’s average opponent GWP was 0.51—essentially average. I can compute the average logit of Arizona’s opponents by reversing the process I’ve used so far.

The odds ratio for the Cardinals’ average opponent is 0.51/(1-0.51) = 1.03. The log of the odds ratio, or logit, is log(1.03) = 0.034. I can add that adjustment into the logit equation we used to get their original GWP.

Logit = Logit(ARI) – Logit(Avg) + 0.034
= 0.11

This makes the odds ratio e0.11 = 1.12. Their GWP now becomes 0.53. If you think about it intuitively, this makes sense. Their unadjusted GWP was 0.51. They (apparently) had a slightly tougher schedule than average. So their true, underlying team strength should be slightly higher than we originally estimated.

I said ‘apparently’ because now that we’ve adjusted each teams GWP, that makes each team’s average opponent GWP different. So we have to repeat the process of averaging each team’s opponent GWP and redoing the logistic adjustment. I iterate this (usually 4 or 5 times) until the adjusted GWPs converge. In other words, they stop changing because each successive adjustment gets smaller as it zeroes in on the true value."

The purpose of this post is to show how this iterative, multi-step adjustment can be translated into a single matrix, and how that matrix is actually independent of the ranking system being used. This matrix can then be used more generally as a measure of each team's "interconnectedness", based on the season-to-date games played so far.

First, to define some terms:

R0 = A 32 row vector whose ith row contains the "raw" ranking of team i. This ranking can be anything you want: Brian's logit model, win percentage, average margin, number of Tebows on the team, etc.

S = A 32 by 32 matrix where the ith row jth column entry contains the percentage of team i's games that have been played against team j.

In Brian's description of the model, he states that "For each team, I average its to-date opponents’ GWP to measure strength of schedule". This is just equivalent to multiplying the S matrix by the R0 ranking vector. That adjustment is then added to the original ranking. This creates a new ranking R1 = R0 + S * R0 = (1 + S) * R0. Then Brian just keeps applying that same step to each new adjusted ranking.

R2 = R0 + S*R1 = R0 + S*(1+S)*R0 = (1 + S + S^2)*R0

R3 = R0 + S*R2 = R0 + S*(1+S+S^2)*R0 = (1 + S + S^2 + S^3)*R0

and so on.....

RFinal = (1 + S + S^2 + S^3 + .....) * R0

If you're familiar with infinite series, you know that the sum in the parentheses would be equal to 1/(1-S) if S were a normal number less than 1. Fortunately, this also works for matrices, as long as we interpret 1/(1-S) as the matrix inverse of (1-S) (I'm glossing over some mathematical niceties here, but trust me that the math works in this case, with one caveat below).

Let's define this inverted matrix as the SOS matrix -> SOS = (1 + S + S^2 + S^3 + ...) = 1/(1-S).

So, your final strength of schedule adjusted ranking is just:

RFinal = SOS * R0

Where, as mentioned earlier, the SOS matrix is solely a function of which teams have played each other and has no dependence on the ranking system used.

I have compiled the details of the calculation (for the 2011 NFL Season through Week 9) in a Google Docs Spreadsheet. One technical note: In order to get the matrix inverse to exist, I had to tack on a "normalizer" matrix to S. This matrix takes a 32 row vector and subtracts out the mean of the vector. The net effect is to convert any ranking vector to one where the average ranking is zero.

One of the nice things about the SOS matrix is that it tells you how interconnected each team is to another team, based on the games they've played so far. For example, Green Bay has played both Denver and Chicago once, but the matrix is showing that GB is far more connected to Chicago than to Denver (an 0.20 factor vs. an 0.08 factor). This makes sense given that Green Bay and Chicago are in the same division and so have had more common opponents (their season to date performance is far more intertwined). So, to get a measure of Green Bay's schedule adjusted strength, you would add 0.20 of Chicago's strength, but only 0.08 of Denver's strength. Or, to get Indy's true strength, you would have to subtract 0.11 of PHI's strength. Indy hasn't played Philly, and they don't have many common opponents (the AFC South is not slated to play the NFC East this year). The +/- nature of the matrix is intuitive in that it penalizes teams that either are connected to poor teams (positive SOS times negative ranking), or disconnected to strong teams (negative SOS times positive ranking). Note that this only works when your ranking system is normalized to an average of zero, such that a below average team has a negative ranking.

To get a bit more technical, I think this adjustment is mathematically equivalent to a regression model with 32 variables (a dummy variable for each team) where each game outcome is modeled as:

game outcome = Team A - Team B

Where a positive outcome is one that favors Team A (but I haven't done a full derivation).

In the Google Docs spreadsheet, I used "Margin" as the game outcome dependent variable, but you could also use wins, difference in logit based on efficiency stats, etc. In addition, I think this is also equivalent to the very simple ranking system published at pro-football-reference.com.

Note: After typing this up, I realized that the calculation I've described differs somewhat from Brian's adjustment. It appears as if Brian averages GWP, converts that to logit, makes the adjustment, and then converts back to GWP for the next step. Mathematically, I think that introduces a non-linearity that my matrix approach couldn't handle. Still, I think the approach I've outlined still has merit, even if it's not mathematically identical to Brian's approach.

Peyton Manning - Colts Defensive MVP??

2011-11-01T22:44:00.002-04:00

by Steven Buzzard

A growing sentiment that has started to crop up with a lot of the talking heads in the league is that the Colts would be pretty terrible if Peyton Manning was playing because the defense has been so atrocious. These same people love to state the obvious and point out that Peyton Manning doesn’t make tackles. However, a lot of stats analysts have known over the years that the Colts offense has actually helped the Colts defense in 3 key ways.

1) They stay on the field a long time and limit the total number of drives per game
2) By staying on the field they give the defense great field position despite terrible special teams
3) By getting leads the defense can force more turnovers

So approximately how much of the collapse of the defense can be attributable to the defense collapsing and how much to the offense collapsing? Since 2003 the Colts have allowed approximately 20 points per game. This year they are allowing 31.5 for an increase of 11.5. Also note that this year league wide scoring is at a record pace and is trending at about 1.1 points over historical averages. These changes are due to a variety of things such as increased passing efficiency, increased passing attempts, changes on kickoff rules, etc. This is very important and is something we will keep in mind throughout the evaluation.

By failing to stay on the field the Colts offense has extended the game fairly substantially. Since 2003 the defense has faced approximately 10.3 drives per game. So far through 8 games the Colts defense has had to defend against 11.1 drives per game. Additionally due to league wide changes there has actually been a decrease in total drives this year of 0.65. So the Colts defense has seen an increase of 0.82 drives per game when they would have expected to see .65 less for a net effect of 1.47 more drives per game. At their current clip of 34.7 yards per drive these additional 1.47 drives per game has been worth 51 additional yards per game. If we use an approximate 12.5 yards per point that is an approximate impact of 4.1 points per game.

In addition to the additional drives per game the defense starting line of scrimmage has also declined as anticipated. From 2003 through 2010 the Colts defense had an average starting field position of 29.5. This year they have faced an average starting position of 31.65 for an increase of 2.15 yards. Additionally, due to changes to the kickoff rules the actual league wide starting position has decreased by 1.85 yards. So essentially the Colts defense is facing 2.15 yards of worse field position where as the league average is facing 1.85 yards better putting the Colts defense at 4.0 yards worse per drive than we would have expected for an average historical Colts defense. Over 89 drives that is equivalent to 357 yards or 28.5 points and a 3.6 per game clip.

The one thing that many people will recognize about the Colts defense is that they are “built to play with the lead”. This essentially gives them the chance to send their star DE’s after the QB creating strip sacks, force bad throws early, and creating turnovers. We can see this clearly in the numbers as well. With the Colts not building leads they aren’t creating turnovers. Historically the Colts defense has forced 1.7 TO’s game compared to 0.9 thus far this year. Many websites have approximated the value of a turnover at somewhere between 40-45 yards. For simplicity’s sake let’s calculate the value of a turnover as 45 yards. In this example, the lack of turnovers is costing the Colts 38 yards per game or 3.0 points. Clearly part of the value of the turnover is better field position for the offense and not just less points allowed by the defense but it is still an impact to the final point differential at the end of the day. Additionally, this entire decrease can’t be attributable to the offense the way the first two items can be but certainly some percentage of it can be. Even if an amount as small as 50% is due to playing with a lead the lack of turnovers may end up affecting the total points allowed by at least 1 point per game.

Now that we have seen that the defense is giving up approximately 7-10 points more per game due solely to the collapse of the offense we can see how much of the collapse can be directly attributable to the defense. Again we will start with yards per drive as our basis to keep things consistent. Historically the Colts have allowed about 30.8 yards per drive vs 34.7 that they are allowing this year for a change of about 3.9 yards. Offenses on average are getting 1.1 yards per drive more than historical averages meaning the Colts defense is playing 2.8 yards per drive worse per game than would be expected. This equates out to about 20 yards per game and 2.5 points per game directly attributable to the defense.

The current year Colts team is giving up about 11.5 points per game more than they have historically given up. Based on some basic analysis it appears that approximately 7-10 of those points are because the offense is not helping them out as much as they have in the past and about 2.5 of those points are due to the defense just underperforming. While 2.5 points per game is a fairly significant decline in defensive performance it isn’t unprecedented, in fact the standard deviation in points allowed by the Colts is 3 points per game and has underperformed historical averages by 2.5 twice in 9 years. The thing that is unprecedented is the number of drives, field position, and TO rates all of which are at all time extremes. Clearly these aren’t the only aspects that go into total points allowed but it is a significant portion. At the end of the day maybe Peyton Manning was the most valuable player on the Colts defense even if he wasn’t and never will be making tackles.

MRE - Measure of Random Events through week 5

2011-10-13T20:20:00.003-04:00

by Bruce D

MRE = (good luck points)-(bad luck points), so positive numbers are the luckiest teams.

For a more in-depth explanation of what "luck" points are, go to a previous post here.

If random events can't be repeated, then past points due to MRE can NOT be considered as being due to skill. Likewise, past performance due to MRE can't be included in analyzing future performance. In a nutshell, "lucky" teams can't be expected to be so "lucky", and "unlucky" teams are better than we may think.

Points for(+) the lucky team, are the same amount of points against(-) the unlucky team.

MRE is valued as follows:

punts blocked=3
interceptions=2.5
fumbles lost=2.5
field goal miss/block=2.5
punt returns for a TD=4.5
ko returns for a TD=4.5

Team	All Season	Last 2 Games	Last Game
ARI	-8	-5	-5
ATL	2.5	5	-2.5
BAL	10.5	-2	bye
BUF	27.5	15	10
CAR	-16.5	-9.5	0
CHI	17	12	2.5
CIN	-2.5	-2.5	2.5
CLE	5	0	bye
DAL	-13	-5	bye
DEN	-10.5	-2.5	2.5
DET	20	2.5	-2.5
GB	17.5	7.5	2.5
HOU	17	0	-5
IND	-2	-2.5	0
JAC	0	5	-2.5
KC	-20	2.5	0
MIA	-17.5	-5	bye
MIN	9.5	2.5	5
NO	-12.5	-7.5	0
NE	5	2.5	-2.5
NYG	5	-5	-5
NYJ	10	4.5	2.5
OAK	8	0	5
PHI	-25	-15	-10
PIT	-38	-10.5	-5.5
SD	-14.5	2.5	-2.5
SEA	-9	-2.5	5
SF	39	10	5
STL	0	2.5	bye
TB	-2.5	-2.5	-5
TEN	5.5	5.5	5.5
WAS	-7.5	-2.5	bye

NFL QBR Differential after week 5

2011-10-13T20:08:00.007-04:00

by Jeff Anderton

After reading several articles about Passer Rating Differential being the most relevant stat correlated to winning NFL football games, I decided to see what the current year to date QBR Differentials were for the NFL. For those that don't know, QBR is the "new" rating that ESPN developed and introduced this summer(2011). ESPN was looking to build off the "traditional" passer rating formula and take into account specific things that happen during a play.

For example, a QB makes a bad pass on a 5 yard "out route" but the receiver makes amazing catch, the Defensive Back falls down, and the receiver then turns it up field for a 30 yard gain. Under the QBR system the QB would not get as many "points" for this play since he made a bad throw, the DB fell down, there were a lot of yards after the catch, and the receiver made an amazing catch. There are also factors that figure out how to differentiate between "garbage time" and clutch scenarios, taking into account the current score, time left in the game, type of defense being used(prevent defense dink and dumps score low), etc.

So with that quick background behind us, lets take a look at what I did to compile these numbers. I took the individual QBR rating for each teams opponent for every week of the year, then simply added them up and divided by games played. I then took the team's own QBR rating(what their man under center scored for the year so far) and subtracted what they "got" from what they "gave up". Nothing major here in terms of math, just some down and dirty research.

For games that involved teams who used 2 QB's I simply added both ratings together for that game and divided by 2. I realize there could be some flaws with this method if we look at it from a "weighted performance perspective", but it would be such a small variance I don't think it much matters.

Not a whole lot of suprises as most of the good teams are at the top and the bad teams are at the bottome, but still interesting to see where a few teams fell. I was surprised that the Texans and Eagles were this high, and also surprised that the Jets, Bears, Falcons and Redskins were this low. These numbers are through and including week 5 and account for teams that had a bye week already.

Team by Team QBR Differential through and including week 5 of the 2011 NFL Season

Team	QB Differential
Cowboys	47.56
Packers	43.48
Titans	42.2
Saints	37.96
Bills	32.48
Texans	30.84
Lions	30.12
Patriots	29.76
Chargers	29.37
Panthers	24.12
Eagles	22.52
Giants	19.78
Broncos	18.79
Ravens	14.27
Steelers	13.62
Raiders	12.36
Chiefs	10.84
49ers	10.32
Falcons	9.2
Bucs	6.72
Browns	2.54
Redskins	2.02
Bengals	0.95
Jets	-4.22
Vikings	-5.12
Seahawks	-6.73
Bears	-8.14
Cardinals	-15.24
Jaguars	-15.78
Dolphins	-18.8
Colts	-28
Rams	-35.98

Joe's numbers, and the moral of the story

2011-10-08T08:54:00.020-04:00

Appreciating how the Old Ones played. Or: Joe Namath in the 2000s. Part III -- by Jim Glass.

Part I explained what is going on here and why. Part II presented the statistical background behind this comparison of the 1970s and 2000s.

Namath in the 2000s

"Namath's numbers were shockingly bad. You tend to remember Namath as this seminal figure, and of course he was, and then you see those stats and just go: 'Yuck.'" -- Joe Posnanski, Sports Illustrated.

This has become a popular notion among many football fans who never saw Namath play, and who have a little knowledge of football statistics - but not enough.

"Joe Namath is in the Hall of Fame because of his celebrity - getting a big contract, winning one famous game, being the first pro football player to wear pantythose in public - not for achievements on the football field." - comment at Football Outsiders.

Is this true? Let's see. Before examining his 1972 numbers in some detail and putting them in 2010 terms, a few other facts...

* In 1967 Namath became the first QB to break the 4,000-yard barrier. His 4,007 yards weren't matched until after the season was lengthened to 16 games and the passing rules were liberalized, a dozen years later. Those 4,007 were 42% more than the pro average, as 5,351 would have been in 2010 (the all-time record is 5,084) - so it's easy to see the electric impact they had on the football world.

* PFR.com selected Namath's famous shoot-out victory over Unitas and the Colts in 1972 as the Best Single-Game QB Performance Since 1970. (some video of the game)

* What matters is a QB's (and team's) performance relative to competitors. This can be measured by standard deviation, which can be used to produce corresponding numbers relative to average across eras.

For instance, Namath's 3,147 yards passing in 1968 (the year of Super Bowl III) was 1.28 standard deviations above the pro average. During 2006-10, 1.28 standard deviations above average was 4,198 yards. Making the corresponding adjustment for attempts, completion%, yards-per-completion, Int%, TD%, and sack% we can generate annual number lines for Namath's career in 2000s terms that relative-to-average are the same as his numbers were in his own day.

If we then take Namath's five best years total and compare it to corresponding totals of QBs in the post-1978 rule change era, we can gain some perspective on how his performance compared to theirs.

I did this with ten of the top post-1978 QBs. Namath had only seven mostly healthy full seasons in a 13-year career, so he's handicapped in this comparison compared to QBs who played many more healthy seasons (for Favre we'd pick the best 5 of 20). To equalize the playing field a bit, I took his five highest-yardage seasons and the five highest-yardage of the first 13 seasons in the careers of the other QBs. (The 5-of-first-13 selection had no effect on any active QB, and only minor effect on the others apart from Favre.) Result:

All 11 QBs are ranked in three categories: total yards; yards/attempt as a measure of efficiency; and ANY/A to adjust for TDs, INTs and Sacks. "Score" is combined rankings in all categories, so smaller is better.

	Top 5 years YDs	Y/A	ANY/A	Score
Manning	22567 (3)	7.92 (3)	7.78 (1)	5
Young	18827 (10)	8.24 (1)	7.50 (2)	13
Rivers	19513 (8)	8.04 (2)	7.30 (4)	14
Brees	22918 (1)	7.66 (9)	7.10 (5)	15
Marino	22854 (2)	7.68 (8)	7.02 (6)	16
Namath	21123 (4)	7.80 (5)	6.76 (7)	16
Fouts	20997 (5)	7.90 (4)	6.50 (9)	18
Brady	20978 (6)	7.61 (10)	7.38 (3)	19
Montana	18702 (11)	7.80 (5)	6.76 (7)	23
Favre	20536 (7)	7.74 (7)	6.42 (10)	24
Elway	18907 (9)	7.02 (11)	6.08 (11)	31

There's nothing scientifically precise about this and it doesn't pretend to be any kind of definitive ranking. But there's absolutely no indication here that Namath wasn't fully in the class of these later HoFers and likely HoFers-to-be, relative to his competitors of his own time.

Now for the 1972 season.

We can be more precise looking at a single season. Namath's 1972 is convenient because it wasn't his best, so it can be considered representative, and it was his first healthy season after the AFL-NFL merger, so no "AFL adjustments" are needed.

Namath's actual 1972 numbers:

Attempts	324
Completions	162
Comp %	50.00%
Yards	2816
TDs	19
INTs	21
Sacks	11

Posnanski sees a meager 50% completion rate, only 2,800 yards, that negative TD-pick ratio, plus a passer rating of only 72.5, and says "Yuck!"

PFR.com replied in defense of Namath's honor, saying about 1972:

"He led the league in passing yards, touchdowns, yards per attempt, adjusted yards per attempt, net yards per attempt, and adjusted net yards per attempt. Oh, and he completed only 50% of his passes, so he sucked."

Namath's TD-pick ratio wasn't bad enough to prevent him from being #1 by ANY/A, which subtracts 45 yards for every interception, and he was #2 in sack rate.

And unmentioned (as always) is the "killer stat" of the era, yards-per-completion. Namath was #1 in that too, with his 17.4 yards each being was four standard deviations(!) above average. That number that has never been matched since, and likely never will be unless they change the rules again. (The highest Y/C of the 2000s has been 14.7 by Donovan McNabb in 2006.)

On to the regressions. By the passing game coefficients for 1971-5, Namath's passing numbers are at a .767 winning percentage level of play. For perspective, the passing game coefficients for 2006-10 give the performances of the top five QBs of 2010 by passer rating as being at these winning percentage levels...

Brady	0.714
Rivers	0.680
Rodgers	0.663
Vick	0.620
Roethlisberger	0.653

Now to convert Namath's 1972 to 2006-10 levels in two ways. First is the simple adjustment by standard deviation, mentioned earlier. Taking Namath's standard deviations over/under average for all the rate figures and for attempts per game, and multiplying by 16 games of attempts, we get...

Namath's 1972 adjusted to 2010 by SD:

Attempts	515
Completions	304
Completion %	59.0%
Yards	4378
TDs	28
INTs	19
Sacks	12

In 2010 these numbers would have ranked: by attempts #9; TDs #6, yards #4, yards-per-attempt #2, yards-per-completion #1 (obviously, four standard deviations above average), sack percentage #2, ANY/A #2.

"Shockingly bad"? You decide.

But there are problems with these numbers. Although they are accurately adjusted relative to average, the ratios among them were set in an earlier era when yards-per-completion was the winning stat, and teams won by accepting the lower completion rates and higher interception rates that came with longer throwing. That's shown by the huge yards-per-completion anumber combined with below-average completion percentage (23rd) and TD-Int ratio (18th) -- and also by the 2006-10 passing coefficients, which drop these numbers from a .767 level of play to a .724 level.

Don Shula called Namath "one of the three smartest quarterbacks of all time". A QB that smart wouldn't keep hurling the ball deep after the key to winning changed to high-percentage passing with a high TD-Int ratio. (Nor would his coaches let him!) What would Namath's numbers look like with modern game planning?

To reach a guestimate I expanded the numbers above by increasing all the standard deviations proportionately (thus further increasing yards per catch, while reducing completion percentage, etc.) until the net result was a .767 level of play by the 2006-10 passing coefficients - then reduced yards-per-catch while improving completion percentage and interception rate proportionately in the amount needed to maintain the .767 level of play. Rather arbitrarily, I set yard-per-completion high enough to remain #1 by half a yard, at 13.8 - still quite high (hey, the guy liked to throw long!) but not absurdly so. The result...

"Modern Namath"

Attempts	515
Completions	321
Completion %	62.3%
Yards	4430
TDs	28
INTs	15
Sacks	8

The change is modest overall, but now both completion percentage and the TD-Int ratio are above average, while the other rankings are: yards #4, yards-per-attempt #2, yard-per-completion #1, sack percentage #1, and ANY/A tied for #1.

Whether Joe would actually have played this way if miraculously transported through time to 2010 from 1972 nobody can ever say.

But the regressions do say that Namath's .767 level of play in 1972 was equivalent to this as the .767 level of play in 2006-10.

One more closing thought about Namath: NFL football is a team game, the performance of the team has a significant effect on the QB's numbers. Brady, Rodgers, Brees, Rivers, and Roethlisberger, the top-rated QBs in 2010, all piled up their numbers with the support of winning-quality teammates - Brady's team played a season without him and won 11 behind a sub who hadn't started a game since high school. Namath in 1972 played on a bad team that finished only 7-7 and would have gone 3-11 or 4-10 without him.

The moral of the story

The purpose of all this is not to prove that Joe Namath was a great QB - it's really not about Namath at all.

The main point is that when we use measures that matter to us today to evaluate the past, without realizing that the measures that mattered then were different, we are prone to making serious mistakes. And among football fans this has caused many of the greats of yesteryear to be seriously under-appreciated today, as the earlier parts of this story have pointed out. Recapping...

* Yards-per-attempt, a credible measure of passing performance today, becomes steadily less so when applied backward in time as yards-per-completion becomes more important, because it obscures whether yards are coming from high yards-per-completion (relatively good) or high completion percentage (relatively bad).

* Passer rating is outright perverse when applied back to the years when yards-per-completion trumped completion percentage in winning value. Its bias in favor of completion percentage over yards gained is ... unfathomable.

An example speaks more than words. Three QB performances and their ratings...

10 of 10	-100 yards	Y/A -10.0	rating 79.2
6 of 10	+45 yards	Y/A +4.5	rating 70.8
4 of 10	+80 yards	Y/A +8.0	rating 68.8

'Nuff said about passer rating.

A second point is that the opinions of those who witnessed and experienced events in the past should not be glibly dismissed just because we know we're smarter.

A generation of MVP, All-Pro and Pro Bowl voters deemed John Unitas the dominating QB of his era. Today a well known football stat site looks back with revisionism and declares Starr absolutely the much better QB because of his better passer ratings and occasionally higher yards-per-attempt (though they tied, career-wise). If that site had paused to ask, "Why did the people who actually saw these two play, and who played against them, have such a different opinion?", it might have figured out that there is a problem with passer rating and have had something worth writing about. Instead, it just repeats itself peddling soft-headed football tripe to whoever will buy it.

We may indeed know more than did the people of days gone by, overall. I hope so. But what they knew and we've forgotten counts too.

Appreciating how the Old Ones played. Or: Joe Namath in the 2000s, continuing...

2011-10-06T08:08:00.012-04:00

by Jim Glass

If you haven't read Part I of this, you probably should to get the context and some details about the numbers being used here.

[] Passing game changes, 1970s to 2000s. These numbers for passing statistic averages and standard deviations show how passing norms have changed since the 1970s.

("SD%" = the standard deviation divided by the average for the stat. For instance, for yards-per-completion the SD% of .128 for is the SD of 1.47 divided by the average of 11.53)

The bulk of the difference between eras results from rule changes. In 1978 the NFL adopted major rule changes to favor the passing game (see "The Top Ten Things that Changed the Game") and has steadily followed up on them since. The result has been shorter, safer, higher-percentage passing, and more of it.

	1970s	2000s	Change
Comp%	0.518	0.606	17.00%
SD	0.048	0.041	-13.60%
SD%	9.30%	6.80%

Yards/C	11.53	10.7	-7.20%
SD	1.47	0.93	-36.80%
SD%	12.80%	8.70%

TDs/attempt	0.043	0.041	-4.70%
SD	0.015	0.012	-20.90%
SD%	35.70%	29.60%

INTs/attempt	0.054	0.03	-44.40%
SD	0.016	0.009	-40.10%
SD%	29.00%	31.20%

Sacks/attempt	0.089	0.067	-24.70%
SD	0.03	0.023	-22.20%
SD%	33.70%	34.90%

Yards/attempt	5.97	6.48	8.50%
SD	0.92	0.8	-13.40%
SD%	15.40%	12.30%

ANY/attempt	3.51	5.17	47.30%
SD	1.5	1.3	-13.20%
SD%	42.70%	25.20%

The result of more, safer, less-aggressive passing is seen in the numbers for the average game.

[] Average game passing:

	1970s	2000s	Change
Attempts	25.8	32.9	27.50%
Completions	13.4	20	49.30%
Yards	153	214	39.90%
TDS	1.1	1.4	27.30%
Interceptions	1.4	1.1	-21.40%

With the norm for pre-1978 passing being 22% fewer attempts than today ... 33% fewer completions ... a meager 51% completion percentage ... and a TD-to-INT ratio of 15 to 19, we can see how so many fans of today may take even the middling passers of today as being better than the top performers of yesteryear.

But there have been more changes than just shifting averages.

[] What wins, and what won.

Regression analysis relating team winning percentage to performance by standard deviation, on both offense and defense, via rushing yards/attempt, pass completion percentage, yards per completion, interception percentage, and sack percentage, gives these notable coefficients for passing offense...

	1970s	2000s
Comp%	0.0343	0.0394
Yards/C	0.0699	0.0425

In the 1970s, compared to completion percentage, yards per completion contributed twice as much to winning. Today in the 2000s they contribute nearly equally.

Now we are getting to why those who actually watched Unitas and Starr play voted Unitas All-Pro five times to Starr's once, while many who know only today's game think Starr's passing numbers look at lot better.

[] Yards-per-attempt: less than it seems. Yards-per-completion: more!

Yards-per-attempt (in its many variations) has become the standard for measuring QB performance for those who don't use passer rating or a proprietary stat (such as WPA or DVOA). And only Y/A and passer rating are easily applied back though history.

But there is a problem with Y/A: it is a compound stat equaling completion percentage multiplied by yards-per-completion. It is accurate only to the extent its two components contribute equally to winning, and their relative values don't change over time.

Take two QBs with an identical 8.0 yards per attempt: Sam Slinger gets his by throwing for 16 yards per completion while completing 50% of his passes, while Percentage Pete completes two-thirds of his passes at 12 yards per completion. With all other passing numbers at league average, in the 2000s the 8.0 Y/A corresponds to about a 63% winning percentage for both QBs.

But in the 1970s, Slinger's numbers correspond to a 70% winning level of play versus 63% for Pete's. That 70% is 20 points over 50%, versus only 13 for the 63%, so Sam's play contributes 54% more to winning than Pete's (20/13 = 1.54) due to his throwing longer completions - and that 54% is a lot.

In the 1970s and earlier a strong-armed QB could win more games by reducing his completion percentage in the course of throwing longer –– an idea pretty much unheard of in the 2000s.

The low completion percentages of Unitas and Namath in their best years, held against them today, were not a "bug", they were a feature. High-yards-per-completion was worth much more than high completion percentage - and this is something that Y/A applied backward misses completely.

Unitas had MVP seasons in 1958 and 1959 with completion percentages of only 51.7% and 52.6% - well below his career average of 54.6%, and thus his "poor" years to modern eyes - but with top Y/C numbers of 14.8, and 15.0.

In 1964 Unitas and Starr had pretty much "mirror image" rate stats. Unitas' 51.8% completion percentage was well below average both for him and the league, only 9th of 14. Starr was first by completion percentage at 59.9% (and also first by today's passer rating). But Unitas was first by Y/C at 17.9, while Starr was 11th at 13.2.

The voters picked Unitas as NFL MVP. Applying the regression developed for 1971-5 (a bit of a fudge, but a lot better than using the passer rating of the 2000s) the results say the voters were right.

Unitas' mere 51.8% completion rate, good 2% interception rate, and top 17.9 Y/C produces play at a fantastic .910 winning level!

Starr's top 59.9% completion rate, superior 1.5% interception rate, and lowish 13.2 Y/C, produces play at .760 winning level ñ very good, but not even close to a match.

In the 21st century we don't get QBs repeatedly winning MVP awards while posting career-bottom completion percentages. That's the difference that yards-per-catch used to make.

For a bit more perspective, the career high Y/C numbers of today's top QBs don't reach even the career average Y/C numbers of the top QBs of the past.

Career	average Y/C	Career	high Y/C
Graham	16.1	P Manning	13.6
van Brocklin	15.2	Rivers	13.4
Namath	14.7	Brady	12.8
Unitas	14.2	Rodgers	12.7
Bradshaw	13.8	Brees	12.4

That's how the passing game has changed, and it is no accident - it's happened because what wins the game has changed.

Yards-per-completion may be considered the great overlooked statistic of NFL football, certainly in historical analysis - the "killer stat" of the pre-1978 game, the single offensive stat that contributed by far the most to winning. After 1978, it has become steadily less so, but even during 2006-10 it has contributed a little more to winning than completion percentage.

[] Passing rating: Poor enough for today, awful for historical evaluations.

If yards-per-attempt neglects the importance of yards-per-completion, the official NFL QB passer rating system is openly hostile to it.

A completion that loses yards can increase the QB's passing rating. Every completed pass that loses yards gets a rating of 79.2. So if a QB's rating is below 79, he can improve it by intentionally completing passes that lose yards.

On the 2010 passer rating list eight QBs were in this situation - a quarter of the league's starters. That's bad enough, but back in 1970 when the average rating was 62.5, fully 19 of the 24 rated QBs (79%) had ratings below 79 and could have improved their ratings by intentionally losing yards. (This is like a batter in baseball increasing his batting average by intentionally striking out.)

One can hardly think of a worse system to rate strong-armed QBs who help their teams most by throwing long passes for high Y/C while reducing their completion percentage.

Passing rating is always biased against long-throwers and in favor of short-throwers. This is not too bad when kept to the short-throwing era of today. But applying it backward in time produces ratings that are ever more distorted by (1) the increase in completion percentage over time, compounded by (2) the greater importance of long-throwing and drop of importance of completion percentage ñ even in then-current terms - to winning in earlier eras. It produces the totally absurd historical rankings noted in the first part of this story.

Applied back to the 1970s and 1960s it especially penalizes the deep throwers like Unitas and Namath, while giving a big boost to their short-throwing competitors such as Starr and Len Dawson.

Time to break again. Everything I write runs longer than expected.

Next: Joe Namath in the 2000s .... and the end.

Appreciating how the Old Ones played. Or: Joe Namath in the 2000s.

2011-10-04T22:29:00.011-04:00

by Jim Glass

The way NFL football is played has changed over the decades. Statistics in part reflect this, as seen in the steady inflation of passer rating.

But more importantly, what wins games has changed – and this is not reflected in commonly used rating and ranking stats. So even using "inflation adjusted" ratings leads to mistaken conclusions about players of the past when the ratings are based on performance measures that matter the most to us today – but not the ones that mattered most to them.

This article opens with a little rant, then presents the results of multivariate regressions run for the periods 1971-5 and 2006-10 to identify changes in performance measures that matter most to winning.

To illustrate how big these changes have been, it ends by translating Joe Namath's passing numbers – particularly for his 1972 season - into 2010 terms.

MY PET PEEVE, AS A SOON-TO-BE OLD TIMER MYSELF

Pro football fandom is unappreciative of the players of past decades, compared to the fans of other sports.

The 56-game hitting streak of Joe DiMaggio is legendary to baseball fans. But John Unitas' record of throwing TD passes in 47 consecutive games – statistically, a once in 2,000 years achievement! - is unknown to most of my football-fan friends.

"How soon before we stop pretending that Tom Brady isn't the most dominant passing quarterback in the history of the league?, was asked recently a in discussion at Outsiders, reflecting the big part of football fandom that rushes to proclaim the hot player of the moment as the best of all time.

Brady just had his second recent year as #1 passer by AYNA - following seven other seasons with an average rank of 10.4 and a highest of tied 5th-thru-8th, which hardly appears to be the most dominant career in all history. But everyone objecting cited Peyton and other contemporary contenders, not one mentioned a pre-ESPN QB.

One of the reasons for this surely is the immense bias in statistical ratings and rankings in favor of today's players over those of the past which gives the impression that the best players of today are always the best ever.

Zach Sanders last week noted the steady inflation in passer rating. The 1970 league-average of 62.5 would have been 31st in 2010. The NFL Hall of Fame a little while back published an historical passer rating list that ranked Mark Bulger #4 all time. By the NFL's official passer rating formula, the top 17 QBs of all time, and 29 of the top 30, played after 1978.

But Sanders' recommendation of using of inflation-adjusted QB ratings leaves the problem unfixed.

John Unitas was universally considered the dominant QB of his era, voted 5-times First Team All Pro and a 10-time Pro Bowler. Yet a well known football stat site recently proclaimed Bart Starr (one-time All Pro, 4-time Pro Bowler) much the better QB. "We looked at passer rating leaders, and there was Starr ñ not Unitas or Jurgensen or Tittle – atop the leaderboard five times in the 1960s". True, there he is – and as Starr and Unitas were contemporaries, rating inflation is not an issue. But does this mean that the MVP and Pro Bowl voters who actually saw them both play were wrong?

Joe Namath has become the favorite target of revisionists using today's stats to question the HoF status of yesterday's players. SI writer Joe Posnarski in "Reconsidering Namath" describes Namath's numbers as "shockingly bad. You tend to remember Namath as this seminal figure, and of course he was, and then you see those stats and just go: 'Yuck.'".

This has become a popular belief. In a recent discussion at Outsiders comments included: "Namath was a mediocre QB who doesn't belong in the HoF ... if you don't care about interceptions, Namath was wonderful ... he had a very good season in 1967. He got his completion % way up to 52.5%! ... No one thinks Namath's raw numbers match Brady's..." and so on.

Since Namath has become the most denigrated of the HoF old timers, I chose his numbers to convert to 2010 terms.

Were the Hall of Fame voters who saw him play that wrong about Namath? How bad was Namath, really?

OK, that ends the rant. On to the numbers that answer these questions.

ERA CHANGES

Data below for "the 1970s" are for the five years from 1971 through 1975, prior to the big passing rule changes of 1978. Data for "the 2000s" are from 2006 through 2010.

Average points scored per game increased by 2 from the 1970s to the 2000s, from 19.6 to 21.6. That's about 10%, but really not much in light of the scale of some other changes. For instance....

• Defense really did win championships.

The decline in the standard deviation of scoring on both offense and defense reflects both greater "parity" and also a general increase in quality of play. It is seen across-the-board, in many different measures of play. As the average skill and ability of players increases, variance in the level of play from top to bottom diminishes.

The bottom line: Regressing points scored (offense) and allowed (defense) by standard deviation to winning percentage gives these coefficients:'

This is a very significant shift from "defense winning games" to "offense winning games". The defensive coefficient compared to the offensive falls from 18% greater to 24% smaller, a big drop that is bad news for Rex Ryan.

As this is running long, I'll break here.

Part II will look at passing offense statistics, examining what the passing numbers of the past would be today if adjusted by impact on winning percentage – and vice versa.

It will take another look at Unitas vs Starr, and examine just how bad Joe Namath really was.

To be continued....