***

Since 2012, Roberto Perez is among the best catchers at throwing out basestealers. With 114 stolen base opportunities of 2B, basestealers are successful only 55% of the time, well below the 72% league average.

Perez has had four primary pitchers (all RHP as it turns out) in that time:

24 opps, 8 SB with Bauer (33%)

16 opps, 7 SB with Carrasco (44%)

14 opps, 4 SB with Kluber (29%)

12 opps, 11 SB with Shaw (92%)

48 opps, 33 SB with rest (69%)

As we can see, the Perez combos with Bauer, Carrasco, Kluber is well better than league average as well as the average of Perez with anyone else. So, some of that low 55% stolen base rate is a result of Bauer+Carrasco+Kluber. Or… is it?

We can also repeat the exercise going the other way, showing how these pitchers perform without Roberto Perez:

36 opps, 29 SB Bauer-noPerez (81%)

42 opps, 26 SB Carrasco-noPerez (62%)

72 opps, 51 SB Kluber-noPerez (71%)

28 opps, 19 SB Shaw-noPerez (68%)

As you can see, the Bauer-Perez pairing was far better than the Bauer-nonPerez pairing, while the Carrasco-Perez pairing was, in comparison, slightly better than Carrasco-nonPerez. And suddenly, Shaw is better off without Perez.

Indeed, Perez without his big 3 was close to average, and the big 3 without Perez were close to average. But, when Perez is paired with the big 3, suddenly, each of these batteries was well-above average.

The question is how much to rely on the actual battery combination, and how much to rely on the performance of these players when they are not a battery.

In studying all the battery combinations in MLB since 2012, we can break down the pairings as follows:

- the battery in question

- the performance of the pitcher without that catcher

- the performance of the catcher without that pitcher, but with the same pitching hand

- the performance of the catcher without that pitcher, but with the opposite pitching hand

If everything was random, then all the data would get weighted proportionate to the number of observations. But, we know that not everything is random.

And in fact, the weightings, for each observation, comes in at:

100%: the battery in question

40%: the performance of the pitcher without that catcher

13%: the performance of the catcher without that pitcher, but with the same pitching hand

13%: the performance of the catcher without that pitcher, but with the opposite pitching hand

My prior expectation was 100/30/20/10. So, these numbers are, kinda, inline with my prior. The biggest surprise to me was that the pitching hand, once you account for the 5% points of bias, had no additional information.

In other words, how Bauer-Perez truly interact is going to be based, disproportionately, on our observation of the two as a battery. And the battery performance generates well over twice the signal as their non-battery performance (pound for pound).

The end result, the “true talent” of the batteries are:

54%: Perez with Bauer

55%: Perez with Carrasco

58%: Perez with Kluber

70%: Perez with Shaw

66%: Bauer with average catcher

63%: Carrasco with average catcher

67%: Kluber with average catcher

74%: Shaw with average catcher

62%: Perez with average RHP

In the end, we can see that there is the most synergy with Bauer, and the least with Shaw. The Bauer-Perez combo is 12 points better than the Bauer-average-catcher, while the Shaw-Perez is only 4 points better.

Further research is required to determine if we want to apply a “familiarity factor”. After all, maybe all these popular batteries has a synergy factor that allowed the pairings to shine when you have a familiar battery, but not shine, when not familiar.

***

It’s alot of effort to go through this process. A simple regression toward the mean will get you almost all the way there. For catchers, you add 58 opportunities at league average, and for pitchers, you add 38 opps. And then you apply a standard Odds Ratio Method to get the true-talent for the battery in question. That is, we apply no synergy effect and no familiarity effect. That’s the Marcel-like method, and it works almost as well as WOWY Battery.

***

This process actually opens the door to a whole host of possibilities. Do you want to know if the observations we witness of a direct Kluber-Betts pairing as pitcher-batter gives us any additional insights beyond their individual talents? Well, WOWY Battery will get you there. How about Felix-Safeco? Yes, that works too.

And we’re just scratching the surface with possibilities. I’ll detail more in the future, though you may be able to guess at a few already.

]]>

For the next 4 spots, it’s a weird scenario because of Alex Wood. Take him out of the equation, and the order is: Gio, Stras, Greinke. Include Alex Wood, and he either is above Gio, or behind Greinke (and Robbie Ray). Maybe we’ll get more clarity by the end of the season. There’s also Kenley, who will get plenty of down-ballot support. I don’t know where he’ll land, but it won’t be in the top 2.

Over to the AL: it’ll be Kluber getting most of the 1st place votes, and Sale getting most of the 2nd place votes. Then it’s all down-ballot from there. It should be Severino, Verlander, Carrasco, with Stroman and Santana lurking. I expect Kimbrel to suffer/enjoy the same fate as Kenley, plenty of down-ballot support, and he won’t finish in the top 2.

Kimbrel’s best showing ever was when he finished 4th, and that’s pretty much what a reliever is relegated to finish, especially given that Britton last year finished 4th (behind a good, but not great, Kluber), and he had the best stats of a reliever relative to his competition in quite a while.

]]>Help me, help you, help everyone else, and vote for your team:

]]>Why did I say “should be”? Because we are NOT using whether outfielder actually caught the ball. We are determining what they should have caught given the distance and time to cover the opportunity provided by the batter+pitcher.

The home Rockies outfielders however were provided with an opportunity, by their pitchers (and opposing hitters) to only catch 79% of the outfield balls. That is, the home pitchers made it 3 percentage points tougher on their home fielders than the visiting pitchers did to the visiting outfielders. Per 500 batted balls, that’s 15 fewer outs. In other words, the Rockies pitchers did not get the balls hit close enough to the outfielders at Coors.

Tropicana is apparently very easy for the pitchers+fielders to be in-synch. The visiting pitchers give their outfielders an opportunity to catch 87% of the outfield balls. But the home pitchers give their outfielders only 85%. Here again, the Rays pitchers are 10 fewer outs than their opponents at the Trop.

The home teams whose pitchers are able to get the ball closer to their outfielders than their opponents are the Marlins and A’s. They get the ball closer to their outfielders by about 3 percentage points, being worth about 15 more outs.

Now, whether all this happens because the home team better positions their outfielders and/or their pitchers better able to get the hitters to “place” the balls closer to the outfield and/or Random Variation, is still to be seen. But this is the path we’ll follow, breaking down each component to try to find who is impacting what, where.

]]>

You play 9 more matches, of which you win seven of them. Each time you win, you earn 50 cents. Each time you lose, you lose 50 cents. So, in these seven wins, you added another 3.50$ to your 50 cents from the first game. So your 8 wins generated 4$ of profit. But your two losses cost you 50 cents each time, or 1$. Overall, after the 10 matches, you made 3$. You now have an 8-2 record.

What record would you have needed in order to have neither made a profit or a loss? A 5-5 record. In other words being +3 wins above average is +3$ above not having played at all (or having split the 10 games evenly). Each win ABOVE EXPECTED is worth 1 dollar. That ABOVE EXPECTED is important to remember.

***

The next day, you ask your buddy if he wants to go for round 2. Your buddy, having known you a long time, and knowing that you are a pretty good pool player, and him being passable, said: “You know, if this is going to be fair, you gotta give me some odds.” So, you guys agree that you will put up 75 cents and he puts up 25 cents. So, each time you win, you gain your friend’s quarter (+0.25$), while each time he wins, it’ll cost you -0.75$.

You think this is fair. Your 8-2 record from the day before might be indicative of the strength of your play. If you went 8-2 today, you’d get your buddies 25 cents 8 times (+2.00$), and you’ll give up 75 cents twice (-1.50$). You would still be up +0.50$.

***

If you have an opportunity to make an out on a play that you’d expect an average outfielder to make 25% of the time, you’d earn +0.75 outs for each catch.

If you have an opportunity to make an out on a play that you’d expect an average outfielder to make 75% of the time, you’d earn +0.25 outs for each catch.

Suppose you have 4 opportunities to make a tough play, of which you catch two. And you have 6 opportunies to make an easier play, of which you catch all but 1.

For the 4 tough plays, you earn +0.75 each for the two catches (+1.50 total), and -0.25 for the two tough ones you didn’t make (-0.50 total). For these 4 tough plays, you will have earned +1.00 outs.

For the 6 easier plays, you earn +0.25 for each of the five catches you made (+1.25 total), and it cost your 0.75 outs for the one you didn, for a total of +0.50.

Overall, you will have earned +1.00 +0.50 = +1.50 for these 10 plays (7 outs, 3 hits). This is your value, your “profit”. You made +1.50 more outs than an average fielder would have, GIVEN THE SAME NUMBER AND DIFFICULTY of opportunities. Remember this number. +1.50.

***

Now, you don’t have to add up every single one like this. All of this gets reduced to simply:

profit = (actual minus EV*opps)

where EV = expected value per play

In this case, you had 4 tough plays, with an EV of 25%, and 6 easier plays with an EV of 75%.

4 x 25% plus 6 x 75% all divided by 10

= 55%

In other words, in YOUR OPPORTUNITY SPACE, the expected value is to have caught 55% of the balls. Given 10 plays, you are therefore expected to have caught 5.5 outs.

And what did you actually do? You were 7-3, so you caught 7. Going back to this:

profit = (actual minus EV*opps)

We plug in our numbers

profit = (7 minus 5.5)

profit = +1.5 outs

Remember the number I mentioned? That’s how partial plus/minus works.

]]>You can see a few studies I’ve done in this regard, and it works out well enough. Anyone can reproduce what I do with very little effort, and armed just with the speed of a pitch.

What follows is one little extra step, making the researcher go from “very little effort” to “little effort”. After you’ve established a pitcher’s “top speed” (i.e., the average of his 25% fastest pitches), choose a baseline that is 3mph below that line. This becomes a pitcher’s “minimum hardball speed”. You go back to all his pitches, and any pitch that is above his minimum hardball speed now counts as a hard pitch. And that’s it.

When you do that, you go from making use of 25% of each pitcher’s pitch to, an average of, 53% of each pitcher’s pitch. I should point out that BOTH have their place. The reason to like the “top speed” approach is that you are guaranteed to keep the sample for each pitch proportionate to their actual number of pitches: 25%. The reason to like the “hard pitch” approach is that you are focusing on those hard pitches, while allowing few to no breaking pitches in there. On a pitcher by pitcher basis, you end up with each pitcher have 30% to 92% (Britton) of his pitches identified as “hard” pitches. Sale is interesting as he’s at 35%, and that’s because he has a wide range on his fastball/sinker.

Why 3mph below the line rather than 2 or 5 (and you can definitely make a case to use a threshold anywhere between those two numbers)? This breakdown of pitches at various levels points to somewhere close to -3 mph below the average of the top speed as being heavily fastball pitches. And as I said, choosing -3 lets you end up with 53% of the pitches.

Anyway, I hope you find this as useful and simple as I do.

Note: I’m excluding Dickey and Wright for knucking reasons.

]]>Catch Probability is determined primarily based on the proximity of the fielder to the (eventual) landing spot of the ball, relative to where the fielder was at the release of pitch. This becomes the “opportunity space” of all nine fielders.

Unlike a batter, who we KNOW is at the plate, and who we KNOW has a strike zone that is fairly fixed and fairly similar to other batters, fielders are completely different. First, there are nine possible fielders, so for any batted ball, we don’t know before hand who is mostly responsible. Secondly, the “catch zone” is unique for every batted ball. Not only is the distance to cover different for every batted ball, but so in the time in which the fielder has to make the play. Contrast that to a strike zone where the batter has a set time and set area to cover (more or less).

So, this is how Catch Probability works, for outfielders. For every single batted ball, we decide who is the responsible fielder.

- If an outfielder makes the putout, or the error, we assign that batted ball to him.
If there is a base hit, we assign whichever fielder was closest to the eventual landing spot of the ball (based on his starting position at time of pitch release). The exception to the base hit rule is any batted ball that hits the fence at least 8 feet above the ground, or we have an outside the park HR: we throw those out. We deem those unplayable.

Using distance-time, we take a (perfectly) smoothed version of this chart. For any batted ball that is deemed “is-back” we lower the catch probability by 0 to 25% points. Is-back is any batted ball that is +/- 30 degrees from straight-back. The simplest way to think about the difficulty it is that we remove and extra 4 or 5 feet and an extra 0.1 to 0.2 seconds to the play. It gets more involved, but that’s the basic way to think about it, that we acknowledge that when you run straight back, you really don’t have the same opportunity as otherwise.

The exception to the above is the wall-balls. Any basehit that is within 8 feet of the base of the fence, or would have otherwise landed beyond the fence (if not for the fence) is given a catch probability of 0. While this may seem otherwise generous to the outfielder who allows the ball to drop in for a hit, also consider the treatment of putouts, where the outfielder doesn’t get the extra benefit of making a play at the wall. Basically, these two treatments are in balance so we have no bias. In the off-season, we’ll be looking at treating wall-balls with more subtlety. In the end, whatever the treatment, whther the simple solution implemented, or the more complex method we’ll explore, the end result won’t be more than a couple of outs above average.

Since everyone will ask about Fenway Park, the outs above average for leftfielders:

- Home fielders at Fenway are minus 5.7 outs, while Away fielders at Fenway are +1.4
- Redsox fielders at home are minus 5.7 outs, while Redsox fielders on the road are -2.1

It would seem that the treatment of Redsox LF is fair, or at least, not unduly biased. In any case, the Catch Probability Leaderboards you will see will allow you to do breakdowns based on:

- outfielder (without regard to position, team, park)
- park, home-away, position
- team, home-away, position

We’re getting into the top of the third…

]]>I shall not today attempt further to define the kinds of material I understand to be embraced within that shorthand description; and perhaps I could never succeed in intelligibly doing so. But I know it when I see it, and the motion picture involved in this case is not that.

—Justice Potter, Jacobellis v. Ohio

I think I got it, but just in case… Tell me the whole thing again, I wasn’t listening.

—Emmet, Lego Movie

Some of the metrics were introduced breathlessly by their respective authors as a completely new way to look at the game.

—Brandon Heipp, http://www.hardballtimes.com/bases-and-outs-ad-nauseum/

***

Most people seem to BELIEVE in The Hot Hand. But can they DEFINE it? They seem to KNOW it. They think they got it. But, really, let’s talk about the whole thing from the beginning.

The main issue with Hot Hand is its conflation with Recency. Let me give you an example of what we can all accept as a Hot Hand situation: Armando and Felix are perfect through 7. Hot Hand suggests that what happens to the next 1 to 6 batters (or say the next 5 to 20 pitches) is highly (somewhat? slightly?) influenced by what has happened in the prior 7 innings, much more (a little more?) than what has happened in the careers of Armando and Felix to that point and (just as important) what will happen in the careers of Armando and Felix AFTER THE GAME IS OVER.

That is, Hot Hand is (a) transient, and not persistent, and (b) has a level of magnitude THAT IS WORTH TALKING ABOUT. So, in order to know if you are seeing a Hot Hand, you have to have a baseline: you have to know what level of talent you expect to see if there was no Hot Hand at play.

The standard way to determine the level of talent is to apply a Daily Marcel. Marcel is fairly ubiquitous (I’m its trustee). Like all things, we can trace its origins to Bill James, in this case, Bill’s Brock 2 forecasting system. Marcel does something very standard which is to weight more recent seasons higher. In this case, it gives a weight of “5” for most recent season (year T), “4” for the season prior (T-1), and “3” for the season before that (T-2). We do this unequal weighting because (a) players age, meaning their talents change and (b) players get injured, meaning how they are feeling today is more indicative of what they will do tomorrow than how they felt a year ago.

And while 5/4/3 works fairly well, we can get better weights, and we don’t have to limit ourselves to three years. We can actually formalize this into something pretty simple:

weight = 0.999^daysAgo

So, today’s performances get a weight of “1”, performances from yesterday get a weight of “0.999”. Performances from 360 days ago get a weight of “0.7”, and so on. Even performances from 3000 days ago get a weight (“0.05”). That becomes our baseline.

If we believe that Hot Hand is transient, you can also use future performance in a similar manner. You can decide that there’s a “window” that is off-limits because the player might still be Hot. If we can agree to some window, say 30 days (60 days?), then we can include all future performances as well in a similar manner. We can do:

weight = 0.999^daysFromNow

So, performances 60 days in the future get a weight of “0.94” and performances 85 days in the future get a weight of “0.92” and so on.

By doing this, we now establish the talent level of the player inside the Hot Hand Window, by using performances from outside the Hot Hand Window.

Going back to our Armando+Felix situations: find ALL games where a pitcher was perfect through 7. The Hot Hand Window is THE ENTIRE GAME. The OBSERVED Hot Hand is the first 7 innings. The IMPACT of the Hot Hand is felt the REST OF THE GAME. So, you, dear aspiring saberist, tell me, (a) what did we think each pitcher’s talent level was, if we use their Daily Marcel, from outside the Hot Hand Window. And what was their observed performance in the Hot Hand Window from the 8th inning onwards.

I would expect there to be some Hot Hand influence. How much? Well, I can tell you we kinda looked at this on my blog a few years ago, so you will get some sort of payoff here. Is it enough to talk about? Well, you tell me.

Now, perfect-through-7 is a pretty strict control of Hot Hand. So, feel free to loosen it. And instead of single-game, feel free to suggest that Hot Hand will impact a pitcher’s game in the future. Maybe 2 or 3 games? You tell me.

Now, to define it even further, perhaps what you will find with Hot Hand is the following weight:

weight = 0.900^daysAgo from OUTSIDE the Hot Hand Window

weight = 1.000 from the observed performance INSIDE the Hot Hand Window

That is, even if we find Hot Hand influence for the Armando+Felix situation, what is the MAGNITUDE of that influence? Are we going to use weights of 0.998 for outside the Hot Hand Window and 1.000 for inside? In which case, it’s not worth talking about. Is it 0.9 and 1.0 respectively? Then, it’s DEFINITELY worth talking about.

So, let’s do this. Let’s first define it, let’s come up with a structure so we can actually formalize this in a way where we can move the discussion forward. Then we can evaluate the claims.

]]>This is easiest seen with trading deadline deals. A replacement level player does/should/may cost the same to a playoff contender as to an also-ran. But a high quality player has a “multiplier” effect, which is what I think Rachel’s beta is. I didn’t follow too well if Rachel intended to say the Beta changed for each player-team, but I think it must. This is why a contender will trade for a “star rental”.

Anyway, the key point in all this is that we’re dealing with asset value, no different than your house. It’s the value of the house minus the mortgage. And if you can think of the house being potentially modular, how much value it can gain or lose by going to a different location. And how we determine that price.

The one thing I will say is that in multi-year deals, you CANNOT assume that a team will maintain a .550 win% throughout. And even if you did, you CANNOT allow the new player for the player-team beta to be different from all the other players on the team. Basically, the new player is leveraging the team’s fortunes, and so, he can “absorb” that beta all to himself. Well, you CAN, but I think that’s a pretty risky thing to allow the model to do.

]]>It’s like saying that Vlad should chase fewer outside pitches, when in reality, he probably chased exactly the number he needed to. Every hitter and pitcher is optimizing his approach based on his skillset, so, my expectation is that we should likely not see trends.

]]>In this poll, it was 75-12, with a 13% fat-finger. Assuming the fat-finger breaks proportionately to 75-12, we can discard the 13%, and assume the breakdown is 86-14.

HOWEVER, without a fat-finger option, this is what would happen: 13% of the 86 would vote the other way. And 13% of the 14 would vote the other way. The final SELECTIONS would therefore break as: 77-23. Even though the INTENDED selections would be 86-14.

I know this is kind of a goofy little poll, but think of the implications in terms of “hanging chads”. Electronic-elections can rest on fat-finger.

My phone is fairly sensitive, so that I don’t even have to touch the screen, I just need to hover close enough. So it’s possible that on your way to a selection, you end up clicking something you didn’t even click.

I’d love to see research in this area.

]]>http://tangotiger.com/images/uploads/linear_weights_2014_to_present.html

There are two ways to calculate these values. One way was described in Table 5 in The Book. You take the “run value” of the starting state of the event. And then you add up all the runs that actually scored following that event, to the end of the inning. The second was described in Table 7 in The Book. You take the “run value” of the starting state and of the ending state, subtract the two and add up the runs in-between. The results will be very close to each other, either way you do it.The above chart was done the first way (the Table 5 method) mostly because given the dataset I have to work with, it was easier to do it that way.

]]>We can quantify the ball-strike count. If we look at all 0-2 counts, we can see how that plate appearance ended. As you’d expect, it’s highly in favor of the pitcher. We can do the same with all 3-0 counts, and ignoring IBB, you realize that it’s highly in favor of the batter. I published this chart several months back:

The key column there is the overall wOBA, which you can think of as analogous to OBP in terms of impact. But, let’s represent wOBA by its base value, which is runs, relative to the average. Linear Weights Runs, if you think of Pete Palmer. (That’s where the w in wOBA comes from… weighted.) So, for the first pitch, the 0-0 count, the run value of 0 runs. For a 3-0 count, the run value is +0.20 runs. That is, if you pick up a plate appearance at a 3-0 count, then by the time the plate appearance will have ended, that plate appearance would have increased the number of runs in that inning by +0.20 runs. For an 0-2 count, the number of runs scored will be -0.11 runs, relative to the average.

In a further nod to Pete, we can represent the Run Expectancy by Ball-Strike count in this manner:

To read the chart, you look for the ball-strike count you are in, and that will tell you how many runs your team will gain, or lose, by the time the plate appearance is complete, relative to being in an 0-0 count.

Now suppose you hit a homerun. We know that gains you +1.40 runs, via Palmer. But, what if we want to distinguish between an 0-2 homer, and a 3-0 homer? A homer is a homer you say. Yes, you are correct. But, perhaps you are interested in the components of that. What if we want to include Working The Count as a metric? What if we realize that a HR on an 0-2 count is more impressive than a HR on a 3-0 count? It looks like this:

0-2 count HR: -0.11 for working the count, +1.51 for hitting a homer IN THAT COUNT

3-0 count HR: +0.20 for working the count, +1.20 for hitting a homer IN THAT COUNT

Does this help us evaluate a hitter? Maybe. Maybe if the hitter who finds himself in alot of 0-2 counts who can improve his count-skills, he’d be able to leverage his HR skill much more than a guy who already knows how to work the count.

In any case, since everything about baseball is about the strike zone, and by extension the count, then let’s create a metric that recognizes that.

Joey Votto, you will not be surprised, is the best hitter at working the count. For our metric, what we will do is simply count the number of times he is in particular ball-strike count ON HIS LAST PITCH. That is, we’re going to break down his skill set into two components: getting to his last count, and then finishing off the plate appearance. This is how often Votto has reached each ball-strike count, excluding IBB:

Since each ball-strike count has its own value, and we have the frequency of Votto entering each of these counts on his last pitch, we simply multiply one chart by the other. Those 12 times he entered a 3-0 count as his last pitch? That’s worth a total of +2.4 runs. We repeat this for all 12 ball-strike counts, add them up, and we get a total of +5.5 runs.

You can also think of it more simply: Votto’s average ball-strike count on his last pitch was: 1.52 balls, 1.15 strikes. That’s basically his “average” count when he faced his last pitch. An average ball is worth around +0.06 runs and an average strike is worth around -0.07 runs. So, you can simply do: 1.52 x 0.06 - 1.15 x 0.07 = 0.011 runs. Since Votto has 400 plate appearances, that gives us 400 x 0.011 = +4.4 runs. That’s the simple way of treating each ball equally and each strike equally. In the more precise way, we get +5.5 runs.

We can also apply it to pitchers. You will get the boring answer that the two pitchers who can Work the Count the best are Max Scherzer and Chris Sale. Among relievers, you get the even more boring answer of Kenley Jansen and Craig Kimbrel. Jansen’s average ball-strike count on the last pitch is 0.92 balls, 1.60 strikes. Given that the maximum possible strike count on the last pitch is 2 strikes, it’s fairly impressive to get there at all, and to do so with only 0.92 balls is doubly impressive. Contrast to Trevor Rosenthal, who also has impressive Working The Count numbers, by getting there with 1.62 strikes, with 1.44 balls. In other words, Rosenthal puts himself into trouble much more than Jansen. But overall, Rosenthal is still one of the best at Working The Count. That’s how impressive Jansen is.

Stay tuned as we work to get this automated and into leaderboards.

]]>The simple way to think about this is that if you have a pitcher whose peripherals suggest a 10-16 pitcher, and you have another pitcher whose peripherals suggest a 16-10 pitcher, those two, combined would be equal to 2 league average pitchers (13-13).

A 10-16 pitcher is 0 WAR, a 16-10 is 6 WAR, and 13-13 is 3 WAR. That is, in terms of value of production, two 3 WAR pitchers is equal to a 6 WAR and a 0 WAR. Or, simply equal to a 6 WAR pitcher. Teams MUST pay the same. There are plenty of arguments that you will hear and I have read that suggest otherwise. But if that’s the case, the baseline would change to FORCE linearity. For example, say you think a team would pay more for 16-10 than for two 13-13. What therefore would be the equivalency? Paying the same for 15-11 as for two 13-13? Fine, let’s say that.

That simply set the WAR level so that 11-15 is 0 WAR. 15-11 is no longer 5 WAR, but 4 WAR. 13-13 is no longer 3 WAR, but 2 WAR. And two plus two equals four.

It will always work out like this.

]]>