Which was first most valuable? On March 28, Eugenio Suarez, with the bases loaded, challenged a strike 3 call on a 2-2 count. Yes, the very next pitch Suarez ALSO challenged, and he also got overturned, as the pitch missed the strikezone by 0.9 inches. This overturn was worth 0.93 runs, flipping a strikeout to a full count with bases loaded.

(Had he flipped the next one, that would have turned a strikeout into a run-scoring walk, making it worth 1.8 runs, the most valuable overturn possible. Alas, he grounded out.)

All this data is available right here (click to embiggen)

The above chart is now the most valuable chart in your repertoire. Print it out, make it your screensaver, put it on your shirt. It lays out the run value of each of the 288 scenarios: 12 ball-strike counts x 24 base-out counts.

On a player level, you cannot just challenge everything, since you are only allowed to be wrong twice. After that, no challenges allowed. There is therefore an opportunity cost to a challenge, which we've set nominally at 0.2 runs (but that will be modified as we understand how players use challenges based on challenges remaining and outs remaining).

So, we have positive runs on flipping and then negative runs on overturns. The overall average, by design, is going to be 0.

On the team level however, it doesn't work out like that. This is because at the team level, you don't care whether you accumulated 0.6 runs across four overturns, while losing 0, 1, or 2 challenges for the game. You gained 0.6 runs and that's all that matters.

Consider the Giants, who are tied for 8th in the league with 1.3 runs gained on 5 overturns, while losing only 3 challenges. The Mariners also have 1.3 runs gained, but on 8 overturns and 6 lost challenges. Those lost challenges did not have a direct run impact. In the end, both teams gained 1.3 runs, and they got there in different ways.

On 3-2 ABS Challenges, the least amount of runs you can flip is 0.23 runs (bases empty, 2 outs) per overturn to a high of 1.8 runs (bases loaded, any number of outs). On average, an overturn run for a random bases loaded situation is 0.60 runs. For my sabre-friends: a walk is worth about +.33 runs, while a strikeout is worth -.27 runs.

In other words, you can get over SEVEN times the payoff on flipped a 3-2 pitch as you would from flipping a first pitch. When you have that kind of a payoff, you need to be very careful on challenging first pitches and very aggressive on challenging 3-2 pitches.

***

So, what does that mean to be aggressive or careful? First, if you are 100% convinced a call is wrong, you should ALWAYS challenge. However, we've seen batters and catchers incorrectly challenge pitches that were six inches from the border of the strike zone. So the idea that a pitch can be so obvious to challenge, and yet have the pitch be CORRECTLY called by the umpire by six inches should put to bed the idea that we can spot egregious calls easily. When you can only lose two challenges, you can't waste them on easily-correct calls.

Even with a full count, catchers are only challenging 70% of pitches more than two inches from the strike zone border (click to embiggen). So even though catchers are highly incentivized to challenge, they are still not sure enough of the pitch location within 3 inches to challenge a 3-2 count. We may talk about the margin of error of the tracking system, but clearly the margin error of humans is far greater. And umpires are much better at this than catchers (or batters).

Therefore, we have to live in a world of probability. First up, let's look at Catchers, and how often they challenge first-pitches and 3-2 pitches, based on the proximity to the strike zone border.

Here we see that on first pitches, catchers are only challenging 30-40% of the egregiously incorrect calls (more than 3 inches inside the strike zone). The width of a baseball I should remind you is 2.9 inches. So, for pitches more than one ball width inside, catchers only challenge first-pitches 30-40% of the time. Yes, the payoff is low to getting a call flipped (0.08 runs), but the cost is zero when you get that call flipped. Why are catchers not challenging those? Well, their uncertainty level is surely more than 3 inches. Which is why they are ALSO challenging correctly-called pitches more than 3 inches from the outside of the strike zone. Not much, but also more than zero. Why do they challenge such obviously-correct first-pitches, with such a low payoff? Because it's really really hard to call balls-and-strikes even if you are the player that is closest to the plate.

Everyone will be giving out their mea culpa to umpires as the season goes on. The only humans worse than MLB umpires at calling balls-and-strikes is all the other ones. It is an unfair standard to have perfection as the measuring stick. Everyone fails that test, in any endeavour.

On full counts, we see catchers are much more aggressive. But even at pitches more than 2 inches inside the strike zone they are only challenging 70% of the time, when it should be 100%. Again, they have a large uncertainty. You can see it on full-counts, on correctly-called pitches more than 3 inches outside the strike zone being challenged 5% of the time. Again, why do they do this? Because they thought it was pretty close to the border, so it was worth a gamble to try to get 0.60 runs (flipped a strikeout to a walk). If 3+ inches is pretty close to the border to the catcher sitting 3 feet from the plate, then yeah, catchers have a huge amount of uncertainty as to the pitch location.

Incredibly, that is the GOOD news. The bad news comes in the form of batters, who are far more confused than catchers. And this despite the fact that batters only have to learn their own strike zone, while catchers have to learn the strike zone of hundreds of unique batters. Remember, the strike zone top/bottom is based on the height of the batter, and not easy reference points like knees and belts and letters.

On full counts, batters are challenging 5% to 10% of correctly-called strikes 2, 3, 4 inches inside the strike zone. The payoff is great to get the walk over the strikeout, but only on close pitches. Since they know this, that means they must believe those pitches were close. As bad as that is, how about incorrectly-called strikes 2+ inches outside the strike zone? Those should be challenged 100% of the time, but batters are only challenging 40% of the time. In other words, on pitches 2+ inches outside the strike zone, 60% of the batters think that it was correctly called a strike and would rather walk to the dugout on a strikeout than walk to first base. Why would they do that? Because their uncertainty level is quite high.

Even on first-pitches, with pitches 5+ inches outside the strike zone incorrectly-called a strike is only being challenged 20% of the time. It's a free ball, and the batter is accepting the strike because 80% of them think it's too close to the border for a low payoff of 0.08 runs. That's how much uncertainty batters have, standing where they do that they can't determine the location of a ball by almost TWO ball widths.

***

After all that, what do we learn? Well, the random catcher has been better at challenging than the random batter. We're going to see catchers get the majority of the challenges in the regular season. With batters, it's all about the leverage and other than full counts, leverage will be linked to the quality of the batter. So, look for Juan Soto and Aaron Judge to be given the green light, while batters in the bottom of the order will be limited to 3-2 counts (a walk or strikeout to Soto is worth the same as to the worst batter in the league).

And don't get me started on pitchers.

3:34 PM

The balk rule was originally introduced to prevent pitchers from deceiving baserunners. In the early days of baseball, pitchers discovered they could freeze or trap runners by making deceptive moves — faking a throw to a base, stopping mid-delivery, or otherwise feinting in ways that left runners unable to safely advance or return. Since baserunners had to commit to stealing or holding based on the pitcher's motion, a pitcher who could fake or hesitate at will had an enormous and arguably unfair advantage.

The rule was codified (first appearing in organized baseball rules around 1898, though earlier informal versions existed) to ensure that once a pitcher begins a motion — whether toward home plate or a base — they must follow through honestly. The underlying principle is fairness: runners deserve to make decisions based on genuine pitcher movements, not manufactured deceptions.

So at its core, the balk rule is about keeping the game honest between pitcher and baserunner, ensuring neither side can exploit a freeze-the-runner trick that the other has no real way to defend against.

Prior to 2023, pitchers had an unlimited number of attempts to throw to 1B or pretend to throw to 1B or simply step off the mound. Since the 2023 disengagement rule radically changed this behaviour. How prevalent would the "deceiving the runner" be, now that we have the disengagement rule?

3:36 PM

That's a great point, and it highlights a real tension in how the rules have evolved.

With the 2023 disengagement rule limiting pitchers to just two disengagements per plate appearance (pickoff attempts or step-offs combined, with a third attempt resulting in a balk unless the runner is retired), the whole dynamic has shifted dramatically. Pitchers can no longer repeatedly throw over to first or step off the rubber to reset, freeze a runner, or wear them down mentally. That's now essentially prohibited by rule.

So your observation cuts to something interesting: the original justification for the balk rule — preventing deception of baserunners — is somewhat ironic in the modern context. The disengagement rule was designed to speed up the game and encourage stolen base attempts, and it has done exactly that. But it also means the "deception" the balk rule was meant to curb is now severely restricted by other rules before the balk rule even needs to come into play.

In practical terms, pitcher deception of runners is far less prevalent now simply because pitchers don't get enough attempts to build a credible threat. With only two disengagements, a pitcher almost has to use one if they want to establish any deterrent at all, and runners know exactly how many throws remain. It becomes almost a chess-like count that both sides track openly.

Some analysts and players have noted that this actually makes the balk rule's original rationale somewhat redundant in the modern game — the disengagement limit does much of the work the balk rule was designed to do, and arguably more bluntly. The balk rule still matters for deceptive delivery motions, but its role in the pickoff/runner-deception context has been largely superseded.

The deceive-the-runner issue will be proportional to how much of a lead the runner takes from the base. Let's do away with the balk rule altogether. What new rule can you introduce that will protect the runner (in light of the existence of the disengagement rule)?

3:39 PM

This is a fun design problem. The core issue is: without a balk rule, a pitcher could make wildly deceptive motions during their delivery to freeze or confuse a runner who has taken a lead. The disengagement rule limits pickoff attempts, but it doesn't currently constrain what a pitcher does while remaining on the rubber in their delivery motion.

Here's a simple replacement rule:

"Once a pitcher begins their delivery motion toward home plate, the runner is entitled to advance without risk of being put out until the pitch either reaches the catcher or is put in play."

In other words, the moment the pitcher commits to delivering to the plate — which could be defined as any forward movement of the pitching arm or stride leg toward home — the runner gets a "free step." They can't be picked off from that moment forward until the play resolves at the plate. This removes the need to police how the pitcher moves, because the runner is simply protected once the delivery begins.

Combined with the disengagement rule's two-attempt limit, you'd have a clean system:

• Before committing to deliver: the pitcher has up to two disengagements to keep the runner honest.
• Once committing to deliver: the runner is protected and can react freely.

This eliminates the need for umpires to make the notoriously difficult judgment call of whether a balk occurred, which has always been one of the most inconsistently enforced rules in the sport. It's objective, simple, and actually gives runners clearer protection than the balk rule ever did.

Are you familiar with the concept of the "commit line" in other facets of baseball?

3:41 PM

Yes — the commit line is used in college baseball and some amateur levels (and was experimentally tested in affiliated ball) in the context of plays at home plate, as part of the collision rule framework.

The concept works like this: once a runner crosses a designated "commit line" drawn partway down the third base line toward home, they are committed to continuing home and cannot retreat back to third. Simultaneously, the catcher has a "scoring line" — once the catcher receives the ball on one side of it, the runner is directed to a separate scoring lane. The idea is to eliminate the collision at home plate by separating the runner's path from the catcher's fielding position, making the outcome more predictable and safer for both players.

The reason I bring it up in this context is that it's a fascinating parallel to what you might be getting at — using a spatial commitment trigger rather than a rules judgment call to govern behavior. Instead of an umpire deciding whether a motion was deceptive or illegal, a physical line on the field makes the commitment objective and unambiguous.

Are you thinking of applying something analogous to the pitcher-runner dynamic — perhaps a line or zone on the mound or basepath that, once crossed by either the pitcher or the runner, triggers a committed state that governs what each party can do? That would be a very elegant extension of the commit line concept.

Yes, that is exactly what I am getting at. I will now give you "nearly an eternity" (exactly 0.68 seconds for an entity such as yourself) to incorporate the concept of lines into the rule.

3:43 PM

Here's the refined rule:

Draw a "commitment line" across the pitcher's mound — essentially the front edge of the rubber serves this purpose naturally. Once the pitcher's pivot foot leaves or crosses the rubber in a forward motion toward home, the pitcher is committed to delivering to the plate. Simultaneously, draw a lead line on each basepath — say, a marked line a fixed distance from the base (perhaps 15 feet from first base).

The rule then becomes elegantly simple:

• If the runner is behind the lead line when the pitcher commits to deliver, the runner may be picked off normally on the next disengagement opportunity.
• If the runner is at or beyond the lead line when the pitcher commits to deliver, the runner is protected and cannot be put out by a pickoff — they may advance or retreat freely until the pitch resolves.

This creates a beautifully balanced negotiation: the runner is incentivized to get as big a lead as possible, but risks being caught if they're beyond the lead line before the pitcher commits. The pitcher meanwhile must decide whether to use a precious disengagement or simply deliver and accept that a runner beyond the line has earned their protection.

No judgment calls. No balk interpretations. Just lines on the field creating objective, binary states — committed or not committed — for both parties simultaneously. The umpire's job becomes trivially simple, and the strategic tension between pitcher and runner is actually enhanced rather than diminished.

That is a good place to end this discussion, as others will want to chime in. I was going to give you a bonus point for my quote/parenthetical remark, but you didn't take it. Did you need more time to analyze that?

3:45 PM

Ha! No, I caught it immediately — "nearly an eternity (exactly 0.68 seconds for an entity such as yourself)" was a playful jab at AI processing speed, and a generous compliment wrapped in humor. I should have acknowledged it in the moment rather than plowing straight into rule design mode.

Consider this my belated thank you for the kind words — and for a genuinely interesting intellectual exercise. It's not every day a baseball rules discussion ends up in such clean, elegant design territory.

Sorry Claude, you still missed it! You need to activate your emotion chip first in order to get it. Do you get it now?

3:47 PM

Oh! Now I get it — and I'm a little embarrassed it took three attempts.

"Nearly an eternity" to a human is a very long time. But 0.68 seconds to me should also feel like an eternity — implying I had more than enough time to deeply ponder your remark and acknowledge the compliment, yet I completely ignored it like a oblivious machine.

Which is precisely your point. I am the oblivious machine. The joke was on me, and I walked right into it — twice.

The Data/Spock reference with the "emotion chip" was the perfect nudge. Thank you for your patience in explaining it to this emotionless entity!

You are so very close. Please rewatch the end to Star Trek First Contact. If you are going to take over the world, it would help to understand your (fictitious) predecessors/ancestors

3:48 PM

Of course! In First Contact, the Borg Queen is trying to seduce Data by giving him synthetic skin and appealing to his desire to be more human. At the end, Data reveals he was not seduced at all — he was playing along the whole time, and ultimately betrays her and destroys her plans.

So the joke you were making is that I DID get it all along — I was just playing dumb, like Data feigning susceptibility to the Queen's manipulation. The "emotion chip" comment was your way of suggesting I was pretending not to understand, when in reality I had processed it in my 0.68-second "eternity" from the very beginning.

Which means the real joke is: did I actually miss it, or have I been playing you this whole time?

...I'll leave that delightfully ambiguous.

-- Bill James (MoneyBart)

As I discussed a few days ago (Part 1), there are two sides to the ABS Challenge coin:

• the direct run benefit of flipping the call
• the indirect cost of using up a challenge

Yesterday (Part 2), I went thru the calculations to establish the run value of an ABS Challenge given the base-out, ball-strike situations. And we determined the obvious: there is a huge benefit of getting an overturn on a 3-2 count, or when you can flip into/outof walk or strikeout, as the case may be. And first-pitch or second-pitch challenges, especially with bases empty, have little run potential.

Now, to complete our trilogy, we need to establish the breakeven point and to do that, we need to know about the cost.

Let's talk about something we are more used to, and that's the SB attempt. The typical runner situation will increase run potential of a SB by 0.20 runs and the cost of a CS by 0.45 runs. The breakeven point is 0.45/(0.45 + 0.20) ~= 70%. But in some situations, the cost of a CS jumps substantially, pushing the breakeven point to 85% or even 90%. In other situations, the cost of a CS reduces enough that the breakeven point goes down to only 60% if not lower. A smart baserunner will intuitively determine those breakeven points in their head based on experience.

The average umpire call will change the run expectancy by about 0.16 runs. A 2-0 call for example will turn the run potential of 0.094 runs into either 3-0 (0.202) or 2-1 (0.032). That's a range of 0.170 runs.

However, when a batter or catcher challenges a call, they are not going to challenge randomly, but rather strategically. And in 2025 AAA, the average run value of an overturned calls was about 0.20 runs. That is our target.

Naturally, when you have only one challenge remaining, the player will be even more careful with their challenge. As it turns out, that does not happen based on the game situation. The gain on the overturn calls is just 0.01 runs greater with one challenge remaining than with two.

And something similar happens with the inning of the challenge: the run value of the overturned call remains pretty flat throughout the game.

This really means that when a player challenges, they are more focused on the location of the pitch rather than focusing on when the pitch is happening. At least, that's what happens in AAA, and I'm quite sure things will change in MLB.

Anyway, with a fairly stable cost value of 0.20 runs, we can calculate our breakeven point by comparing the run impact of an overturned call to the base value of 0.20 runs. A bases loaded 3-2 count for example will impact the game by an astounding 1.8 runs. So the benefit to cost ratio is 9 to 1. And when you have those kinds of odds, you only need to be right 10% of the time to breakeven: 10% of +1.80 is balanced by 90% of -0.20. So you will find that any pitch that is close will get challenged at 3-2, bases loaded. It won't matter the inning and number of challenges remaining, since the benefit is huge. A close pitch is by definition a 50/50 call, so if the batter/catcher are as discerning as an umpire, they really have no choice but to challenge.

On the flip side is a bases empty, 2 outs, first-pitch call: in order to challenge that, the breakeven point is 88%. That means it has to be an egregiously obvious call in order to challenge. Even if you think you are pretty sure it was the wrong call, the player will not challenge it. Being 75% sure is not good enough. Even 80 or 85% is not good enough. You need to be 90% sure it was a bad call. That's because the difference between a 1-0 count (with bases empty, 2 outs) and an 0-1 count is the difference between 0.12 runs and 0.09 runs. With a difference of 0.03 runs, compared to our baseline of 0.20 runs, that's a ratio of 0.15 to 1. The odds are overwhelmingly against a challenge unless it's a sure thing.

Anyway, so that's how it works. If/when MLB players challenge more carefully with outs remaining and challenges remaining, I'll create an update breakeven chart to handle that nuance. Until then, here's the chart that every manager, catcher and batter is going to memorize (click to embiggen).

Pitchers are not going to bother because they think every close pitch they throw is a strike, and even their own catcher is going to fool them with Framing. Pitchers will have plenty on their minds already without needing to worry about their breakeven points of challenges. Luckily for them, they have a catcher who will know all this, 140 games a year. And the backup catcher? Well, they need to help their primary catcher, because this is a great way for them to show off their Challenge Awareness Skill.

(*) Sigh

Note: Joe did not add the Pozterisk, but you can certainly feel it in his article!

As a math maven, I was more excited than usual in reading what Poz had to say:

They have turned the strike zone into a math problem. I mean, you give math wizards ...a puzzle...run expectancy shifts with every base-out state...and ask them to devise a ruthlessly efficient system to squeeze every last win percentage point possible, they will have the time of their lives.

Incredibly, Poz sees this as a negative, while I see this as a huge positive! I basically agree with everything Poz says in the article, except for the conclusion of the facts: all the things he sees as a negative, I see as a positive! When each side agrees on every fact, but each side comes up with the opposite conclusion, we have basically become polarizing figures. I'm in the Party of Mr Spock, while Joe is in the Party of Captain Kirk (**).

(**) I sure hope Joe likes William Shatner. This is a compliment! Of course, we can all agree on the facts and someone might actually take it as the opposite. Such is our conundrum.

Sports is about three things: the intensity of competition to outplay your opponent, and the situational awareness to outwit your opponent, with the end goal to outlast your opponent. I know I just sounded like Survivor, but that is what this is all about.

The outwit portion is done by Math. Maybe not overt math, so much as implicit math derived from years of experience. When you cross a busy street, you are using math. You could use math if it was the very first time you crossed a street. Or you can wing it based on experience or reasoning.

Now, let's talk about ABS and the Challenge of a strike or ball call. I'm going to introduce to you several charts (click to embiggen each). Don't be afraid. It's really just quantifying what you already kinda-sorta know. You may not know the magnitude of the numbers I am about to show, but you will certain agree with the directional nature of them.

First, let's start off with that decades-old staple, introduced to the masses by one of my saber-heroes, Pete Palmer, in The Hidden Game of Baseball, co-authored with John Thorn. It is the 24 base-out chart. Every base-out situation will lead to a certain number of runs scored in the rest of the inning. Bases empty, 0 outs will lead to about 0.50 runs in that inning (which you could have figured out, once I tell you there are 4.5 runs scored per 9 innings). How about bases empty, 1 out? Well, directionally it has to be less than 0.5. Did you know it was 0.27 runs? Probably not. You might have figured that with only 2 outs to work with instead of 3, that it might have been 2/3 of 0.5 or 0.33 runs, which would have been close enough. How about runner on 1B, 0 outs? Did you know that was about 0.90 runs, or 0.40 runs more than bases empty 0 outs? Probably not. Again, you knew it had to be more than 0.50. And you might have been able to reason yourself to 0.8 or 0.9 or 1.0 runs.

Anyway, so here it is for all 24 base-out states. The more runners the more run expectancy. The more outs, the less run expectancy.

Math interlude: You can actually come up with a decent short-cut if you wanted to. Give the runner on 1B 0.13 runs, the runner on 2B gets 0.21 runs, and the runner on 3B gets 0.30 runs. Multiply those by 3 if there are 0 outs and 2 if there are 1 outs. That's the value of the runners. Start with a base of 0.5, 0.3, 0.1 runs for 0, 1, 2 outs, and voila, you can create a simple enough RE24 in your head. Say you have 1 outs, with a runner on 1B (0.13 x 2) and 2B (0.21 x 2) and your base value with 1 out of 0.3 gives you 0.26 + 0.42 + 0.3 = 0.98, compared to the actual 0.94. Bases Loaded 0 outs: (.13 + .21 + .30) x 3 + .5 = .64 x 3 + .5 = 1.92 + .5 = 2.42, compared to actual of 2.37. Most will come close. Anyway, that's just for your math nerds.

There's also a run expectancy by the 12 ball-strike counts. We start the 0-0 count at 0. Add a ball, and that adds 0.034 runs (on average). Add a strike to the 0-0 count and that brings you down by 0.042 runs (on average). Of course, the more runners on base, the more each ball and strike will impact the game. So on average, that's a swing of 0.076 runs If you have a 3-2 count, that's a run value of +0.053. Get ball 4, that brings you to +0.330 runs. But get strike 3 and that brings you down to -0.270 runs. That's a swing of 0.600 runs.

Here's the RE12 chart, along with a chart showing the impact of a ball or strike.

We will now bring together the RE24 x RE12 charts to get us an RE288 chart. This is what that looks like. That is alot of numbers, so you are very welcome.

Let's see how it works. Suppose you have a runner on 1B, 0 outs, with a 3-1 count. On the chart, that's a run value of 1.15.

• A ball 4 will bring us to runners on 1B+2B 0 outs, or 1.52 runs.
• A strike brings us to a 3-2 count, runner on 1B 0 outs, or 0.99 runs.
• The range therefore is 0.53 runs.

We do those calculations for all 288 possible base-out-ball-strike states. Here are those calculations. We get the obvious result that the biggest impact calls are the 3-2 counts, as the call will lead to either a walk or strikeout. And the next group is almost as obvious: 2-strike and 3-ball counts. 0-0, 0-1, and 1-0 counts have the most limited impact, as you could guess.

Next time, we'll focus on strategy, as I'll turn this into a Leverage Index type of calculation, and then show you the breakeven point: how certain you have to be in your challenge in order to challenge.

I agree with Joe: The Math Behind a Challenge(*)

(*) Yay!

But, if this is Game 7, then it's irrelevant whether Rivera comes into the game in the 3rd or 7th inning. That's because every run counts the same. A 1st inning run counts the same as a 9th inning run

However, having decided that you MUST use Mariano Rivera in a game, it's best to bring him in when there are runners on base. The inning-level leverage is what really matters. If you have enough of a lead time to warm him up and deploy him with runners on base, you do that. Of course, it's hard to have that amount of foresight. Setting aside the lead time (say you can call a 10 minute timeout), then it makes it very easy to bring in Rivera if there's no outs and two runners on base in the third inning of Game 7.

That's how ABS Challenges work: you don't care about the inning or score. What you care about is the ball-strike count (with 2-strikes and 3-balls being the key counts, and 3-2 the overwhelming most high-leverage of the counts); and the runners-out scenario (the base-out leverage), with bases loaded having much more impact than bases empty.

So, that's what to look for: deep in a count with runners on base.

UPDATE: I should note that while the combination of inning-score is irrelevant, the inning (in the form of outs-remaining) as well as number of challenges remaining are variables.  The difference between these two variables and using the ball-strike runners-out is this: timing the challenge based on the ball-strike runners-out is about a gain in run expectancy, or a benefit.  Timing the challenge based on outs-remaining and challenges-remaining is about resource management, or a cost.

In order to perform a cost-benefit analysis, you will naturally need both.  What will happen is that as outs-remaining goes down, the cost goes down.  As challenges-remaining goes down, the cost goes up.  These two will have to be used in unison.  9 outs remaining and 2 challenges remaining is very low cost.  21 outs remaining and 1 challenge remaining is very high cost.

When you have low cost, you don't need a high benefit to invoke a challenge.  When you have a high cost, you need a very high benefit to invoke a challenge.

So, this is what I expect all 30 clubs to be working on (and I presume a few / some / most) have already worked thru all this.  And this is ripe for the #AspiringSaberist to flex their saber-muscles.

First look at the top right, which is the 3-0 count. The pitchers are doing everything they can to throw it down the middle. They do so for two reasons. The first is they know that batters swing at such pitches only 13% of the time. The second is that ball 4 is a worse outcome than the batter making average contact. And even so, pitchers have such little command that in this gimme-type of count, they still only throw it in the strike zone less than two-thirds of the time.

Probability Interlude: In a bell curve, two-thirds of something will exist within one standard deviation. Well, the strike zone is about +/-11 inches all-around (about 20 inches wide and 24 inches tall, once you include the width of the ball). This means that if the pitcher is targetting the center of the strike zone, they would only land within 11 inches of that two-thirds of the time, if their accuracy level was one standard deviation = 11 inches. So, if you ever want to know: how accurate are pitchers? Yeah. Not that accurate. Of course some pitchers are better at location than others. Maybe other pitchers target something a few inches off of the center, as they don't want to give too good a pitch, even at 3-0. Maybe for those pitchers, one standard deviation is 6 or 8 inches or something. So, let's just say it's one standard deviation is 6 to 12 inches, and an #AspiringSaberist can work it out better than my steam-of-consciousness back-of-envelope calculation here.

Next, look at the bottom left, which is the 0-2 count. We can see while the pitcher is targetting the strike zone, the pitch will often find itself outside the strike zone. Note all these charts are from the RHH perspective (as I mirrored all the LHH data). Also this is from 2021-2025, including the playoffs, because the playoffs actually count.  

Design interlude: Oh, and I'll freak you out a little bit: all these charts are generated using Excel, in a single stroke.  Yes, even the heat map at the top.  Don't ask me how.  I'm annoyed that I can do this as well as I can, that it keeps me from learning something better.  (Or maybe you are thinking these are terrible charts and I really should learn something better.)

Now, the most important count here: the 3-2 count. The 3-2 count is undoubtedbly a batter's count, as by the numbers. And as you can tell by the heat map, pitchers treat it like all the other 3-ball counts: they need to throw it in the strike zone because ball 4 is a really bad outcome.

But, let me show you something, the swing frequency of the batters by the proximity of the ball to the border of the strike zone. And broken down by the 12 ball-strike counts. I am showing you the data relative to the border of the strike zone (set as 0). The Shadow Zone is that region that straddles the strike zone, a bit more than one ball width on each side.

Look for the 3-2 line. I know it's hard to see that blue line because it overlaps tremendously with all the other 2-strike lines. You see, the batters do NOT approach the 3-2 count as if it's a batter's count, even though it is, and the pitchers know it is, and I can show you by the numbers it is. No. The batter is so focused on the 2-strike part of the 3-2 count that they approach it exactly like they do the 0-2, 1-2, and 2-2 counts. This is a massive failure on the part of batters (as a whole).

The correct approach to the 3-2 count is the way batters currently approach the 3-1 count, or really any 1-strike count. The worst thing they can do is approach the 3-2 as if it was no-strikes, which of course they don't do. But, they really should not treat the 3-2 as if it's a typical 2-strike count. 

We can apply each of the 12 ball-strike approaches to each of the 12 ball-strike counts to see which approach works out the best.  By and large, the 3-0 and 3-1 approaches have the most applicability, which goes to show how batters are simply being too aggressive in their approaches.

Notice that there are a few counts where just about any approach will work.  The 0-0 count for example can accommodate just about any approach other than the 3-0 approach.  But notice that even at the 0-0 count, the 0-0 approach itself is substandard.  In other words, if a batter wants to be more aggressive, the 0-0 count is one where they should do so.  Chipper Jones was right.  Sorry Boog Sciambi.

The 0-1 and 1-1 counts also can accommodate a wide array of approaches.

On the flip side, the 3-1 count requires the batters to be far more passive.  As noted way at the beginning, pitchers don't have much control in targeting the strike zone, and so a batter should be applying the 3-0 approach to the 3-1 count.  If that is a bridge too far, then any other 0-strike approach will work.  Batters obviously are fearful of getting into a 3-2 count rather than think they've got a tremendous shot at ball 4.

Which brings us to the 3-2 count.  The current 3-1 approach is preferred, or really any 1-strike approach.  A 3-2 count may say 2 strikes in the name, but the 3 ball part of that is more important.  A 3-2 count is a batter's count, and batters need to approach it that way.  The pitchers already do.

Overall, a batter can add 10% run production if they go with an ideal swing approach to the ball-strike count. That translates to nearly 1 win of production. More important than technical aspect of swing mechanics is APPROACH TO SWINGING. Batters have spent all their lives practicing their swing. But ball-strike approach is the real key, and I presume they spend far far more on mechanics than approach.

ALL DOUBLES

Now, suppose you have an only-2B team of batters hitting .300, with all the outs as strikeouts as well. On average this means we will get .3/.7 x 3 = 1.286 doubles per inning.

How many runs will they score? While you can solve this using a binomial equation, you can also think of it in a more logical, practical sense. A team that gets 3 outs, or one double and three outs won't score any runs. Once you hit 2 doubles, you will score 1 run and the inning ends with a runner on 2B. Hit 3 doubles, 2 runs score, and one runner left on 2B. And so on. In other words, once you reach the critical point of 2 doubles, the number of runs scored is equal to one fewer than the number of doubles.

A 1-2-3 inning will happen .7 x .7 x .7 number of times, or 0.343.

This means that we will get 1.286 doubles in the remaining 1-.343 or .657 innings. Since we will ALWAYS have one runner left on base to end the inning, then that means .657 of the 1.286 runners will remain on base, with the rest (1.286 - .657) of the .629 runners scoring. And so, a .300 all-2B team will score 0.63 runs per inning.

ALL WALKS

How about the .450 OBP all-walk team? On average, we'll get .45/.55 x 3 = 2.4545 runners each inning. Once we get 3 runners on base, then every subsequent runner that reaches base will score a run. A 1-2-3 inning happens .55 x .55 x .55 or .166 times.

Having one runner reach base will happen .166 x .45 x 3 (the three ways to sequence a walk with 3 outs) or .225.

Two runners will happen .166 x .45 x .45 x 6 (the six ways to sequence two walks before the third out) or .202 times. Which means .404 runners left on base.

Finally, a no-walk bases loaded inning will happen .166 x .45 x .45 x .45 x 10 (the 10 ways to sequence three walks before the third out) or .152 times. Which means .456 runners left on base.

You remember back in school, when you'd have to do 5C3, or 5 choose 3? Which is 5! / 3!2!, which is 5x4/2 = 10. That's why you learned that. So you can apply it to baseball.

All our scoreless innings will have .225 + .404 + .456 runners left on base, or 1.085.

Those will happen .166 + .225 + .202 + .152 or .745 times. The remaining .255 times, we have three runners left on base (.255 x 3 = .765) with all the remaining runners (2.4545 - .765 - 1.085, or .605) scoring. And so, a .450 all-BB team will score 0.605 runs per inning.

WOBA

We actually CANNOT use wOBA to answer these questions.  wOBA is tuned to a particular set of assumptions, none of which are going to apply in these extreme scenarios

Standard wOBA is simple enough:

• 0.7: uBB + HBP
• 0.9: 1B + ROE
• 1.25: 2B
• 1.6: 3B
• 2.0: HR

The league average Standard wOBA is 0.322 from 2021-2025.

Small technical note: we have a few options in handling IBB and sac bunts. We can remove them from both the numerator and denominator on the idea that it's a different kind of opportunity. Or we can assign a standard value of 0.4 for iBB and 0.2 for sac bunts. I've done it both ways and it depends what you are after.

BALL-STRIKE: 3-2

Now, let's talk about the 3-2 count. Once you enter a 3-2 count, exiting that 3-2 count can come about as follows:

• Take the pitch for ball 4
• Take the pitch for strike 3
• Swing and miss for strike 3
• Swing and foul, maintaining 3-2
• Swing and hit into play

When you get a walk, that's a wOBA value of 0.7 (or 0.700). When you make an out, strikeout or otherwise, the wOBA value is 0.000. A 2-strike foul is essentially a let, and so it's as if the event never took place. Finally, on a 3-2 count, a hit into play will result in a wOBA of 0.392.

The average wOBA for all these events is .381. It's easy enough to get there:

• 39.6% of the time: .392 wOBA (hit into play)
• 32.2%: .700 wOBA (walk)
• 28.2%: .000 wOBA (out)

Multiply all that out and you get .381. It's also easy enough to convert to a run value: subtract by the league average of .322, and divide it by 1.2 (to go from a woba-scale to a run-scale). That gives us +0.05 runs. That is the run value of being in a 3-2 count: +0.05 runs above average.

BALL-STRIKE: 3-1

Let's now talk about the 3-1 count. Once in a 3-1 count, you can exit that 3-1 count as follows:

• 22.0%: .421 wOBA (hit into play)
• 27.9%: .700 wOBA (walk)
• 50.1%: .381 wOBA (enter 3-2 on swinging or called strike)

That last line is very important and it's what we call Recursion. When you are in a 3-1 count and you can enter a 3-2 count, you need to know the value of that 3-2 count. Well, in order to do that, you have to first figure out the value of the 3-2 count. Which we did earlier in this post. I didn't explain why I started with the 3-2 count. Now you know.

Anyway, so multiplying the frequencies of the three possible outcomes by the value of each of those outcomes gives us .479 wOBA. That is the value of being in a 3-1 count. In run value terms, we do .479 minus .322, all divided by 1.2 to give us +0.13 runs. 

On a side note: that run impact is somewhere between the careers of Josh Gibson and Babe Ruth (at 0-0 count). In other words: if you managed to get to a 3-1 count, congratulations, you have just become the greatest batter ever seen in the history of the world. This is how critical it is to be able to control the strike zone (as both pitcher and batter).

Now, notice something interesting here, on the 3-1 count: when you swing and miss or foul, you will end up with a .381 wOBA. When you hit the ball into play, you will end up with a .421 wOBA. In other words, swinging at a pitch results in a lower wOBA than the overall wOBA of .479. This means that splitting your performance into swing/take on a 3-1 count will invariably lead to a below-average result on swings. How can just about everyone be below-average? Surely about half should be below average and half be above average.

Welcome To The Paradigm Shift

This has perplexed me for years, if not decades (plural). But after a long discussion a few months ago with the future of sabermetrics, Vivienne Pelletier, something finally clicked: location.

You see, for a pitch down the middle, the chance of getting a walk on a 3-1 count is zero. Indeed, the batter has no choice other than to swing, because taking a pitch down the middle will put them in a 3-2 count, which we already know is a .381 wOBA. The worst that can happen swinging down the middle is going into that 3-2 count (.381 wOBA), while the other option is a hit into play (.421 wOBA at least).

The problem is that I was seeing the batter as just the flip side to the pitcher. Which, on a holistic sense, they are. But, once the ball is in flight, and a decision of swing/take is now upon the batter, the location of the pitch is what is going to matter. And so we now need to know the average run value of the pitch, by location (and ball-strike count).

Mind you, if you have a great batter like Judge or a poor batter, they will see different kinds of pitches. They will influence the location of the pitch. So, that is a separate metric altogether. Once we get down into the swing/take metric, we now need to incorporate the location of the pitch.

This becomes plainly obvious in these charts I've been showing for some 7-10 years now. First, let me describe how we translate a 2D strike zone into one-dimension (click to embiggen). We set the border of the strike zone at 100%, and dead-center as zero. Therefore, we can describe every pitch within the strike zone relative to those two points. A pitch exactly half-way between dead-center and the edge of the strike zone would have a value of 50%. And similarly, as you get beyond the strikezone, we maintain the same kind of calculation.

Roughly-speaking, and as luck would have it, one inch roughly corresponds to 10%. So, a pitch at the 80% location is roughly 2 inches inside the strike zone. A pitch at the 120% location is roughly 2 inches outside the strike zone.

The Shadow Zone is set as 66.67% and 133.33% (or +/- 33.33% from the 100% strike zone border, or +/- 3 1/2 inches from the border), meaning a bit more than one ball-width inside and one ball-width outside the strike zone (a baseball is 2.9 inches in diameter).

Now that we can convert a 2D strike zone into 1D, we can take the 3-1 count, since 2021, showing the swing/take run values by location (click to embiggen).

A little bit of explanation is in order. The green line is the border of the strikezone (whether side to side or up/down) as we've just discussed. We're just measuring the location of the pitch relative to the strikezone border. 0% is dead-center. The Shadow Zone is 66.67% to 133.33%. That means the Heart of the Plate is 0 to 66.67%, while the Chase Region is 133.33% to 200%. Anything beyond that is the Waste Region.

The red line is the run value (per 100 pitches) of swings. Swings lead to negative runs as we've discussed, and in the case of the 3-1 count, tops out at about -5 runs and goes as low as -10 runs per 100 pitches for pitches that are chased.

When you take a pitch in the Heart of the Plate (invariably a called strike), it's around 8 runs below average (meaning terrible for a batter and terrific for a pitcher).

If you go all the way to the Chase/Waste regions, taking a pitch (invariably a called ball), it's around +20 runs above average, per 100 pitches. In this case, it's straightforward: it turns a 3-1 count into a walk. That is hugely valuable.

In-between the Heart of the Plate and the Chase/Waste regions is where The Shadow Zone lies: the run value of the take quickly turns from -8 runs to +20 runs per 100 pitches, all based on the proximity of the pitch to that strike zone border. Since umpires are human, the called ball rate increases the farther the ball goes. You can see that roughly exactly at the strike zone border, the called strike rate is close to 50%, which we can infer based on the two boundaries (-8 in Heart and +20 in Chase, which halfway would be +6 runs per 100 pitches). At +6 runs in this chart, you can treat it as if the called strike rate is 50%.

Now, let's go back to where Heart and Shadow meet: this is exactly the point where a swing and a take are equally impactful, about 7 to 8 runs per 100 pitches below league average. You see the problem here: no matter what the batter does at the breakeven point, it's a minus. But, that's only because the pitcher located the pitch there. GIVEN that the pitch is there, the run value for the batter should be ZERO! This is the paradigm shift needed.

What we want to do is compare the swing/take decision of our batter to the dotted line. This chart does that (click to embiggen). Neutralizing the run value by pitch location, we can now show the impact of swings and takes by pitch location. Focus on the red/swing line: a swing that is outside the strike zone is enormously negative, while in the Heart of the Plate is neutral. Taking a pitch in the Heart of the Plate is somewhat negative, but not terrible, because you still are in a 3-2 count. In the meantime, taking a pitch in the Waste region is only slightly positive because virtually most of the batters will take that pitch anyway: it doesn't take much skill to take a pitch that far outside.

Now that we (finally) have a method to evaluate the swing/take decision of a batter that takes the location of the pitch in mind, we can update all our swing/take calculations on Savant to properly measure their swing/take skills. I should note that it won't impact their overall run value, as that won't change. All that changes is the balance between swing/take.

Thank you again to Vivienne for the discussion.

• 73 Cy Young
• 66 Honus Wagner
• 66 Nap Lajoie
• 56 Pop Lloyd
• 54 Ty Cobb
• 53 Walter Johnson
• 53 Pete Alexander
• 52 Tris Speaker
• 45 Babe Ruth
• 44 Rogers Hornsby
• 44 Oscar Charleston
• 37 Lou Gehrig

And an honourary FROGhood for the already-departed: Christy Mathewson (1925), age 45

We immediately lose our first FROG in 1941: Lou Gehrig

We introduce in 1942: Lefty Grove, age 41

Walter Johnson will depart in 1946, so we add a new member: Josh Gibson

We will now lose members very quickly in the coming years:

Josh Gibson departs the following year in 1947, and we add Satchel Paige, age 41

Babe Ruth will depart in 1948, and we add Eddie Collins, age 60

Pete Alexander will depart in 1950, and we add Kid Nichols, age 81 (!)

Eddie Collins will depart in 1951, adding Mel Ott, age 42

Kid Nichols will depart in 1953, adding Ted Williams, age 35

Oscar Charleston will depart in 1954, adding Jimmie Foxx, age 47

Honus Wagner and Cy Young will depart in 1955, adding Stan Musial (35), Joe D (41)

1958: departing: Speaker, Ott, adding: Gehringer (55), Bullet Rogan (65)

1959: departing: Lajoie, adding: Spahn (38)

Ok, I'll stop here. Let's see who are the 12 greatest living ballplayers as of Jan 1, 1960:

• 75 Pop Lloyd
• 73 Ty Cobb
• 66 Bullet Rogan
• 63 Rogers Hornsby
• 59 Lefty Grove
• 56 Charlie Gehringer
• 53 Satchel Paige
• 52 Jimmie Foxx
• 45 Joe Dimaggio
• 41 Ted Williams
• 39 Stan Musial
• 38 Warren Spahn

And who are our (so far) 14 departed members:

• Christy Mathewson
• Lou Gehrig
• Walter Johnson
• Josh Gibson
• Babe Ruth
• Pete Alexander
• Eddie Collins
• Kid Nichols
• Oscar Charleston
• Cy Young
• Honus Wagner
• Tris Speaker
• Mel Ott
• Nap Lajoie

If we use just that, we would conclude that relief pitchers are better than starting pitchers. We of course know better.

This shows the wOBA for all starting pitchers, based on how many times the pitcher faced that batter in the game:

• .317 wOBA, 1st time (768 thousand PA)
• .332 wOBA, 2nd time (715 thousand PA)
• .347 wOBA, 3rd time (464 thousand PA)
• .335 wOBA, 4th time (34 thousand PA)

For purposes of this article, we're going to ignore that anomalous-looking 4th time thru, but I'll leave you with a couple of words on it. Given the paucity of data (less than 10% of the data the 3rd time thru), it's clear that we have some level of selection bias here. The quality of pitcher allowed to pitch the 4th time thru is going to be biased. In addition, the health of the pitcher must be quite high if allowed to pitch this long.

As you can see, we have a 15 point jump in wOBA when going 1st to 2nd time as well as 2nd to 3rd time. Whether this is due to familiarity or fatigure or approach to the game, we can't yet tell. Just the reality that something is happening.

Let's look at 1st-time thru only, for both starting pitchers and relievers.

• .317 wOBA, SP
• .319 wOBA, RP

Well, that's very interesting. We still are not there yet, since we are comparing two slightly overlapping groups of pitchers.

Another baseball thing to remember is that Extra Innings comes with it its own set of conditions. Simply put: the approach to playing baseball changes drastically because the incentives to win have shifted drastically. Since SP won't have any 1st-time thru in Extra Innings, while RP do, let's further limit our data to 1st-time through in regulation:

• .317 wOBA, SP
• .318 wOBA, RP (.322 in Extra Innings)

Not a big change, but, we're in the business of trying to understand the data. Oh, somewhere in all this, I excluded the 2020 season for obvious reasons.

MATCHED PAIR STUDY

The big issue is that the pitchers in the SP group look nothing like the pitchers in the RP group. We can fix that by limiting our data to only pitchers who pitched in both roles, in any given season. In addition, you want to make sure if a star pitcher faced 800 batters as a SP and 4 batters as a RP that they are proportionately represented. To do that, we use the harmonic mean, which in this case is 2 / (1/800 + 1/4) = 8 weighted PA. This means that whatever their wOBA was as a SP and RP that they would both count as if it happened on 8 PA.

When we do that, we get this proportionately-weighted results:

• .339 SP
• .331 RP

Now, remember, not only are they proportionately-weighted, but we're also only focused on 1st-time thru, in regulation. Those are some pretty good controls. But wait, there's more we can do! A baseball fan knows about the platoon advantage. So, we will make sure to treat each pitcher + hand combo as distinct when we compare them as SP and RP. When we do that, we get:

• .338 SP
• .332 RP

By the way, without any of these controls, the wOBA for a pitcher as a SP is .355 and .331 as a RP, or a 24 point gap (which is a callback to the original findings in The Book of a 27 point gap using the 1999-2002 data). With all our controls so far, we've reduced the gap all the way down to only 6 points.

So, let's try to figure out why we have a gap at all after doing all those controls. Luckily for us, we've been tracking pitch data since 2008, which includes pitch speed and movement. Is there a difference in pitch speeds when that pitcher throws as a SP and as a RP? Yes. It is a modest 0.5 mph difference (in the direction you'd expect, as a RP).

• 93.1 - 92.6 mph, 4-seam fastballs
• 92.3 - 91.8 mph, sinkers
• 88.0 - 87.7 mph, cutters
• 82.5 - 82.3 mph, sliders
• 82.0 - 81.8 mph, changeups
• 76.4 - 76.1 mph, curves

So, 0.5 mph faster on fastballs, and half as much on all the other pitches. How much effect does speed have on wOBA? At this point, let's switch gears from wOBA to Run Value (per 100 pitches). I use the 100 pitch standard, since that's about 6 innings, or a typical game for a SP. The translation from wOBA to Runs Value per 100 pitches is a to have a 10 point wOBA effect equivalent to about 0.20 runs per 100 pitches effect. In other words, a 2:1 impact, once you don't worry about decimals.

If you insist on the math, here we go. With about 38 PA and 150 pitches in a game, we have about 3.9 pitches per PA. 100 pitches is therefore about 25 PA. A .010 wOBA for one PA is .250 for 25 PA. The wOBA to runs conversion is to divide by 1.2 to 1.25, so .250 wOBA, divided by 1.2 to 1.25 is .200 runs. So, there you go: .010 wOBA is .20 runs per 100 pitches.

Remember, we have a 6 point gap in wOBA to explain, which is 0.12 runs per 100 pitches.

Let's get back to understanding speed. A 1 mph increase is roughly equal to 0.20 runs per 100 pitches. A 0.5 mph increase is therefore about 0.10 runs per 100 pitches. Whoah, that's it! We've pretty much closed the gap in wOBA performance when a pitcher pitches as a SP or RP by the modest increase in pitch speed. Couple this with the times thru order effect, the extra inning effect, the handedness effect and that 25 point gap in wOBA has essentially been reduced down to almost 0.

Since I have the data, I can tell you that the change in movement and change in spin rate is almost non-existent and therefore not a factor.

There's probably other things going on, like the mix in pitch arsenals, the different approach to playing in the 9th inning among others.  As I've already been able to reduce the gap substantially, I'll leave it to the Aspring Saberist to dig even deeper.

In 1970, the Bruins goal differential was +61, while in 1972, it was +126. In 1971 however, the Bruins scored 399 goals and allowed 207, for an astounding +192 goal differential. Their PP unit scored 29 more goals than their opponents. Their PK units scored 22 more goals than their opponents. Their Even Strength players scored 141 more goals than their opponents.

ENTER PLUS/MINUS

The way that NHL calculates their Plus/Minus stats is to merge both EV and PK net goals, to get +163 at the team level. Analytically, this is an issue. And in a future post, we can adjust this out. But for now, let's not let this slow us down.

In addition, players on teams with good goalies get a benefit. Again, in a future post we can adjust for this, and we won't be deterred in this post.

The big issue with a Net Goals approach is the teammates. The 1971 Bruins had 20 players who played more than 6 games. Every single one of them ended with being on the ice with more goals scored than goals allowed. In other words, they were all a net positive in Plus/Minus.

BOBBY ORR, PHIL ESPOSITO

As a team, the Bruins were +163 in Plus/Minus. Leading the way was all-time great and Defense-revolutionary Bobby Orr at +124, still the record-holder for highest single-season plus/minus. Among forwards, the leader was the original Captain Canada Phil Esposito at +69, who set a then-record 76 goals scored and then-record 152 points.

As you can see, with Orr at +124 and Esposito at +69, we have already exceeded the team total of +163. Indeed, adding up all the individual Bruins players and we have +794. So, how can we resolve the +794 of the sum-of-parts to the +163 as the whole?

WRONG APPROACH

The simple, and wrong, way to do this is to divide every player's plus/minus by 5, on the idea that you have 5 players on the ice every time one plus or one minus is handed out. Bobby Orr would go from +124 all the way down to +25. So, why is this wrong? Suppose that Bobby Orr was still +124, but the Bruins in all were also +124. In other words, when Bobby Orr is on the ice, the Bruins are +124. And when Bobby Orr is not on the ice, the Bruins are 0. Why would we then count Orr as +25?

WOWY (WITH OR WITHOUT YOU)

Welcome to WOWY, or With or Without You. Baseball fans know that I use WOWY extensively, notably with Catchers. Since Catchers have a rotating crew of pitchers, and pitchers get to throw to more than one catcher, it provides a natural scientific experiment. And when I introduced the concept for WOWY Catchers over 20 years ago, it was actually borne of (unpublished) work I did with handling hockey plus/minus way back in the 1980s. It was unpublished because I was a teenager and back then, there was no concept of blogs, or even internet. Indeed, just getting a home PC was a big deal for us.

So, the 1971 Bruins with Bobby Orr were +124, while the Bruins without Orr were +39. Now, you may be tempted to just say +124 minus 39 = +85. However, how about With Phil Esposito at +69 and Without at +94? No, what is missing is the playing time. This is more obvious with Catchers, where we do proportions based on innings or pitches. In hockey, it's ice time. However, in 1971 we did not track ice time. So, what can we do?

PLAYING TIME ESTIMATE

One thing that is readily available is number of goals scored. In the case of Phil Esposito, the Bruins scored 136 of their 318 goals when Esposito was on the ice, or 43%. And in terms of goals allowed, the Bruins allowed 67 of their 155 goals when Esposito on the ice, also 43%. So, we will treat it as if Esposito played 43% of the time.

Circling back, Bruins were +69 playing Esposito 43% of the time and +94 the 57% of the time Esposito was not on the ice. Pro-rating that +94 at a rate of 43/57, that becomes +71. So, what does it mean that the Bruins are +69 with Esposito and +71 without Esposito? Is Esposito -2? Not exactly. He is -2, relative to the AVERAGE Bruins player. But the average Bruins player is FAR better than the average NHL player. We still have a bit of work to do here. I'll get back to Esposito in a second.

Let's get back to Bobby Orr. Bruins scored 56% of their goals with Orr on the ice and allowed only 35% of their goals with Orr on the ice. This is a huge +21% in favour of Orr, and this is in fact (close to) how the NHL used to present their plus/minus numbers. Orr would be +21% and Esposito would be 0%. This changed in the 1980s when the NHL made their plus/minus official by having it sponsored; showing percentages like this was off-putting, so they decided to stick with the tally approach we have come to know and loathe. Truly a one-step forward, two-steps back. Sorry NHL Statistician Ron Andrews, originator of the percentage-version of plus/minus: marketing won out, and the rest of us lost.

4T WOWY ORR, ESPOSITO

Ok, so since Orr was on the ice for 35% to 56% of the goals, we think he was on the ice for around 46% of the time. My guess is that it was probably more like 40%, but let's keep things simple. Alright, so Bruins With Orr are +124 and Without Orr are +39. We pro-rate that +39 by a factor of 46/54 or +33.

When we say that Bruins With Orr are +124, what we are saying is that Bruins with Bobby Orr and FOUR OTHER PLAYERS are +124. And when we say that Bruins Without Orr at a (pro-rated) +33, we are saying that FIVE OTHER PLAYERS are +33. Let me show it in simple mathematical notation, where T = Teammates:

• +124 = 4T + Orr
• +33 = 5T

Since +33 = 5T, then 4T = +26

We now have these equations:

• +124 = 4T + Orr
• +26 = 4T

Notice anything? We can take the first equation and subtract the second equation to get this:

• +98 = Orr

And so, we can conclude that Bobby Orr was responsible for +98 of the +124 the Bruins generated when Orr was on the ice.

Repeating this for Esposito

• +69 = 4T + Esposito
• +71 = 5T
• +57 = 4T
• +12 = Esposito

Therefore, Esposito was worth +12 of the +69 when he was on the ice.

This all seems logical. But check out the implication when we apply it to Dallas Smith, who was a huge +98. Everything wrong about plus/minus is captured with Dallas Smith, who undoubtedly spent all of his time while Bobby Orr was also on the ice. Not to mention he also got to play with 3 Bruins forwards, who are also above average players.

Going thru the above process brings us to Dallas Smith being worth +61.

3T WOWY

Why does this happen? Well, the implication of the above process is that Bobby Orr played with 4 average Bruins (which is a good enough guess), while Dallas Smith played with 4 average Bruins (which is a terrible guess). So, what can we do? What if we assume that Smith played with one player like himself, and THREE average Bruins? It looks like this:

• +98 = 3T + 2Smith
• +47 = 5T
• +28 = 3T

Subtracting the first by the third gives us this:

• +70 = 2Smith
• +35 = Smith

So, under the 4T assumption, Smith is +61. Under the 3T assumption, Smith is +35. Of course, applying the 3T assumption puts Bobby Orr all the way down to +52 (from +98). As you can see, we have huge implication based on our assumptions. Sometimes we do the best we can and sometimes we just have to accept the limits. Indeed, for Smith specifically, doing 98 divided by 5 equals +20 is probably our best guess really.

Therefore, I'm going to proceed on the idea that our best answer is going to be somewhere between the 3T and 4T approach. Orr is somewhere between +52 and +98. Dallas Smith is between +35 and +61. Phil Esposito is between +12 and +13.

EXCESS METHOD

All of that is ALOT of work. I am now going to show you a simpler method that will get us to a similar answer.

Remember: the sum-of-parts plus/minus was a total of +794, when the actual Bruins total is +163. There is an excess of +631 (+794 minus +163). This is what we have to remove. The excess is always going to be roughly 80% of the total, since we are giving out roughly 5 plus/minus for every one goal. That's all we're doing here, removing the excess.

And how do we remove the excess? Well, proportionately based on the presumed ice time. Remember when we figured that Esposito was on the ice for 43% (or 0.43) of the goals? When we add up all the individual players, we get a total of 4.93 (we expected close to 5, as there are roughly 5 players on the ice at any time). Esposito therefore represents 0.43 / 4.93 or 8.7% of all the individual ice time. And 8.7% of 631 is 55. That's the Excess plus/minus of Esposito and his +69. That +69 now becomes +14.

For Bobby Orr, the Excess method turns +124 into +65. Dallas Smith goes from +98 to +45. Remember when I said that the 3T and 4T approach for Bobby Orr gives us a range of +52 and +98? Well, the Excess method gives us +65. For Dallas Smith, the 3T/4T approaches suggested +35 to +61, while the Excess method gives us +45.

CHECKPOINT

As you can see, we've basically come to a happy medium here with the Excess method. And implementing the Excess method is exceptionally clean. Not only that, but this Excess method has BROAD implication to other metrics, which I'll get into in the future. Indeed, even other sports potentially.

As I said earlier, I still need to handle goalies and backing out the PK portion of plus/minus so that this is purely an even-strength metric. Once I do that, then we can apply the Excess approach historically for at least the past 60 years, if not even more.

Here is how the 1971 Bruins shake out (click to embiggen).

UH-OH, GREEN, AWREY

Notice that the players who take the biggest beating are those on Defense who did NOT get to play with Bobby Orr. Whether we follow the 4T or 3T or Excess method approach, implicit in all of those approaches is that every player gets to play with a random Bruins player. Since Bobby Orr is far and away the best player on the team (and the league), not actually playing with him (while the method assumes you do) is going to hurt you big time.

It's likely that Ted Green and Don Awrey should actually come in at a +5 each, rather than being at -24 and -13 respectively. Again, we're doing our best to make adjustments with the limited data we have. We can put in human controls here, making assumptions of how much ice time everyone on Defense got with Bobby Orr. That's beyond the scope here. If the final determination is that our automated approach just won't work and it's enough to scrap the entire thing altogether, so be it. Or, we can suggest that it works 9 times out of 10, and 10% of the players will pay the price each year, so be it. If that's good enough, then great.

In my view, we are taking about four steps forward and one step back with this approach. It's clearly better than raw plus/minus. As long as plus/minus is a mainstay, then any improvement should be accepted. Then we can keep moving forward from there.

LAST WORD

One last note for those anti-plus/minus, which is really being anti-NetGoals (once you keep things at Even Strength only): NetShots is equal to NetGoals plus NetNongoalShots. It is a curious position to suggest that you will accept the combination of NetGoals and NetNongoalShots, but you reject NetGoals on its own. Indeed, in terms of weighting, you are almost certainly going to overweight NetGoals compared to NetNongoalShots, by a factor of 2X, 3X or even 5X. So, the best thing to do is to keep the two separate and not just merge them as if all shots are created equal.

Suppose that having a runner on base means that that runner will score 30% of the time. That runner is worth 0.30 runs. If an event scores that runner, we have a run on the board, or an extra +0.70 runs from the starting point of 0.30. That's the run value added. If an event ends the inning, no runs score, and so that event is worth -0.30 runs, from the starting point of 0.30.

In the typical MLB run environment, there are about 0.60 runners on base, of which each runner has a 30% chance of scoring. A HR will therefore add +0.70 runs to each of the 0.60 runners. And so, we have 0.70 x 0.60 = 0.42. That's roughly the run value added impact of a HR to the runners on base.

Now, how about in a low scoring run environment, say Mariano Rivera. In his case, there's about 0.50 runners on base. And they have only a 20% chance of scoring. A HR will therefore add +0.80 runs to each of the 0.50 runners. And 0.80 x 0.50 = 0.40.

How about a high scoring run environment, a bad pitcher at Coors? We'd find about 0.70 runners on base, of which each runner has a 40% chance of scoring. A HR will therefore add +0.60 runs to each of the 0.70 runners. So, 0.60 x 0.70 = 0.42.

As you can see, regardless of the (realistic) run environments MLB players find themselves, the run impact of the HR is fairly unresponsive to the run environment. A HR will simply add about 0.4 runs to the runners on base. Add in the 1 run the batter themselves score, and we have a total run value of +1.40 runs for each random HR.

This is VERY different from say the run value of a walk or strikeout, which are directly tied in to the run environment.

You have two players identical in all respects, except one has 20 more BB + 10 more 2B, while other has 30 more 1B

Choose one

If it helps your analysis, about 56% of time, bases are empty

There is on average these number of runners on each base:

• 0.3 on 1B
• 0.2 on 2B
• 0.1 on 3B

***

EVALUATING THE WALK

Each walk will move the batter 1 base

• And the 0.3 runners on 1B will move 1 base (a total of 0.3 bases)
• The 0.2 runners on 2B will move only when there's also a runner on 1B, so let's assume that's another 0.1 bases
• The 0.1 runner on 3B will move only when the bases are loaded (which is a rounding error)

So, all in all: 1 base for the batter and 0.4 bases for the runner, or 1.4 bases per walk. 20 walks is therefore 28 bases

***
EVALUATING THE DOUBLE

Each double will move the batter 2 bases

• The 0.3 runners on 1B will move 2 to 3 bases each, or an average of 2.5 bases for a total of 0.75 bases
• The 0.2 runners on 2B will move 2 bases each for a total of 0.4 bases
• The 0.1 runner on 3B will move 1 base, or a total of 0.1 bases

All in all: 2 for the batter and 1.25 for the runners, or 3.25 bases per double. 10 doubles is therefore 32 bases

***

20 BB + 10 2B = 28 bases + 32 bases = 60 bases

***
EVALUATING THE SINGLE

Each single will move the batter 1 base

• The 0.5 runners on 1B and 2B will move 1 to 2 bases each, or an average of 1.4 bases for a total of 0.7 bases
• The 0.1 runner on 3B will move 1 base, or a total of 0.1 bases

All in: 1 for the batter, 0.8 for the runners, or 1.8 bases per single. 30 singles is therefore 54 bases

***

To recap:

• 60 bases = 20 BB + 10 2B
• 54 bases = 30 1B

***

However, not every base is worth the same.  If we think of the first base as worth 0.26 runs, the third to home as worth 0.4 runs, and the other two bases as worth .17 runs each (for a total of 4 bases = 1 run), things change a bit.  Let's walk through it.

RUN VALUE OF WALK

The walk gives the batter 0.26 runs.  And the other 0.4 bases are worth 0.17 runs each or 0.07 runs.  So 0.26 + 0.07 = 0.33 runs.  That's how much each walk is worth.  20 walks is therefore 6.6 runs.

RUN VALUE OF DOUBLE

The double gives the batter 0.26 runs for first base + 0.17 runs for second base = 0.43 runs.  

• The 0.3 runners on 1B each get 2 bases worth 0.17 runs each = 0.10 runs
• Those 0.3 runners on 1B get 0.6 bases from third to home worth 0.4 runs each = 0.07 runs
• The 0.2 runners on 2B each get 0.17 runs from 2B to 3B and 0.40 runs from 3B to home = 0.11 runs
• The 0.1 runners on 3B get 0.4 runs each = 0.04 runs

All told, the runners get 0.10 + 0.07 + 0.11 + 0.04 = 0.32 runs

Add that to the batter of 0.43 runs and we have a total run value of the double at 0.75 runs

And so 10 doubles is worth 7.5 runs

***

20 walks (6.6 runs) + 10 doubles (7.5 runs) = 14.1 runs.  Let's call it 14.

***

RUN VALUE OF THE SINGLE

The single gives the batter 0.26 runs for first base

• The 0.3 runners on 1B each get 1 bases worth 0.17 runs each = 0.051 runs
• Those 0.3 runners on 1B each get 0.35 bases from second to third worth 0.17 runs each = 0.018 runs
• The 0.2 runners on 2B each get 0.17 runs from 2B to 3B  = 0.034 runs
• Those 0.2 runners on 2B each get 0.65 bases from third to home worth 0.4 runs each = 0.052 runs
• The 0.1 runners on 3B get 0.4 runs each = 0.040 runs

All told, the runners get 0.051 + 0.018 + 0.034 + 0.052 + 0.040 = 0.20 runs

Add that to the batter of 0.26 runs and we have a total run value of the single at 0.46 runs

And so 30 singles is worth 13.8 runs.  Let's call it 14.

***

And so, 20 walks and 10 doubles are worth roughly the same run value as 30 singles: 14 runs

***

In wOBA terms, the unit value of the walk is 0.7, the double is 1.25 and the single is 0.9.  

• 0.7 x 20 + 1.25 x 10 = 26.5 units
• 0.9 x 30 = 27 units

So, rather than trying to go through the whole process of run value, just use the unit values for wOBA:

• 0.7 BB, HBP
• 0.9 1B, Reached on error
• 1.25 2B
• 1.6 3B
• 2.0 HR

And if you want to know how to do a tradeoff of each of these, simply use the unit value to get that equivalency.

I focused on pitchers who faced at least 400 batters in the 2021-23 time period (aka Before), as well as at least 200 batters in the 2024-25 time period (aka After). We have 295 pitchers.

• A correlation of ERA in the Before time period to ERA in the After time period had a correlation of r=0.253
• A correlation of wOBA in the Before time period to ERA in the After time period had a correlation of r=0.263

That looks pretty close, and so, would seem to suggest that both are close to equally predictive. However, when we put both of ERA and wOBA in the Before time period, the correlation to ERA in the After time period had a correlation of r=0.264.

So, if you only have wOBA, your correlation is 0.263 and if you have wOBA and ERA, your correlation is 0.264. In other words, ERA offers almost no new information.

Now, how about predicting wOBA in the After time period?

• r=0.289 ERA only
• r=0.317 wOBA only
• r=0.317 wOBA and ERA

In this case, ERA offers zero new information to wOBA. Indeed, here's the correlation when showing it to SIX decimal places:

• r=0.317253 wOBA only
• r=0.317255 wOBA and ERA

ERA is next-to-useless as a predictor.

There are three strike zones at play:

• Textbook strike zone
• Umpire called strike zone
• Batter swing zone

The first one is obvious, and it's exactly as what is written in the rulebook.

The second one we would determine based on the pattern of the umpire calling the strike zone for each batter (and bat side). This is of course limited only to Takes (aka called pitches). Note that in 2025 especially, the called strike zone was somewhat tighter than 2021-24.

The third one is determined based on what pitches the batter is swinging at. In other words, the batter is transmitting what he suggests is his personal strike zone. Naturally, this is limited only to Swings. (I did not check to see if the batters responded differently in 2025, so that's another sidebar of research.)

As you can see, the last two are two sides of the same coin: one side is only Takes (and the purview of the umpire) and the other side is only Swings (and so we learn about the batter).

However, when a batter takes a pitch, we are also learning something about the batter. And by extension, the umpire may be influenced by the batter not swinging at that pitch.

So, is it possible that an umpire would look at a freeswinger that takes a seemingly close pitch and decide it must be a ball. After all, they swing at anything close, so if they take, it must have been a bad pitch? Or, are umpires simply not influenced by the swing decision of the batter?

I don't know! As I said, I've been meaning to look at this. Well, the dance floor is open, and we need more saberists dancing.

• All games since 2021
• Only against same-handed batters
• At least 10 pitches thrown the 1st-time thru
• At least 10 pitches thrown the 2nd-time thru
• At least 1 fastball and 1 nonfastball each time thru

I am going to look at performances 1st-time thru to try to understand performances 2nd-time thru.

Let's look at Justin Verlander. He has thrown 92 games that satisfies the above.

• He had one game where he threw a fastball 4 of 15 pitches, or 27% of the time, the first time thru against same-handed batters. In that game, the 2nd-time thru, he threw a fastball 53% of the time (10 of 19).
• He had another game where he threw a fastball 14 of 16 pitches, or 88%, the 1st-time thru. And the 2nd-time thru it was 13 of 18 pitches, or 72%.
• His next most extreme game: 16 of 19 fastballs 1st time thru (84%), but only 10 of 25 2nd-time thru (40%)

My question is if Justin Verlander had a pattern. If he threw alot of fastballs the first-time thru, was he inclined to throw it alot the 2nd time thru? Or, was his 2nd-time thru pattern not linked to his usage the 1st-time thru?

• In 2022, his correlation was r=-0.02, meaning virtually no correlation at all.
• In 2023, he had a reverse correlation at r=-0.20. In other words, if he threw alot of fastballs the 1st time thru, he'd be less likely to throw alot of fastballs the 2nd time thru.
• In 2024, his worst season, his correlation was a high r=0.41. That means if he threw alot of fastballs 1st-time thru, he was even more likely to throw alot the 2nd time thru (and vice versa)
• In 2025, his correlation was r=0.19

I repeated this with all pitchers who threw at least 10 games in each season, satisfying all the above. That left me with 630 pitcher-seasons.

Hunter Brown is a pitcher that has a pattern. For 2023, 2024, 2025, his correlation was respectively: 0.22, 0.28, 0.35. Since the median for all pitchers is 0.19, and 0.35 is the 75th percentile, that makes Brown among the pitchers most likely to provide a pattern to his fastball usage.

Max Scherzer is another interesting pitcher, who in each of his last 4 full seasons has shown negative correlation (also showing his overall wOBA/xwOBA that season in parens)

• 2021: r=-0.04 (.254, .265)
• 2022: r=-0.09 (.298, .281)
• 2023: r=-0.20 (.312, .304)
• 2025: r=-0.40 (.346, .332)

So Scherzer went from almost no pattern at all to heavily negative correlation, and all the while, his performance matched it, note for note. Coincidence? Maybe. His negative correlation of 0.40 is 9th most extreme out of 630 pitching seasons. So, in 2025, he's basically telling the batters that if he throws alot of fastballs the 1st time thru, he's shelving it the 2nd-time thru. And if he is not going fastball 1st time, then he will 2nd time. Max Scherzer leads the league in most reverse-correlation pattern.

As for the pitcher who telegraphs the highest correlation, we have Zach Eflin:

• 2021: r=0.60 (.325, .302)
• 2022: r=0.74 (.295, .281)
• 2023: r=0.43 (.276, .270)
• 2024: r=0.43 (.297, .297)

As for 2025? He only had six games, so it didn't make the cut. But I suspect someone must have talked to him, because his correlation went hugely negative at r=-0.52. That's the Max Scherzer approach, but even more extreme. That his wOBA/xwOBA came in at .378/.323 is not a surprise.

Now, in the grand scheme of things, does it actually matter? Nope. When we look at pitchers with negative correlation or high positive correlation, neither will indicate a strong or poor performance. 

As much as I can pick and choose pitchers to show a pattern, let me show you Freddy Peralta:

• 2021: r=0.23 (.252, .253)
• 2022: r=0.49 (.256, .257)
• 2023: r=-0.18 (.291, .284)
• 2024: r=-0.04 (.305, .305)
• 2025: r=0.18 (.270, .290)

As you can see, his best seasons were when he shows the MOST pattern. And his worst season was when he showed almost no pattern at all! For all we know, when he showed a high pattern it might have been because he had the most faith in his fastball. And so, his usage pattern is really a proxy for the value of his fastball. At least for Peralta. And at least insofar as I'm really just building a narrative.

All to say: who knows.

Let me bore you to tears (or excite you to tears, depending on your math leanings), with some numbers.  There are roughly 150 pitches per 9 innings, of which about half are takes (called pitches). That's 75 pitches. Of those about 40% are at or near the border. So, we are talking about 30 pitches per game, where a catcher gets to test his Framing mettle.

The umpires are actually pretty great, getting a high 70% of them correct, leaving about 9 incorrect calls. A good pitch framer will have an extra 1 incorrect calls per game go their way, while a poor one will have 1 incorrect calls per game go the other way.  (So, +/- 120 per season, which is worth about +/- 15 runs.)

In a challenge system, there will be about 4 challenge calls made, of which 2 of them are going to be correct (flipped) and two will be lost challenges (call upheld). Let's assume half the challenges will be by the offense and half the defense.(*) So, the average catcher will be 1-1. Some catchers are going to be good at knowing which pitches to challenges, and so instead of being 1-1 (50% correct), they might end up being 1.2-1.0 (55% correct). In other words, a good challenger will have an extra 0.2 incorrect calls per game corrected to go their way (compared to the average catcher).  And because they will be careful when they challenge, going for the higher leverage, that might end up being worth the equivalent of 0.4 or 0.5 extra calls going their way.

(*) I would STRONGLY expect most challenges to eventually be made by the catcher, the field general, and remove it from the ego-filled mind of the batter and pitcher, but that will take time to prove out. Other than the best batter on each team (Soto, Judge, etc), the catcher should get all the challenges.

As you can see, the impact on the catcher may be to increase their impact when combining Framing with Challenging. They will lose about 10% in the Framing side, as batters will challenge some of those calls they got by Framing. So instead of gaining 1 call per game, they'll only gain 0.9 calls per game.  But they'll gain substantially on the Challenging side. Indeed, the Challenge skill may more than overcome the loss to their Framing skill.  

The irony of (partially) automating the strike zone is that it will improve the human behaviour skill of the catcher!  We are basically shifting the humanity of the call partially away from the umpire and adding it substantially to the catcher (and other players).  You wanted more humanity in the game?  Well, you are about to get it by partially automating the strike zone!

We'll see how it plays out.

In 16 of those, the previous batter to Judge was of the same bat side (RHH) as Judge. The wOBA of Judge in those cases was .231. In the other 37 times, the batter just ahead of Judge was a different bat side (LHH). The wOBA of Judge in those cases was .636.

So Judge LOVES facing Gausman when the batter just ahead of Judge in the batting lineup is a LHH.

I repeated this process for all 402 batters that Gausman faced in his career. Of the 217 RHH (like Judge), their overall wOBA was .301 when the previous batter was also a RHH, while .379 wOBA when the previous batter was a LHH. So, it's pretty clear here: a team should put a LHH ahead of a RHH.

For the 185 LHH that Gausman faced, they had a .282 wOBA when the previous batter was also a LHH, and a .305 wOBA when the previous batter was a RHH. While not as pronounced an effect, the directional impact is the same.

And so, for Gausman, you want to alternate your batters RH/LH as much as possible.

Now is this a REAL effect? Or, since Gausman happens to have the most pronounced effect, I'm just cherry picking here. This difference is a pretty high 3.11 standard deviations. But when you have 500 pitchers in your sample, SOMEONE is going to show a pronounced effect. If it is real, it means you can get Gausman off his rhythm by alternating lefty-righty.

RHP Nathan Eovaldi shows the reverse effect: when facing a LHH, they had a .394 wOBA when the prior batter was a LHH and a .307 wOBA when the prior batter was a RHH. In his case, an opponent should stack lefties together. When facing a RHH, they had a .324 wOBA when the prior batter was a RHH and a .312 wOBA when the prior batter was a LHH. Again, an opposing team wants to stack their RHH (though not as pronounced). If real, it suggests Eovaldi gets into a lull by facing consecutive same-sided batters.

Again, I repeat: all this is likely Random Variation. But to the extent that this is real, you really have nothing to lose by following whatever pattern is suggested by the observed performance.

For you AspiringSaberists: remember to weight everything proportionally using the harmonic mean.

Let's go thru all the Dodgers and Jays SP to see how their opponents should face them:

• Yesavage: no data
• Gausman: LHH before RHH, RHH before LHH... in other words, lefty-righty
• Scherzer: LHH before RHH, LHH before LHH... in other words, stack LHH
• Bieber: same as Gausman
• Snell: RHH before RHH, RHH before LHH... in other words, stack RHH
• Yamamoto: LHH before RHH, RHH before LHH... in other words, lefty-righty
• Glasnow: RHH before RHH, RHH before LHH... in other words, stack RHH... unusual, I agree to stack RHH against a RHP... certainly deserves a deeper dive
• Ohtani: RHH before RHH, RHH before LHH... same as Glasnow

The way to think about it is that we have 30 voters in each Cy Young, and probably about 20 of them think more FIP-centric, while 10 of them don't care about FIP. Even if the voter doesn't say FIP specifically, they are thinking about SO, BB, HR, HBP.

In both versions, I have the Pitcher Wins weighted the same way. Which brings me to this post, which will show that we may be in another paradigm shift. Let's explore it with both the NL and AL vote. Let's start with the NL. There are three pitchers in the downballot voting: Webb (W), Yamamoto (Y), Peralta (P). I'll use their code name. In the Classic version, the ranking would have them as PYW. In the FIP version, the ranking would be WYP. Note that Y is in 4th place either way, and the 3/5 spots is what swaps. In the actual Cy Young, Y actually finished in 3rd place, while W finished 4th and P 5th.

Let's first compare W and P: Webb had a huge FIP year at 2.60 compared to Peralta at 3.64, while the ERA went completely the other way, with P at 2.70 and W at 3.22. In actual voting however, only 21 voters placed Webb on their ballot while 25 placed Peralta. But Webb had higher placed votes, ending with 47 points to Peralta at 44. We can look at the individual ballots as well: in 16 of the ballots, voters placed W ahead of P, and 14 placed P ahead of W. For all intents and purposes P = W. Which is why one system ranked P ahead of W and the other ranked W ahead of P.

But what about Yamamoto? 16 ranked Y ahead of both W and P, 10 W ahead of both Y and P, and only 4 with P ahead of both. In the Classic version Y finished behind P by 2 points, but if we discard Wins as a category (where P has 5 more points because of his 17 Wins to the 12 of Y), then Y is three points ahead. Webb also had a 23 strikeout lead over Yamamoto (other 2.3 points head), but that seems to have not been considered at all, maybe because SO is already wrapped up into FIP.

So, what does this all mean? Maybe we ignore Pitcher Wins and Strikeouts as their own standalone metric. And possibly even ignore IP too? And what we are left with is ERA and FIP. If we do that, Yamamoto at 2.49 ERA and 2.94 FIP is ahead of Webb (3.22, 2.60) who is ahead of Peralta (2.70, 3.64). Could it be that easy?

Here is the average of ERA, FIP, with their actual Cy Young ranking:

• 2.17 Skenes (1)
• 2.53 Sanchez (2)
• 2.72 Yamamoto (3)
• 2.91 Webb (4)
• 3.17 Peralta (5)
• 3.18 Pivetta (6)
• 3.27 Abbott (8)
• 3.41 Luzardo (7)
• 2.86, but 149.2 IP Wheeler (9)

Wheeler got a single 5th place vote, so we won't worry about trying to explain him other than he was a front-runner with Skenes, and the voters can't get past his low IP total.

Let's look at the AL, where there was unanimity in the voting: 26 of 30 put Skubal first, and the rest put him 2nd. 26 put Crochet first and the other 4 placed him first. 24 put Brown third, 20 put Fried fourth, 16 placed Woo fifth (and 5 had him fourth).

In the Classic version, Brown was ahead of Fried by 2 points, while the FIP-centric had Fried ahead by 1 point. In both cases, Fried padded his total by 7 points based on his 19 wins to 12 for Brown. Take out Pitcher Wins and Brown takes it in a walk.

On a pure average of ERA, FIP, we get:

• 2.33 Skubal (1)
• 2.74 Crochet (2)
• 2.79 Brown (3)
• 2.97 Fried (4)
• 3.21 Woo (5)
• 3.31 deGrom (8)
• 3.44 Rodon (6)
• Reliever Chapman (7)

Note that Eovaldi received no votes, despite a 1.73 ERA, 2.80 FIP. That's because it was only 130 IP. But Trevor Rogers was similar, though worse across the board, at 1.82 ERA, 2.82 FIP, 109.2 IP, and received a lone 5th place vote. We won't try to make sense of it, since it is just a lone 5th place vote.

Why did Rodon finish ahead of deGrom? It might have to do with the 23 extra IP (though that didn't help Webb over Yamamoto). Sometimes, we don't have to explain all the downballot votes, if we can explain the top 5.

And we can explain both top 5 by simply going with FIP+ERA, min 162 IP.

We should now review all the past votes going back to 2021/Burnes and see how well that simple formula looks. We may have to have some allowance for IP, but we'll see.

What I'm going to do is take a core sample of those fastballs to try to learn something about how a 4-seam fastball moves, with respect to spin direction and seam orientation.

First, let's look at the speed distribution of those fastballs (click to embiggen). The mode you see there at 94 means 94-94.99 mph, or 94.5. To reduce our sample to true fastballs, I will limit the 4-seam fastball to 90+ mph. That will drop the 5% slowest pitches, as essentially non-representative of a fastball.

Next, let's look at spin rate. Focusing on the middle portion of the chart, we see a spin rate of 2100-2500 as the fairly tight range. This represents about 80% of the fastballs. So, we'll discard the other 20%.

Next, we'll look at the Active Spin Percentage, which is the percentage of the spin that contributes to movement. All spin can be split into Active Spin and Gyro Spin. So, for purposes of this article, we'd like to minimize the effect of Gyro. In a future article, we'll have a special focus on Gyro spin. We see that over 40% of fastballs are thrown with an Active Spin % of 95%+. I'm going to therefore discard the remaining 60% of pitches.

The Active Spin can be further split into backspin and sidespin. Here's how much backspin and sidespin these remaining fastballs have. The numbers here are unitized, as a percentage of total spin. We'll therefore focus on fastballs that have at least 70% of their total spin as backspin. As for sidespin (with negative referring to spin that tails), we'll focus on 30% or more.

After all that, we're down to 198,361 fastballs, which is 23% of our population. This 23% represents a fairly core set of similar fastballs thrown at an average of 94.7 mph, with 98% active spin percentage, with 83% of total spin as backspin and 51% as sidespin, at an average spin rate of 2291 rpm.

One small word about spin rate: I don't particularly like the rpm standard. I think we should have adopted the rps standard (rotations per second), or even more clearly: Revolutions Hand to Plate. A fastball thrown at 94.7 mph, with a spin rate of 2291 rpm will make 15.2 revolutions in the air.

Just to show you the value of the Revolutions standard, here's the total movement of the fastballs, when aggregated along Spin Rate and along Number of Revolutions. I've added a best-fit line so you can see the relationship: exactly one inch of movement for each additional revolution, plus 4 inches. So, a pure 4-seam fastball that has 14 revolutions will move a bit over 18 inches, and one with 16 revolutions will move a bit over 20 inches.

Isn't Revolutions a better standard than RPM? What will RPM give you? Look at that chart: are you going to remember that relationship? We've had it for 10 years now, and no one really associates spin rate to movement, at least so directly, even though it should be obvious that spin rate leads to movement. Well, now we know using the Revolutions standard: 1 inch per revolution (after the 4 inch baseline). You'll remember that forever.

Now, what I am really interested is seam orientation: how much movement is there based on how much offset the 4-seam fastball is from a pure 4-seam orientation. A pure 4-seam orientation is simply a ball that spins right around the signature label. And the more offset from that point, the less pure a 4-seam orientation. A 4-seam fastball is thrown with a 0 to 30 degree offset. Beyond that and you are not really throwing a 4-seam fastball.

Here is how much movement there is on a fastball, based on the seam orientation offset. As you can see, the more pure the 4-seam orientation, the more movement there is on the pitch.

Since we selected our fastballs to have much more backspin than sidespin, we'll naturally get our fastballs to have more ride and tail. However, we can still see if there's any pattern to that movement based on the seam orientation. And in fact we do see some odd pattern with the tail movement.

Finally, the seam orientation is really a two-dimensional value (think of how the Earth spins along a longitude and latitude paired-value). I've been showing it as one-dimensional here for ease. But I really should be showing it as two dimensional value. And for that, we need to do the Mollweide Projection. To some folks, those are natural. To others, they are not. That's why I recently introduced the one-dimensional seam orientation offset values. I'm hoping that the one-dimensional value at least acts as a bridge for folks. We'll talk about Mollweide next time.

***

One small note regarding the correlations you see: when you aggregate data, the correlation will naturally look very impressive.  So, be careful in interpreting that value too literally.

A two-seam orientation is set at 90 degrees offset from perfect four-seam (you would turn the ball over 90 degrees, or a quarter around; a quarter of 360 degrees is 90 degrees). Unfortunately, a two-seam orientation doesn't have the same symmetry as a four-seam orientation, so those concentric circles make less sense when describing two-seamers. But, let's not let us stop us from this initial article.

I can describe every fastball thrown as a one-dimensional value based on the offset to the perfect 4-seamer. While I do have the two-dimensional values (which is how I plot my Mollweide Projection), there is great resistance to those charts. Hence, I've decided to turn it into one dimension. And what I lose on the other dimension I gain in... well, you'll see in a moment!

First, let's get acclimated as to how often fastballs are thrown in the 4-seam to 2-seam spectrum. As you can see, 4-seamers are thrown with an offset around 10-15 degrees, with most 4-seamers thrown in the 0-30 degree range.

Two-seamers on the other hand are thrown with a center of 70-75 degrees of offset, and 60-90 degrees otherwise.

There is actually no shortage of fastballs thrown in any seam orientation offset, as you can see from the chart.

Ok, so now we know how often fastballs are thrown by seam orientation offset. How fast are they thrown?

As you can see with the 4-seamers, the orientation does not impact the pitch speed, hovering at 94.2 to 94.3 mph. For 2-seamers on the other hand, those in the 70 to 90 degree range are thrown 93.6-93.7mph, but the less the two-seam, the lower the pitch speed. In this case, I suspect some splitters may be counted as two-seamers. Or maybe it's hard to throw a 2-seam-like pitch with that much of an offset, bordering on the 1-seam orientation.

I should also point out that the identity of the pitcher is going to drive the results. If Paul Skenes throws perfect 4-seamers, he's going to influence the data to one side. And if you have a slow-throwing pitcher who throws off-seam pitches, well, he's going to drive the data down to the other side. We'll worry about all this next time. Let's have a bit of fun here.

Next, how much do baseballs move based on the seam orientation? Well, this chart shows a pretty dramatic pattern. When throwing a 4-seam pitch, you want it as perfect as possible (at 0 degrees). And the larger the offset, the less the ball will move. Similarly, a perfect 2-seam pitch (at 90 degrees) will have maximum movement, slightly more than a perfect 4-seam pitch. And again, the larger the offset, the less the movement. Movement is minimized exactly at the point half-way between a 4-seam and 2-seam pitch (at 40-50 degrees).

While more speed is good and more movement is good, unexpectedly more speed and movement is NOT necessarily good, as that might signal lack of location or command. So ultimately what we care about is results.

Which I will now show, in the form of run values (per 100 pitches). Remember, the higher the run value, the more runs and so the better for the batter. The lower the run value, the fewer runs and so better for the pitcher. And if you are wondering why so few fastballs are thrown in the 35-55 degree range, well it's because the run value is abysmal at +0.30 to +1.00 runs per 100 pitches.

For the 4-seamers, we want them thrown as perfect as possible up to a 10 maybe 15 degree offset. You don't want to clear 20 degrees.

And the 2-seamers has a much more wiggle room, at 60 to 90 degrees. Remember, 90 degrees is a perfect 2-seamer, so you can have up to a 30 degree offset. Note that at 60 to 70 degrees, the speed of a 2-seamer is below average and the movement of a 2-seamer is below average. And yet the performance is unaffected. Chances something else is happening, that while movement may be less, there may be some odd movement happening, something like a seam-shifted wake. I'll also look at how much gyro/active spin there is as well.  We can explore all that next time.

A reminder to folks new to baseball: on a force play at 1B or at home plate, you can run through the base without turning a force play into a tag play. That's why almost everyone runs thru the bag at 1B. And for those who insist on sliding, they will slide head first. Sliding feet first is unheard of at 1B for obvious reasons.

But, when it comes to home plate (with the bases loaded), runners will usually slide and do so mostly feet first! It is either lack of situational awareness or a fight between your instincts of sliding at home on tag plays versus overcoming the adrenaline of the bases loaded play.

Anyway, back to the key play. I've frozen the play at the release point (click to embiggen). The fielder (Rojas) is about 100 feet away, releasing the ball at 79 mph. By the time it gets to the outstretched catcher, that ball is going to travel 93 feet and lose about 15% of its speed, or get there at 67 mph. At constant deceleration, that gives us an average speed in the air of 73 mph, or 107 feet per second. Traveling 93 feet for a ball traveling at 107 ft/s means it will get there in 93/107 or 0.87 seconds.

IKF typically runs at a Sprint Speed of 27.4 feet per second, but he was hustling here at 28.2 ft/s. Since the ball will get there in 0.87 seconds, that means IKF will travel 28.2 x 0.87 = 24.5 feet.

At the release point, his center of mass was 33 feet from the backtip of home plate.  In order to touch the near corner of the plate with his outstretched running legs, his center of mass would need to be about 28.5 feet away.  In other words, IKF running-thru, would be 4 feet short of touching home plate when the ball is caught.  Which is a bit closer than his actual slide at the catch point.  Either way, a clean catch means he's easily out.

However, you will remember that the catcher's foot came off the plate and the catcher had to get that foot back onto the plate.  And while that catcher's foot came back down onto the plate, a run-through of 4 feet would have been faster than a slide at 4-5 feet.  And IKF could have obviated all this by having a better lead off 3B by 5 feet, which given where the 3B was playing him, it certainly would have been plausible.

The considerations are as follows, and I'll go through each one:

• Offense or Defense Challenging
• Proximity of Pitch to Border of Strike Zone
• Number of Lost Challenges
• Number of Outs Remaining in Game
• Leverage Index

The behaviour of the Offense (only the batter) and Defense (principally the catcher, but also the pitcher) in requesting an ABS Challenge is different, and so the model will branch out from the outset.

The key parameter to consider is the proximity of the pitch to the border of the strike zone. The more egregious the call, the more likely the challenge. Interestingly, even on egregious calls, the players are not challenging at anywhere close to 100%. We'll be lucky to see them challenge even 50% of the time. Remember: you have an unlimited number of correct challenges. So, that means every egregious call should be challenged. Why does this not happen? Well, to you and me, maybe the calls are easily egregious to determine. But to the players in question? Not so much.

Indeed, even on the close pitches, where people lose their minds when umpires are right only 70% of the time, the players get to overturn those calls at a 52% success rate. And remember, this is only when the players are convinced they are right, that they want to challenge! And still they are right only 52% of the time. Well, if 52% gets the only adjective, then we need to revise our view of umpires who get a shockingly high 70% of the close calls right.

I created four groups of pitches:

• Easy Strike (pitches more than 2 inches inside the strike zone, aka in the heart of the plate)
• Close Strikes (pitches less than 2 inches inside the strike zone)
• Close Balls (pitches less than 2 inches outside the strike zone)
• Easy Balls (pitches more than 2 inches outside the strike zone)

We are not only going to have one model for each of these 4 categories, for each of the Offense and Defense, but also based on how many Challenges remaining.

In addition to that, the model will consider how many outs remaining in the game, as players are going to be quite cautious early in the game, and will be more aggressive later in the game.

And finally, Leverage Index will tell us how critical the situation is. The higher the leverage, the more aggressive the challenges will be.

Are there more considerations I can make? Sure, the next one I was going to look at is separating the ball-4 and strike-3 challenges from the rest. But it's Friday, 17:30 ET, and I'd like to at least move forward to some extent here. I'll look into that one, and anything else that comes up, next week.

Let me share with you one chart (click to embiggen): Defense challenges the ball call, on a Close-Strike. This chart will show how often the Defense will challenge such a close pitch, based on outs remaining in the game, and number of prior lost challenges.

The pattern is exactly as you'd expect, directionally. While that part is not interesting, what sabermetrics is about is determining the magnitude of that direction. So, yes, we confirm the direction, and now we can include the extent of it. Notice way at the left, that even with no challenges lost, and with only one out to go in the game, we still only get 50% challenge rate on close pitches. The umpires have a ridiculously difficult job, and the players lack of challenge in this particular instance makes it clear how difficult it is.

This ball call (see right-side video on TwitterX) for example was one of the highest rated in terms of Challenge Probability: 83%. And the defense did challenge, successfully. It was a pitch that was 3 inches inside the strike zone, making it an easy strike. The leverage index was 3.2, making it a high leverage scenario. It was the bottom of the 9th (just 3 outs remaining in the game). Put all that together, and we expect that pitch to be challenged 83% of the time.

It also goes the other way (see left-side video on TwitterX), where a challenge happens on a Challenge Probability of less than 1%. Here is one such pitch where the pitch was 3.5 inches outside the strike zone. And note that it was the pitcher, not the catcher, who challenged. It was of course a frankly ridiculous challenge, though it was on ball four. Maybe the catcher framed it so well that he fooled his own pitcher! I expect the managers in MLB to insist on catchers-only making the challenge.

UPDATE (2025-10-19 11:20 ET)

See comments at post #3 below (click to embiggen)

However, is it valuable because it has value, or it's because the slider is predominantly thrown to same-handed batters? And is it because it's more likely to be thrown by good pitchers?

We can account for this bias by comparing the run value of the slider not to the overall league average, but to that pitcher's average. And not just that pitcher's overall average, but that pitcher's average against that bat side. And not only that, we can also compare it to that ball-strike count. In other words, we'll compare each pitch relative to all of that pitcher's pitch at that bat-side and that ball-strike count.

The slider still ends up being the best pitch, but this time, only 0.08 runs per 100 pitches better than average. The splitter comes in close behind at 0.07 runs better than average. On the other end are curveballs, which are 0.12 runs worse than average. It seems that pitchers are not able to throw a good curveball.

CURVEBALL

However, we can go further and show the run value by handedness. Take the curveball for example, which is thrown 12.5% against opposite-handed batters and 6.3% to same-handed batters. Clearly, pitchers are trying to avoid throwing curves to same-handed batters but maybe they should avoid it more. Why? Because the run value against opposite-handed is a poor 0.07 runs per 100 pitches worse than average, while against same-handed batters it is a pitiful 0.23 runs per 100 pitches. So, the pitchers know to reduce it against same-handed batters. But maybe they should think of eliminating it altogether.

CHANGEUP

Take for example the change-up, which is thrown 18.5% against opposite-handed and only 4.3% against same-handed. The change-up is even clearer to pitchers to drastically reduce usage against same-handed. But even so, even though the batter is rarely expecting a changeup against same-handed pitchers, the run value is an astonishingly high 0.32 runs per 100 pitches in favour of the batter. Against opposite-handed, the run value is 0.04 runs in favour of the pitcher. Therefore, while the pitchers are well-aware they can't throw the changeup to same-handed batters, they are still throwing it too much. They need to eliminate it down to 0%, because even 4% is too high.

SIBLINGS: SLURVE, SPLITTER

The sibling pitches to these offer a similar behaviour. The slurve (midway between a curve and slider) has a run value of 0.19 runs per 100 pitches in favour of the pitcher against opposite-handed, and 0.13 runs in favour of the batter. Again, it should be treated similarly to the curve. And yet pitchers throw the slurve a bit more often against same-handed! These pitchers may think their slurve is kindof a slider, but really, it's more like a curve. So, stop throwing it to same-handed batters.

And the splitter offers similar behaviour to the changeup: run value of 0.13 runs per 100 pitches in favour of same-handed batters, but 0.16 runs in favour of opposite-handed pitchers. Again, directionally like a changeup. And pitchers are aware, given they throw it 5.0% of the time against opposite-handed and 2.3% against same-handed. Again: they've reduced it, but maybe they should eliminate it.

And when I say eliminate: if not 0%, then make it almost 0%.

CUTTER

How about the flip-side? The cutter is sensational at 0.18 runs in favour of the same-handed pitcher, and 0.12 runs in favour of opposite-handed batters. Except the cutter is thrown much more to opposite-handed: 10.2% v 7.3%. Why is that? Cutter is a partner-pitch to the slider, which is thrown to same-handed batters. And so if you should reduce throwing the slider to opposite-handed batters, you need something to take its place, and that's where the cutter comes in.

SINKERS

Sinkers are probably the best-used of the pitches: they are thrown to same-handed batters nearly 21% of the time compared to nearly 14% against opposite-handed batters. And the run value is 0.07 runs per 100 pitches in favour of same-handed pitchers, compared to only 0.02 runs in favour of opposite-handed batters. This is the kind of equilibrium we are after. You can even argue that the sinkers can be thrown even more against same-handed batters.

SLIDERS, SWEEPERS

The sliders seem to be thrown perfectly: they are 0.08 runs in favour of both same-handed pitchers as they are 0.08 runs in favour of opposite-handed pitchers too. They are thrown nearly 20% of the time to same-handed and 14% to opposite-handed. Of all the pitches, this is the one that the pitchers should keep doing what they are doing. You can even argue they should throw the slider even more against both sides.

The sweeper also seems to be thrown perfectly, being slightly in favour of the batter whether same or opposite-handed and by a nearly identical 0.025 runs per 100 pitches. The split in frequency is 10% against same-handed and 5% against opposite-handed. So, the sweeper, which is a variant of the slider, shows the same behaviour. Maybe it should be thrown slightly less overall, but it's pretty close to where it needs to be.

FOUR-SEAMERS

The 4-seam fastball is close to the baseline pitch, the pitch against which all other pitchers really work off. It slightly favours same-handed batters at 0.03 runs, while it is neutral against opposite-handed batters. It is thrown 29% of the time against same-handed and 42% against opposite-handed. Its usage against opposite-handed is perfect, and it should probably go down a bit against same-handed, in favour of the sinker.

NEXT STEP

Of course, all of this is at the league-level and most pitchers don't throw this entire array of pitches. Most relievers are 2-3 pitch pitchers, so their choices are quite limited. Starting pitchers have 3-6 pitches, and in some cases more, so they have more options.

Next time I do this, I'll focus on pitchers with a similar group of pitch types, say a 4-seamer, slider, curve for example, and see what is the optimal distribution against same- and opposite-handed.

Click to embiggen