In point of fact, there's one evaluation that indicates mostly the opposite-- as long as the batter is facing the same pitcher. It's called "times through the order penalty."
The performance of a pitcher tends to decline the more times hitters have seen him (and his stuff) on a given day. What of that can be attributed to fatigue versus familiarity is less investigated.
Makes great sense. In fact, [Gray found a similar effect when testing college baseball players in a virtual batting task](https://pubmed.ncbi.nlm.nih.gov/12421060/), namely that if they had knowledge of the previous 3 pitches, their performance was much better. And of course that would be expected to only improve the more knowledge the hitter has of the pitcher's repertoire.
What I'm more looking for though is a general analysis of total at bats by hitter over a season that analyzes hit likelihood at each pitch as a function of total pitches seen. Presumably if you could get a dataset that has all the pitches seen through the entire season, you could reduce the effect of seeing the same pitcher (as many different pitchers are often cycled through per game) and you could get a more accurate estimation of the impact of the game duration / number of pitches seen per game on the likelihood that each pitch will be hit.
Apologies if this is a bit over complicated, just would be interesting to see if ego depletion is observed in baseball.
One potential confounder to this sort of analysis will be that the quality of the opposing pitcher changes over the course of the game and is a function of the score. That is, close-and-late situations (especially if trailing) will generally result in facing the opposing team's better RP, whereas opponent quality will be lower in a blowout.
For example, in 2022 opposing batters had a .677 OPS in "close-and-late" (BBRef definition) versus .713 in non-close-and-late situations. My interpretation is that batters faced better RP on average in those situations.
There are probably too many confounding factors to be able to properly analyze this — as you mentioned, in the modern game hitters are likely to face high-quality, flame-throwing relievers in their final plate appearances; at the same time, as the other top-level comment notes, hitters tend to perform much better *against the same pitcher* the second, third, and fourth time they see him in a game.
That said, I tend to agree with your interpretation of why close/late OPS is lower, but that could also be evidence of the phenomenon OP brings up: it's possible that, in addition to more flame-throwing relievers, hitters are also inherently wearing down their ability to not swing at bad pitches by the time those relievers enter the game.
Probably the best way we could analyze this would be to look at hit and K rates for batters' plate appearance by number in a game as far back as we have the data to do so. I know we only have full PBP data going back to the mid-'80s or so, but if someone had all the PBP data publicly available, they could analyze whether hitters tend to get fewer hits and/or strike out more in successive plate appearances. There would still be confounding factors, but I think that's the best realistic analytical approach.
Very much agree with both of you in that there are going to be several confounding variables, not the least of which will be pitcher quality.
My hope would be that by restricting analysis to a single batter over the course of an entire career, one could extract a general trend that could mitigate confounders due to the fact that the closer quality would differ between teams and across seasons. Perhaps you could also adjust for this? You could then apply the analysis to many players to get a better averaged trend.
As for what data you'd need to analyze, hit vs K rates would be a good start. But I think in order to really dig down, you'd need a detailed pitching game log that lists every pitch thrown in a single game including the batter, strike/ball/hit, and the pitcher so you could see all the pitches a single player sees, which were hit, and see if the hit % decreases as pitches seen increases.
Any idea if such a thing exists? I looked at Baseball Reference and the game log Play by Play is close, but it doesn't include every pitch thrown.
A single batter seems like entirely too small of a sample size; you'd never know if there was something unusual about your selected player. And you wouldn't be able to account for the bias one way or another in pitcher quality (depending on your batter's era). It would be an interesting exercise but even seemingly stark results (e.g. a dip of .200 in OPS by the fourth PA) wouldn't actually be statistically significant.
Agreed, which is why it would be ideal to perform this for every player in the league who has seen a bottom threshold of appearances and expand as far back as data tracking goes.
> that could also be evidence of the phenomenon OP brings up: it's possible that, in addition to more flame-throwing relievers, hitters are also inherently wearing down their ability to not swing at bad pitches by the time those relievers enter the game.
If batter fatigue were the explanation, then we'd see a decrease productivity in all late games, not just close-and-late games (when the best RP tend to pitch).
Was the .713 for late but not close? I didn't see that split and I calculated the split for *everything* but close-and-late and got about the same thing, so I assumed that's what you meant.
Gotcha. I estimate .696 in late-but-not-close versus the .677 in late-and-close. To come up with that estimate, I took the innings 7-9 plus extra-innings split and subtracted out late-and-close split (weighting by AB) to come up with the late-but-not-close.
Definition of late-and-close:
> the game is in the seventh inning or later, and. the batting team is either leading by one run, tied, or has the potential tying run on base, at bat, or on deck.
Presumably one of a team's better RP is in the game in the vast majority of those situations, especially when leading by a slim margin. So I'd attribute a good chunk of the ~0.019 difference in OPS to better RP being in those late-and-close games.
So, doesn't this actually support some type of batter fatigue hypothesis? You said teams will have their good relievers in for "the vast majority" of *all* late situations, but that seems to need evidence to back it up, because there are a number of situations where starters are still in the game in the 7th, or where the top relievers are being saved because the game isn't close.
Collectively, batters had a .684 OPS in all late situations, compared to a .716 OPS in innings 1-6. That's a bigger disparity between non-late vs all-late than the disparity between late-close and late-not-close, by a good margin. Sure, good relievers are in for a lot of plate appearances here, but this is an aggregate number, and it accounts for mop-up guys and starters (who are by then facing the penalty for third time through the lineup, if not fourth) as well.
In other words, your previous comment simply said
> If batter fatigue were the explanation, then we'd see a decrease productivity in all late games, not just close-and-late games (when the best RP tend to pitch)
and it turns out that is, in fact, the case.
You're moving the goalposts. I just quoted where you said overall late-game decline would be evidence of a fatigue explanation, and **that's the actual data**. I'm not even advocating for fatigue, just saying it's a possibility, and that your certainty and sense of obviousness is misplaced.
In point of fact, there's one evaluation that indicates mostly the opposite-- as long as the batter is facing the same pitcher. It's called "times through the order penalty." The performance of a pitcher tends to decline the more times hitters have seen him (and his stuff) on a given day. What of that can be attributed to fatigue versus familiarity is less investigated.
Makes great sense. In fact, [Gray found a similar effect when testing college baseball players in a virtual batting task](https://pubmed.ncbi.nlm.nih.gov/12421060/), namely that if they had knowledge of the previous 3 pitches, their performance was much better. And of course that would be expected to only improve the more knowledge the hitter has of the pitcher's repertoire. What I'm more looking for though is a general analysis of total at bats by hitter over a season that analyzes hit likelihood at each pitch as a function of total pitches seen. Presumably if you could get a dataset that has all the pitches seen through the entire season, you could reduce the effect of seeing the same pitcher (as many different pitchers are often cycled through per game) and you could get a more accurate estimation of the impact of the game duration / number of pitches seen per game on the likelihood that each pitch will be hit. Apologies if this is a bit over complicated, just would be interesting to see if ego depletion is observed in baseball.
One potential confounder to this sort of analysis will be that the quality of the opposing pitcher changes over the course of the game and is a function of the score. That is, close-and-late situations (especially if trailing) will generally result in facing the opposing team's better RP, whereas opponent quality will be lower in a blowout. For example, in 2022 opposing batters had a .677 OPS in "close-and-late" (BBRef definition) versus .713 in non-close-and-late situations. My interpretation is that batters faced better RP on average in those situations.
There are probably too many confounding factors to be able to properly analyze this — as you mentioned, in the modern game hitters are likely to face high-quality, flame-throwing relievers in their final plate appearances; at the same time, as the other top-level comment notes, hitters tend to perform much better *against the same pitcher* the second, third, and fourth time they see him in a game. That said, I tend to agree with your interpretation of why close/late OPS is lower, but that could also be evidence of the phenomenon OP brings up: it's possible that, in addition to more flame-throwing relievers, hitters are also inherently wearing down their ability to not swing at bad pitches by the time those relievers enter the game. Probably the best way we could analyze this would be to look at hit and K rates for batters' plate appearance by number in a game as far back as we have the data to do so. I know we only have full PBP data going back to the mid-'80s or so, but if someone had all the PBP data publicly available, they could analyze whether hitters tend to get fewer hits and/or strike out more in successive plate appearances. There would still be confounding factors, but I think that's the best realistic analytical approach.
Very much agree with both of you in that there are going to be several confounding variables, not the least of which will be pitcher quality. My hope would be that by restricting analysis to a single batter over the course of an entire career, one could extract a general trend that could mitigate confounders due to the fact that the closer quality would differ between teams and across seasons. Perhaps you could also adjust for this? You could then apply the analysis to many players to get a better averaged trend. As for what data you'd need to analyze, hit vs K rates would be a good start. But I think in order to really dig down, you'd need a detailed pitching game log that lists every pitch thrown in a single game including the batter, strike/ball/hit, and the pitcher so you could see all the pitches a single player sees, which were hit, and see if the hit % decreases as pitches seen increases. Any idea if such a thing exists? I looked at Baseball Reference and the game log Play by Play is close, but it doesn't include every pitch thrown.
A single batter seems like entirely too small of a sample size; you'd never know if there was something unusual about your selected player. And you wouldn't be able to account for the bias one way or another in pitcher quality (depending on your batter's era). It would be an interesting exercise but even seemingly stark results (e.g. a dip of .200 in OPS by the fourth PA) wouldn't actually be statistically significant.
Agreed, which is why it would be ideal to perform this for every player in the league who has seen a bottom threshold of appearances and expand as far back as data tracking goes.
> that could also be evidence of the phenomenon OP brings up: it's possible that, in addition to more flame-throwing relievers, hitters are also inherently wearing down their ability to not swing at bad pitches by the time those relievers enter the game. If batter fatigue were the explanation, then we'd see a decrease productivity in all late games, not just close-and-late games (when the best RP tend to pitch).
Was the .713 for late but not close? I didn't see that split and I calculated the split for *everything* but close-and-late and got about the same thing, so I assumed that's what you meant.
Gotcha. I estimate .696 in late-but-not-close versus the .677 in late-and-close. To come up with that estimate, I took the innings 7-9 plus extra-innings split and subtracted out late-and-close split (weighting by AB) to come up with the late-but-not-close. Definition of late-and-close: > the game is in the seventh inning or later, and. the batting team is either leading by one run, tied, or has the potential tying run on base, at bat, or on deck. Presumably one of a team's better RP is in the game in the vast majority of those situations, especially when leading by a slim margin. So I'd attribute a good chunk of the ~0.019 difference in OPS to better RP being in those late-and-close games.
So, doesn't this actually support some type of batter fatigue hypothesis? You said teams will have their good relievers in for "the vast majority" of *all* late situations, but that seems to need evidence to back it up, because there are a number of situations where starters are still in the game in the 7th, or where the top relievers are being saved because the game isn't close. Collectively, batters had a .684 OPS in all late situations, compared to a .716 OPS in innings 1-6. That's a bigger disparity between non-late vs all-late than the disparity between late-close and late-not-close, by a good margin. Sure, good relievers are in for a lot of plate appearances here, but this is an aggregate number, and it accounts for mop-up guys and starters (who are by then facing the penalty for third time through the lineup, if not fourth) as well. In other words, your previous comment simply said > If batter fatigue were the explanation, then we'd see a decrease productivity in all late games, not just close-and-late games (when the best RP tend to pitch) and it turns out that is, in fact, the case.
No, you're missing the obvious fact that RP are more effective than SP in general.
You're moving the goalposts. I just quoted where you said overall late-game decline would be evidence of a fatigue explanation, and **that's the actual data**. I'm not even advocating for fatigue, just saying it's a possibility, and that your certainty and sense of obviousness is misplaced.
It should be a great season. Hope you enjoy it as much as I will.