During this year’s All-Star Game, in the first inning as Joe Mauer came up to bat, and Tim McCarver wanted to emphasize to the viewers just how amazing Mauer’s batting titles in 2006 and 2008 were, as well as his current production in 2009. McCarver said that one of the reasons that catchers don’t win batting titles is because their batting average goes down late in the game with all of the bumps and bruises they get from donning the tools of ignorance. This seemed an interesting little theory from an ex-catcher that begged for some numbers to back it up. This comment also got me thinking about a potentially even larger issue: Does the wear and tear of playing at certain defensive positions on the field lead to reduced offensive production? Does this happens during the course of the game, and/or throughout the season?

In-Game Fatigue

I looked at the 2008 play-by-play data for Retrosheet to test McCarver’s theory that catchers typically see their batting average fall toward the end of the game. Like most every position on the field, catchers actually see their batting average rise on the fourth or fifth time up in a game:

Times up in a game
Pos   PA 1-3   PA 4   PA 5+
C     .251    .269   .300
1B    .266    .273   .324
2B    .270    .274   .325
3B    .260    .272   .335
SS    .267    .264   .329
LF    .265    .265   .323
CF    .265    .259   .316
RF    .271    .279   .315

While all batting averages rise in the fifth time plate appearance (likely due to poor pitching by the opposition if the lineup is getting to bat a fifth time), the only two positions who saw their batting averages drop the fourth time up are shortstops and center fielders, the most active defenders in the field besides the catcher.

Now if we look at just the fifth plate appearance, the catcher does have the second-lowest increase (behind the right fielder) over their first three plate appearances. If we are thinking of batting titles, however, a fifth plate appearance occurs about two-fifths of the time that a fourth plate appearance does. (In 2008, there were a total of 31,811 fourth plate appearances, versus 13,074 fifth or greater plate appearances.) So let’s combine the fourth and fifth plate appearances (and those rare occurrences beyond five plate appearances) into one statistic, and compare each position which is sorted in descending order.

     Times up in a game
Pos  PA 1-3   PA 4+   Difference
3B   .260     .289    +.028
C    .251     .276    +.025
2B   .270     .291    +.021
1B   .266     .286    +.020
RF   .271     .289    +.018
SS   .267     .284    +.017
LF   .265     .282    +.017
CF   .265     .277    +.012

If there’s the case to be made for fatigue, it seems the center fielder has more of a reason to gripe, as he saw his batting average increase the least. Catchers had the second-highest increase in batting average, behind only the third basemen. However, is this just a one-year phenomenon? As a check, I also did the same analysis for 2006 and 2007, with the following results:

Late-Game Batting Average Increases
Pos    2006    2007    2008   Average
SS    +.033   +.031   +.017   +.027
C     +.024   +.029   +.025   +.026
3B    +.025   +.024   +.028   +.026
2B    +.028   +.018   +.021   +.022
LF    +.025   +.018   +.017   +.020
RF    +.011   +.024   +.018   +.018
1B    +.016   +.015   +.020   +.017
CF    +.014   +.015   +.012   +.014

Interestingly enough, in all three years, the center fielders are at or very near the bottom of the list, while catchers actually are at the top of the list in showing the most improvement in their batting average late in ballgame. Could the constant running required to patrol the outfield (since both the left fielder and right fielders are pretty low as well) take more of a toll within the game?

So what does this say about the original point, about Joe Mauer? Is he even better at staying at his level throughout the game, and is that is leading to the batting titles? It is interesting to note that his batting average was pretty consistent in his first three times up year-to-year, but in the one year he didn’t win the batting title, he had a very low batting average in his late-game plate appearances. One thing to point out is that every in year, he typically performed worse in late-game plate appearances than he did in his early-game plate appearances, as compared to other catchers.

Joe Mauer's Batting Average in his Times Up
       PA 1-3   PA 4+   Difference
2006   .324     .351    +.027
2007   .317     .243    -.074
2008   .332     .333    +.001

Season Fatigue

So there seems to be no evidence of catcher fatigue during a game hurting their batting averages. However, couldn’t the constant beatings that they take throughout the year take its toll? For all players who had at least 400 plate appearances at a single position, I compared their batting averages in their first 300 plate appearances to their batting averages from plate appearance 301 and above.

Season Plate Appearances
Pos  1-300   301+   Difference
C    .292    .268    -.024
1B   .270    .285    +.015
2B   .279    .290    +.011
3B   .273    .271    -.002
SS   .273    .291    +.018
LF   .283    .290    +.007
CF   .270    .270     .000
RF   .288    .286    -.002

So an initial look at 2008 suggests that maybe catchers do wear out as the season progresses. However, if we increase our scope and go back to 2006, we see that this just happened to be a one-year occurrence:

Batting Average Difference Between First 300 PA and 300+ PA
Pos    2006     2007     2008
C     -.004    +.011    -.024
1B    +.005    -.001    +.015
2B    -.001    +.001    +.011
3B    -.003    +.021    -.002
SS    +.014    +.006    +.018
LF    -.003    -.003    +.007
CF    +.001    -.004     .000
RF    -.018    +.008    -.002

When we see the three years in perspective, the data suggest that there isn’t really a significant impact on catcher performance in terms of batting average during the latter portion of the long regular season. Perhaps the likely cause is that any fatigue that might occur with any one position’s performance at the plate is likely to be equaled by pitcher fatigue, such that it all evens out in the end.

Tim Kniker is a conributor to Baseball Prospectus.

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Great article Tim and glad to see you writing here :)
Isn't it great how Faux Sports let's Tim McCarver just make stuff up?
Another reason to shake our heads at Tim McCarver in amazement....or more accurately,to the credibility he is given.
Love this article...reads like one of the chapters in "Between the Numbers".
Why batting average? Tired players may be slapping single, but not necessarily hitting for power late in the game.
Because Tim McCarver's claim was about batting average, not slugging percentage, so that was the angle Tim Kniker took in this article...
Why batting average?

"McCarver said that one of the reasons that catchers don't win batting titles is because their batting average goes down late in the game with all of the bumps and bruises they get from donning the tools of ignorance. This seemed an interesting little theory from an ex-catcher that begged for some numbers to back it up."
I got that and that's why I assumed that there would be a second part addressing overall offensive production.

"Now that we've looked narrowly at batting average, we'll move onto..."

This was a nice read and well presented, but without that second part it does seem a touch superficial.

I would've liked to see more about the SLG etc, but I had no problems with the scope of the article. Actually, I wouldn't mind seeing OBP on the theory that a catcher's understanding of the umpire's strike zone improves as the game goes along.
Fascinating. I would love to see a more long-term analysis of this over several decades or eras. Is it possible that catchers' averages used to suffer more later in games and seasons when nutrition and training regimens were not nearly as advanced? I think there's a lot more to examine here, but this is a great start.
Maybe the lights in the stadiums for night games weren't as good in those days.
I think there's something of a selection problem in your analysis. Good-hitting catchers are more likely to hit higher in the order and less likely to be lifted for pinch-hitters, meaning the 4 and 5+ PA samples have better hitters than the 1-3 sample. You can get around this by using some type of repeated measures model.
Is it really a selection problem if the underlying argument is that good hitting catchers tire upon further plate appearances and those good-hitting catchers are being selected for?
Quick mock-up of an example (it's a gross oversimplification). There are exactly three catchers in the league, and they each get the same number of starts. For convenience, lets assume none of these guys walk (or walk at equal rates), so PA=AB.

Catcher A hits .340 in his first three PAs, .330 in fourth PAs, .320 in his fifth PAs. He leads off for his team, and gets exactly 5 PAs every game.

Catcher B hits .300 in his first three PAs, .290 in his fourth, and would hit .280 in his fifth. He never gets a fifth plate appearance, as he gets exactly 4 PA a game.

Catcher C hits .260 in his first PAs. He would hit .250 and .240 in his fourth and fifth+, but he gets exactly three PA a game.

These three catchers all get the exact same number of PAs., so the average BA for the first three PAs is

(.340*PA_A+.300*PA_B+.260*PA_C)/(PA_A+PA_B+PA_C) =
(.340*PA+.300*PA+.260*PA)/(3*PA) =
(.340+.300+.260)/3 = .300

Saving the math, the average BA for the fourth PA is the average of players A and B is (.330+.290)/2 = .310, and the average BA for the fifth PA is the average for player A, which is .320. If there were no selection, then the averages would run (.300, .290, .280). Put this in a table:

Without selection:
A .340 .330 .320
B .300 .290 .280
C .260 .250 .240
Mean .300 .290 .280

With selection:
A .340 .330 .320
B .300 .290
C .260
Mean .300 .310 .320

You'll see a similar effect when you look at pitcher performance by inning or trip through the order. Starters still going in the 8th or 9th tend to be good or having good days.
Ok I understand, thanks for the great breakdown.
Not just that, but you see this selection effect with the 1-300, 301+ samples too. Everyone gets at bats 1-300, but only starters (and therefore better players) get over 300 at bats.
But on that one, I did limit it to players who got at least 400 PAs in the season at a single position. It's likely that only starters (and probably good starters at least for their team) are going to get 400 PAs for their position.

What I'll do in the next day or two is the following:

1) Just do some of the analysis for those catchers who were 1 - 5 in the lineup and see if the general thing still holds

2) To give those that also wanted to focus on overall production (and not just BA in reference to McCarver's comment), I'll show what happens with OBP, SLG, and OPS as well.
Nice article, by the way.

Different slices of the data can help get around the selection issue, but I think the basic problem is aggregation. Your question is about how players change, so you may want to analyze change directly by somehow accounting for each player's level of ability. If you get a sample such that selection issues don't matter (either by selecting the right group or by using weights), that would work. There are two other ways that allow you to use the whole sample.

The sophisticated way to do this is via a mixed-effect (random-effect, HLM, repeated-measures ANOVA, etc) model, so that you account for individual differences by estimating an initial level or "intercept" for each catcher. Then, you can evaluate the effects of repeated PAs in terms of deviations from one's initial level.

The simpler way is simply to turn the statistics you have into change scores. In the example I gave, Catcher A's .340/.330/.320 line would become .340/-.010/-.010. That would yield the following table:

With Selection:
A .340 -.010 -.010
B .300 -.010
C .260
Mean .300 -.010 -.010

This method could fall victim to some selection problems if there are individual differences in how catcher's change, and players that change a certain way are inclined to play more often. However, it does allow you to answer your questions about change.
So I made some adjustments based on only looking at batting positions 1-5 (assuming these are the better hitters). I've also included the change in all the slash statistics: AVG/OBP/SLG/OPS

C --- +.019/+.023/+.019/+.042
1B--- +.010/+.015/+.027/+.042
2B--- +.011/+.014/+.015/+.029
3B--- +.000/+.005/-.006/-.001
SS--- +.011/+.013/+.012/+.025
LF--- +.011/+.010/+.012/+.022
CF--- +.011/+.016/+.022/+.038
RF--- +.013/+.021/+.021/+.041

It's interesting that 3B flipped by focusing on the top of the order, however, this data does suggest that no position seems to be a distinct advantage or disadvantage based on in-game fatigue.

In terms of 1st 300 PAs to 301+ PAs for players who had at least 400 PAs in the season, the position breakdown for the slash stats are:

C --- -.006/+.000/-.004/-.004
1B--- +.007/+.009/+.025/+.034
2B--- +.004/+.005/+.010/+.014
3B--- +.005/+.004/+.008/+.013
SS--- +.013/+.010/+.025/+.035
LF--- +.000/-.004/+.000/-.004
CF--- -.001/+.003/+.009/+.012
RF--- -.003/-.002/-.007/-.010

In this case the C is at a bit of the bottom when averaged over three seasons, but it's not like we can see a huge difference, given that a lot of this drop is given by a significant drop in 2008 end-season production, but 2007 was just as much a rise with Catchers showing the best improvement of any position.
When I read this, I'm reminded that Bengie Molina hits 4th and Jorge Posada isn't in the top 5 of the Yankees order.
Thanks for the further look - I was thinking the same thing, so it's nice to know it doesn't move much.
Next year Tim will tell us: Catchers improve during the game more than players at other positions because catchers are more adept at tuning in on the pitcher's stuff that day...
Or something like that.
Bill Cullen here:
Will the REAL Tim please stand up.
The data presented here proves it's Kniker, not McCarver.
Good work Tim.
Well, you see, back in McCarver's day, this well-known asiom was absolutely true. Without exception. No catcher ever hit for high average. Ever.

But today, these catchers have the benefits of better training and equipment that allow them to overcome the beating that they take back there. These young high-average catcher whippersnappers don't know how good they got it.
Ryne has a very good point. Much bigger difference between good-hitting and the many weak-hitting catchers. I would think. Maybe I should run that by McCarver first. Anyhoo, a very interesting article, but Ryne's possibility sure seems quite possible.
Maybe eighth place hitters in the NL should be excluded since they bat in front of the pitcher the first two or three times but usually not later and all positions are not equally likely to bat eighth.
you def should get more than 3 seasons of half splits data, see if there are broader patterns.
Tim Kniker, thank you! This is precisely the kind of analysis I find in BP and not many places elsewhere. However, let's not be too hard on McCarver, he ain't the only broadcaster reciting received wisdom. In fact, it's possible contributors to BP (I haven't checked, that's why I said "possible") have over the years bought into this received wisdom- that catchers wear down over the season- which has a surface plausibility. Tim Kniker,Terminator of Surface Plausibility, I salute you.
Personally, I have nothing personal about McCarver, and if I'm just watching a game, I actually like him as a color man (not so much as an analyst). I always like the story of when he was amazed one time when he was catching and Mays came up and he realized that the Say Hey kid got manicures.

Anyways, at least from a "pure" baseball standpoint, I actually learned a lot from reading his book "Baseball for Brain Surgeons" just as much as any of Bill James.. it was just a different aspect of the game.
Some colleagues and I began studying this identical issue a few years ago after he made the same statement during a playoff broadcast. Our results are very similar to yours even though we took an entirely different analytical approach - how encouraging! We presented our findings last month as an oral presentation at SABR 39 in Washington DC and I would be happy to send our results to you if you would like (I don't have your email address). Thanks for the excellent write-up.

Pat Kilgo
Pat -

That sounds good. I'm also in the process of trying to do this a different way to see if I get similar results and expanding this out to 10-15 years instead of just 3.

Feel free to send me something at aortim_at_yahoo_dot_com
Actually, I have a theory that with a few exceptions, "the reasons that catchers don't win batting titles" is that young players who have the ability to hit for a high average are discouraged from playing catcher or are asked to change their approach. Further, if a young catcher demonstrates an ability to hit for an extremely high average in the minors, the team that has him would want him in the lineup more than the catching position allows, especially in the NL where few DH or PH opportunities exist. If Ichiro were a catcher coming up (imagine that!), I'm fairly certain he would be moved. Conversely, if Mike Piazza were even remotely capable of playing 1B, imagine the additional productivity the Mets/Dodgers could have realized from an extra 100 plate appearances. Again, just a theory.
Piazza was a low round draft pick... so perhaps there weren't as many believers of his minor league performance, and thus, not as much of a push for him to switch positions.
On the other hand, it's much harder to find a catcher who can hit than a first baseman who can. I think teams are more likely to keep good-hitting catchers behind the plate until they prove they can't play there because it's normally such an offense-deficient position. See Martinez, Victor.