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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"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."
"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.
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.
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.
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.
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.
Or something like that.
Will the REAL Tim please stand up.
The data presented here proves it's Kniker, not McCarver.
Good work Tim.
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.
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.
Pat Kilgo
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