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Age Productivity Research

By Bill James

January 8, 2019

Age Productivity Charts

This is just a little research piece, nothing really. For research that I am hoping to do later, I needed an answer to questions of this nature:

If a player is active and in the major leagues at ages 25 and 34, how likely is it that he is more valuable at age 25 than at age 34?

I considered all players to be eligible for the study who (a) batted 400 or more times in a season (b) between 1900 and 2017. This excludes (most) players from 1981 and 1994, for example, but that doesn’t matter. Those who aren’t in the study don’t influence the conclusion of the study.

The exact answer to that question is that there were 333 players who had 400 or more plate appearances in a season at age 25 and also at age 34. Of those 333 players, 214.5 were credited with more Win Shares at age 25 than at age 34, and 118.5 were credited with more Win Shares at age 34 than at age 25. If a player had the same Win Shares both seasons, he was counted as .50 on each side of the ledger. 64% (almost 65%) of those players had more value at age 25 than at age 34.

That’s non-pitchers. Among pitchers, there were 265 players who had 54 or more game appearance points both at age 25 and at age 34. 160.5 of those had more value at age 25 than at age 34, and 104.5 had more value at age 34 than at age 25. That’s a 61-39 split. Game Appearance points is (Games + Games Started), a common reference point. I guess we’ll have to modify it if the 2-inning-starts thing catches on. If you have 27 games, all of them starts, that’s 54; if you have 54 relief appearances and no starts, that’s 54. If you have 40 games appearances/14 starts, that’s 54. I chose 54 because it is the number that is most comparable to 400 plate appearances.

And, of course, I didn’t just do 25 and 34, I did 20 and 21, 20 and 22, 20 and 40, 26 and 42. . . .any possible combination of numbers between 17 and 48.

If you compare 21-year-olds to 22-year-olds, you have 188 comparisons, 188 players (non-pitchers) who had 400 plate appearances at both ages. If you compare 22-year-olds to 23-year-olds, you have 374 comparisons. I decided that any number less than 200 would be considered unreliable, and any number over 200 would be considered reliable. These, then, are the percentages for each age-to-age comparison, when there were 200 comparisons in the group:

	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36
22	50%	61%	66%	63%	61%	62%	62%	61%	55%	56%
23	39%	50%	58%	56%	59%	57%	53%	51%	55%	47%	42%	41%
24	34%	42%	50%	54%	56%	56%	53%	52%	48%	47%	41%	39%	43%
25	37%	44%	46%	50%	53%	52%	49%	47%	47%	44%	40%	33%	36%	31%
26	39%	41%	44%	47%	50%	49%	46%	45%	44%	40%	37%	32%	32%	31%	19%
27	36%	43%	44%	48%	51%	50%	45%	44%	41%	38%	37%	33%	31%	26%	24%
28	38%	47%	47%	51%	54%	55%	50%	46%	45%	43%	37%	33%	32%	27%	25%
29	39%	49%	48%	53%	55%	56%	54%	50%	44%	45%	34%	32%	31%	27%	24%
30	45%	46%	52%	53%	56%	59%	55%	56%	50%	45%	39%	35%	33%	24%	21%
31	44%	53%	53%	56%	60%	62%	57%	55%	55%	50%	41%	35%	31%	25%	23%
32		58%	59%	60%	63%	63%	63%	66%	61%	59%	50%	39%	34%	28%	24%
33		59%	61%	67%	68%	67%	67%	68%	65%	65%	61%	50%	42%	37%	32%
34			57%	64%	68%	69%	68%	69%	67%	69%	66%	58%	50%	36%	36%
35				69%	69%	74%	73%	73%	76%	75%	72%	63%	64%	50%	41%
36					81%	76%	75%	76%	79%	77%	76%	68%	64%	59%	50%

Helping you to read the chart, because it would take you four seconds to figure it out on your own. . . .of the players who were in the study both at age 22 and 23, 61% were better at age 23 than at age 22, and 39% were better at age 22 than at age 23. Comparing 26 year olds and 36 year olds, 81% were better at age 26 than at age 36, and 19% were better at age 36 than at age 26.

Those are the numbers for batters; these are the numbers for pitchers:

	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37
22	50%	55%	56%	61%	63%	59%
23	45%	50%	46%	51%	50%	48%	49%	46%	46%	50%
24	44%	54%	50%	50%	52%	52%	49%	49%	49%	48%	43%	47%
25	39%	49%	50%	50%	49%	50%	47%	48%	46%	44%	45%	41%	39%
26	37%	50%	48%	51%	50%	47%	47%	46%	45%	41%	40%	41%	43%	39%
27	41%	52%	48%	50%	53%	50%	46%	49%	46%	46%	44%	40%	41%	40%
28		51%	51%	53%	53%	54%	50%	45%	46%	43%	40%	39%	41%	41%	36%
29		54%	51%	52%	54%	51%	55%	50%	46%	45%	42%	36%	42%	40%	34%
30		54%	51%	54%	55%	55%	54%	54%	50%	47%	42%	35%	41%	40%	38%
31		50%	52%	56%	59%	54%	57%	55%	53%	50%	40%	39%	42%	40%	37%
32			57%	55%	60%	56%	60%	58%	58%	60%	50%	44%	39%	45%	38%
33			53%	59%	59%	60%	61%	64%	65%	61%	56%	50%	43%	43%	38%
34				61%	57%	59%	59%	58%	59%	58%	61%	57%	50%	42%	42%
35					61%	60%	59%	60%	60%	60%	55%	57%	58%	50%	39%
36							64%	66%	62%	63%	62%	62%	58%	61%	50%	40%
															60%

As you can see, the data for pitchers is quite a bit different than the data for non-pitchers. Pitchers have much less predictable career paths than hitters. There are 188 entries on the hitters chart, of which exactly half—94—are either 60 or higher or 40 or lower. But on the pitchers charts, there are 170 entries, of which only 46 are 60 or higher or 40 or lower. Whereas it is unusual for a hitter to have a better year at 36 than he did at age 26—only 19% of players did this—it is much more common for pitchers; 39% of pitchers had better seasons at age 36 than at 26 (70.5 of 179.) And whereas only 4% of hitters had better seasons at age 40 than they had at age 31 (1.5 out of 40), 29% of pitchers did this (20 out of 70.) Just totally different career paths.

Well. . . a lot of things to do with regard to these charts, but I’ll get to that. Just wanted to share the charts with you, and then get back to the pitcher stuff that I was doing before.

COMMENTS (9 Comments, most recent shown first)

OldBackstop
I am trying to see how injuries might tag into this, in the aggregate, of course. I suspect that a productive 25 year old is given at least a chance to be a productive 35 year old, although he might have a dip there for some serious injury like TJ or....you know. An example might be....you know a hundred.

So if a pitcher, say, has some time off that takes 800 innings off his elbow, is he more likely to be productive at 34?
2:15 AM Jan 18th

MarisFan61
That's what I was guessing, and, without taking any stance on whether he used or not, we can easily say it's a wrong inference -- because those percentage chances that he cited are actually quite substantial.
10:45 AM Jan 11th

tomindc2334
Maris, I believe Kaiser is implying that Martinez used steroids and that's why his aging pattern was so unusual. For what's it's worth, he had great minor numbers at AAA at age 24 and 25 and his MLB stats those years are pretty good overall, in a limited sample. He struggled in the major at 26, but also had a BABIP that year about 70 points below his career average.
10:47 PM Jan 10th

MarisFan61
Kaiser: If you mean that the reason you think you don't have to explain it is that it's self-explanatory, I don't think it is.
10:22 AM Jan 10th

MarisFan61
At first blush I found it very surprising that there wasn't far more of an advantage for things like age 25 over age 34, but I quickly realized that there's a factor that tilts the result further in that direction than we might expect just from "age curve" considerations: To some extent the group of players who are still around and still playing that much at age 34 are the ones who age better (i.e. less badly).

I realize that the latter isn't a sole or pure thing, because to a very large extent the players who are still around and still playing that much at age 34 are the players who are just better; in fact I'm sure that's a bigger factor than the other. Just saying that to some extent it's a set of players who age better than average, probably including some players who were never among the better players but who just aged better than most.
8:42 PM Jan 9th

Guy123
This is great data. It would be very interesting to see the same tables on a rate basis (WS/PA, WS/IP), to see for each age pair how much of the advantage (if any) is due to a playing time disparity as opposed to performance disparity.

10:30 AM Jan 9th

KaiserD2
This is very interesting and important data. I would like to use it to make a point I have made before about a Hall of Fame candidate--Edgar Martinez.

Edgar Martinez did not reach the majors at all until he was 24 and had cups of coffee at 24 and 25. He had 196 average plate appearances at 26. He had a good 1.9 WAA season at 27.

The table shows me that Martinez had a 45% chance of improving at 28. He did. That fell marginally to 44% at 29 and he improved a lot--to 5.1 WAA. He missed most of 1993 when he was average and he was only slightly above average in strike-shortened 1994. In 1995 he had a 37% chance of being better than he had been in 1990, but he shot all the way up 7 WAA, his greatest season, at age 32. He remained much better than he had been at 27 for six more years, until he was 38. By 1998, when he was 35, his chance of being better, according to the table, was down to 26%--and that's where the table stopped.

I don't think I have to fill any blanks in to explain why I would be reluctant to vote for Edgar Martinez for the Hall. Mark McGwire's career had a similar pattern--he became a completely different player when he was 31, even later, and so remained until he was 35.

David K
8:40 AM Jan 9th

StatsGuru
Given the Age 22 pitchers, does this mean they burn out quickly? No one up at age 22 pitched much in their later years? Should we keep pitchers in the minors longer?
7:28 AM Jan 9th

MattGoodrich
Surprising to me that for position players, age 23-31 all did better than age 22.
1:06 AM Jan 9th

Age Productivity Research

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	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36
22	50%	61%	66%	63%	61%	62%	62%	61%	55%	56%
23	39%	50%	58%	56%	59%	57%	53%	51%	55%	47%	42%	41%
24	34%	42%	50%	54%	56%	56%	53%	52%	48%	47%	41%	39%	43%
25	37%	44%	46%	50%	53%	52%	49%	47%	47%	44%	40%	33%	36%	31%
26	39%	41%	44%	47%	50%	49%	46%	45%	44%	40%	37%	32%	32%	31%	19%
27	36%	43%	44%	48%	51%	50%	45%	44%	41%	38%	37%	33%	31%	26%	24%
28	38%	47%	47%	51%	54%	55%	50%	46%	45%	43%	37%	33%	32%	27%	25%
29	39%	49%	48%	53%	55%	56%	54%	50%	44%	45%	34%	32%	31%	27%	24%
30	45%	46%	52%	53%	56%	59%	55%	56%	50%	45%	39%	35%	33%	24%	21%
31	44%	53%	53%	56%	60%	62%	57%	55%	55%	50%	41%	35%	31%	25%	23%
32		58%	59%	60%	63%	63%	63%	66%	61%	59%	50%	39%	34%	28%	24%
33		59%	61%	67%	68%	67%	67%	68%	65%	65%	61%	50%	42%	37%	32%
34			57%	64%	68%	69%	68%	69%	67%	69%	66%	58%	50%	36%	36%
35				69%	69%	74%	73%	73%	76%	75%	72%	63%	64%	50%	41%
36					81%	76%	75%	76%	79%	77%	76%	68%	64%	59%	50%

	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37
22	50%	55%	56%	61%	63%	59%
23	45%	50%	46%	51%	50%	48%	49%	46%	46%	50%
24	44%	54%	50%	50%	52%	52%	49%	49%	49%	48%	43%	47%
25	39%	49%	50%	50%	49%	50%	47%	48%	46%	44%	45%	41%	39%
26	37%	50%	48%	51%	50%	47%	47%	46%	45%	41%	40%	41%	43%	39%
27	41%	52%	48%	50%	53%	50%	46%	49%	46%	46%	44%	40%	41%	40%
28		51%	51%	53%	53%	54%	50%	45%	46%	43%	40%	39%	41%	41%	36%
29		54%	51%	52%	54%	51%	55%	50%	46%	45%	42%	36%	42%	40%	34%
30		54%	51%	54%	55%	55%	54%	54%	50%	47%	42%	35%	41%	40%	38%
31		50%	52%	56%	59%	54%	57%	55%	53%	50%	40%	39%	42%	40%	37%
32			57%	55%	60%	56%	60%	58%	58%	60%	50%	44%	39%	45%	38%
33			53%	59%	59%	60%	61%	64%	65%	61%	56%	50%	43%	43%	38%
34				61%	57%	59%	59%	58%	59%	58%	61%	57%	50%	42%	42%
35					61%	60%	59%	60%	60%	60%	55%	57%	58%	50%	39%
36							64%	66%	62%	63%	62%	62%	58%	61%	50%	40%
															60%


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Comments:

	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36
22	50%	61%	66%	63%	61%	62%	62%	61%	55%	56%
23	39%	50%	58%	56%	59%	57%	53%	51%	55%	47%	42%	41%
24	34%	42%	50%	54%	56%	56%	53%	52%	48%	47%	41%	39%	43%
25	37%	44%	46%	50%	53%	52%	49%	47%	47%	44%	40%	33%	36%	31%
26	39%	41%	44%	47%	50%	49%	46%	45%	44%	40%	37%	32%	32%	31%	19%
27	36%	43%	44%	48%	51%	50%	45%	44%	41%	38%	37%	33%	31%	26%	24%
28	38%	47%	47%	51%	54%	55%	50%	46%	45%	43%	37%	33%	32%	27%	25%
29	39%	49%	48%	53%	55%	56%	54%	50%	44%	45%	34%	32%	31%	27%	24%
30	45%	46%	52%	53%	56%	59%	55%	56%	50%	45%	39%	35%	33%	24%	21%
31	44%	53%	53%	56%	60%	62%	57%	55%	55%	50%	41%	35%	31%	25%	23%
32		58%	59%	60%	63%	63%	63%	66%	61%	59%	50%	39%	34%	28%	24%
33		59%	61%	67%	68%	67%	67%	68%	65%	65%	61%	50%	42%	37%	32%
34			57%	64%	68%	69%	68%	69%	67%	69%	66%	58%	50%	36%	36%
35				69%	69%	74%	73%	73%	76%	75%	72%	63%	64%	50%	41%
36					81%	76%	75%	76%	79%	77%	76%	68%	64%	59%	50%

	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37
22	50%	55%	56%	61%	63%	59%
23	45%	50%	46%	51%	50%	48%	49%	46%	46%	50%
24	44%	54%	50%	50%	52%	52%	49%	49%	49%	48%	43%	47%
25	39%	49%	50%	50%	49%	50%	47%	48%	46%	44%	45%	41%	39%
26	37%	50%	48%	51%	50%	47%	47%	46%	45%	41%	40%	41%	43%	39%
27	41%	52%	48%	50%	53%	50%	46%	49%	46%	46%	44%	40%	41%	40%
28		51%	51%	53%	53%	54%	50%	45%	46%	43%	40%	39%	41%	41%	36%
29		54%	51%	52%	54%	51%	55%	50%	46%	45%	42%	36%	42%	40%	34%
30		54%	51%	54%	55%	55%	54%	54%	50%	47%	42%	35%	41%	40%	38%
31		50%	52%	56%	59%	54%	57%	55%	53%	50%	40%	39%	42%	40%	37%
32			57%	55%	60%	56%	60%	58%	58%	60%	50%	44%	39%	45%	38%
33			53%	59%	59%	60%	61%	64%	65%	61%	56%	50%	43%	43%	38%
34				61%	57%	59%	59%	58%	59%	58%	61%	57%	50%	42%	42%
35					61%	60%	59%	60%	60%	60%	55%	57%	58%	50%	39%
36							64%	66%	62%	63%	62%	62%	58%	61%	50%	40%
															60%

	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36
22	50%	61%	66%	63%	61%	62%	62%	61%	55%	56%
23	39%	50%	58%	56%	59%	57%	53%	51%	55%	47%	42%	41%
24	34%	42%	50%	54%	56%	56%	53%	52%	48%	47%	41%	39%	43%
25	37%	44%	46%	50%	53%	52%	49%	47%	47%	44%	40%	33%	36%	31%
26	39%	41%	44%	47%	50%	49%	46%	45%	44%	40%	37%	32%	32%	31%	19%
27	36%	43%	44%	48%	51%	50%	45%	44%	41%	38%	37%	33%	31%	26%	24%
28	38%	47%	47%	51%	54%	55%	50%	46%	45%	43%	37%	33%	32%	27%	25%
29	39%	49%	48%	53%	55%	56%	54%	50%	44%	45%	34%	32%	31%	27%	24%
30	45%	46%	52%	53%	56%	59%	55%	56%	50%	45%	39%	35%	33%	24%	21%
31	44%	53%	53%	56%	60%	62%	57%	55%	55%	50%	41%	35%	31%	25%	23%
32		58%	59%	60%	63%	63%	63%	66%	61%	59%	50%	39%	34%	28%	24%
33		59%	61%	67%	68%	67%	67%	68%	65%	65%	61%	50%	42%	37%	32%
34			57%	64%	68%	69%	68%	69%	67%	69%	66%	58%	50%	36%	36%
35				69%	69%	74%	73%	73%	76%	75%	72%	63%	64%	50%	41%
36					81%	76%	75%	76%	79%	77%	76%	68%	64%	59%	50%

	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37
22	50%	55%	56%	61%	63%	59%
23	45%	50%	46%	51%	50%	48%	49%	46%	46%	50%
24	44%	54%	50%	50%	52%	52%	49%	49%	49%	48%	43%	47%
25	39%	49%	50%	50%	49%	50%	47%	48%	46%	44%	45%	41%	39%
26	37%	50%	48%	51%	50%	47%	47%	46%	45%	41%	40%	41%	43%	39%
27	41%	52%	48%	50%	53%	50%	46%	49%	46%	46%	44%	40%	41%	40%
28		51%	51%	53%	53%	54%	50%	45%	46%	43%	40%	39%	41%	41%	36%
29		54%	51%	52%	54%	51%	55%	50%	46%	45%	42%	36%	42%	40%	34%
30		54%	51%	54%	55%	55%	54%	54%	50%	47%	42%	35%	41%	40%	38%
31		50%	52%	56%	59%	54%	57%	55%	53%	50%	40%	39%	42%	40%	37%
32			57%	55%	60%	56%	60%	58%	58%	60%	50%	44%	39%	45%	38%
33			53%	59%	59%	60%	61%	64%	65%	61%	56%	50%	43%	43%	38%
34				61%	57%	59%	59%	58%	59%	58%	61%	57%	50%	42%	42%
35					61%	60%	59%	60%	60%	60%	55%	57%	58%	50%	39%
36							64%	66%	62%	63%	62%	62%	58%	61%	50%	40%
															60%