Aging Patterns

 

              The 26-year-old hitters in my study hit 10,409 triples, which is 1,138 triples more than expected.   +1,138.    At age 27 they drop to +463 in triples, at age 28 to +229, and at age 29, to -38.    By age 30, they hit 396 fewer triples than expected (-396), at age 31 -700, and by age 33 -857.  

              You may remember that last week I published a study in which I had compared each player’s RBI in each season to his career RBI, by finding the RBI per plate appearances for his career, and then projecting that onto his plate appearances in the season.    Luke Appling was +61 RBI in 1936, which is a record; not just RBI, but I also did this for runs, hits, doubles, triples, walks, home runs, hit by pitch, grounding into double play, sacrifice hits and flies, and some other things.   I should also repeat the ground rules:   I didn’t include active players or 19^th century players, and I didn’t include 20^th century seasons by 19^th century players.  

              Even without including those—or pitchers—I did have a very large number of players included in the study, which is kind of the whole point.    At the age of 26 there are 4,052 players included in the study.     It’s a big number.    They bat 250 times apiece, you’ve got a million at bats there.    It’s enough to make pretty good measurements of how skills change over time. 

              Let’s start with the raw totals, not that that is going to tell us a hell of a lot.   These are the raw totals of the players in the study, at each age:

 

Age	Count	G	AB	R	H	2B	3B	HR	RBI
16	3	51	154	18	25	4	0	0	8
17	22	331	877	78	182	17	8	4	71
18	89	1717	4185	480	990	151	46	35	379
19	243	6843	19979	2355	4913	735	188	248	1932
20	560	19649	61540	7709	16035	2538	653	974	6685
21	1130	53689	172144	21976	45035	7211	1992	2757	18910
22	1871	107321	343960	44091	89958	14547	3792	6210	38814
23	2678	169882	545466	71658	144279	23853	5740	10738	62996
24	3464	241444	769564	101051	203634	34126	7746	15499	90660
25	3908	299138	950138	126207	252872	42685	9190	19766	113017
26	4052	331943	1060892	141911	284137	48560	10409	22388	127279
27	3935	339182	1089000	145928	292265	50253	10058	23378	132451
28	3715	325701	1043615	138584	280184	48861	9309	22600	128156
29	3333	301285	971106	130424	262014	45465	8454	21754	120712
30	2997	276693	891466	119447	239408	41677	7501	19748	111235
31	2585	238815	765778	102539	206274	36542	6130	17391	96510
32	2211	201149	639094	85546	171740	29947	4858	14887	81184
33	1855	166507	529914	69864	142470	25099	4003	12376	67534
34	1509	130762	409118	54365	110094	19150	2935	9827	52919
35	1160	99227	306000	40328	82456	14403	2013	7587	40374
36	820	69900	213229	27781	57087	10044	1422	5353	28326
37	567	47093	142775	18700	38437	6807	823	3648	18878
38	375	30036	90472	11527	23974	4203	521	2213	11620
39	235	18311	54360	7062	14453	2591	286	1473	7238
40	146	11165	33285	4348	8936	1573	183	858	4393
41	88	6338	17760	2164	4635	783	107	407	2278
42	55	2999	7503	944	1891	305	47	186	955

 

              And, of course, there are some players who played at age 43, 44, etc., but we’re losing meaningful numbers, drifting into random occurrences.   Don’t ask me why I included the totals for 16-year-olds, but not for 43-year-olds.    Anyway, everything peaks at age 27 except triples and the count of players.   The count and triples peak at age 26.   27-year-olds in the study had 292,000 hits.   Just love those big numbers.  Continuing:

 

Age	BB	SO	SB	CS	Avg	1B	EBH	TB	GIDP
16	8	18	0	0	.162	21	4	29	3
17	44	136	13	2	.208	153	29	227	9
18	281	573	62	21	.237	758	232	1338	48
19	1442	2615	315	156	.246	3742	1171	6768	285
20	4910	7844	1189	495	.261	11870	4165	22801	812
21	14153	21927	4045	1492	.262	33075	11960	64501	2392
22	29772	45496	7573	2809	.262	65409	24549	130719	5050
23	48851	74153	12650	5070	.265	103948	40331	211826	8562
24	69833	104546	17463	6849	.265	146263	57371	299749	12475
25	87667	126121	21226	8287	.266	181231	71641	373235	15907
26	99591	139521	23473	9602	.268	202780	81357	420679	17518
27	104122	140696	23216	9065	.268	208576	83689	432768	18716
28	102809	133510	21361	8828	.268	199414	80770	415463	18163
29	96391	122943	18724	7601	.270	186341	75673	389649	17069
30	90033	111907	16383	6732	.269	170482	68926	355331	16305
31	78062	96699	13618	5454	.269	146211	60063	307249	14074
32	66675	81921	10947	4511	.269	122048	49692	256064	12156
33	55260	67909	8179	3549	.269	100992	41478	212703	10116
34	43354	53580	6156	2718	.269	78182	31912	164595	8277
35	32885	40129	4297	1932	.269	58453	24003	123646	6458
36	23398	28058	2869	1334	.268	40268	16819	86034	4450
37	15852	19114	1897	837	.269	27159	11278	57834	3078
38	10064	12108	1228	518	.265	17037	6937	35858	1966
39	6357	7329	674	312	.266	10103	4350	22035	1228
40	3718	4434	475	227	.268	6322	2614	13449	717
41	2189	2480	217	118	.261	3338	1297	6853	422
42	1053	1076	94	44	.252	1353	538	2848	180

 

              Stolen Bases and Caught Stealing also peak at age 26, and batting average peaks at age 29.  Everything else peaks at 27.   1B is singles; EBH is Extra Base Hits.    In the chart below "RB" is "Reached Base", which is the sum of Hits, Walks and Hit By Pitch:

 

Age	HBP	IBB	RB	SAC	SF	OUTS	PA	OBA	SPct	OPS
16	0	0	33	6	0	138	168	.204	.188	.392
17	0	3	229	17	1	724	942	.248	.259	.506
18	2	23	1294	61	7	3332	4557	.288	.320	.608
19	117	41	6472	312	46	15865	21896	.300	.339	.639
20	361	220	21306	1063	224	48099	68098	.318	.371	.688
21	1131	626	60319	2800	692	134485	190920	.321	.375	.695
22	2301	1390	122031	5627	1456	268944	383114	.323	.380	.703
23	3714	2593	196844	8384	2530	425733	608945	.328	.388	.716
24	5320	3906	278846	11512	3737	600503	860028	.329	.390	.718
25	6768	5016	347307	13909	4862	740231	1063344	.331	.393	.724
26	7621	5943	391348	15449	5456	824780	1189042	.333	.397	.730
27	7926	6269	404323	15821	5900	846237	1222775	.335	.397	.732
28	7539	6252	390532	14704	5722	810848	1174395	.337	.398	.735
29	7118	5969	365523	13377	5417	752556	1093410	.338	.401	.740
30	6601	5296	336042	12172	4912	692179	1005194	.338	.399	.737
31	5561	4728	289897	9978	4443	593453	863831	.340	.401	.741
32	4533	4137	242948	8004	3803	495828	722115	.340	.401	.741
33	3796	3388	201526	6685	3269	411063	598936	.340	.401	.742
34	2943	2710	156391	4750	2506	317275	462675	.342	.402	.744
35	2128	2100	117469	3415	1989	237338	346426	.342	.404	.747
36	1579	1515	82064	2367	1419	165712	241996	.342	.403	.746
37	1152	1080	55334	1463	968	110684	162113	.344	.405	.750
38	646	787	34684	861	625	70468	102669	.341	.396	.737
39	403	534	21213	496	386	42329	62002	.345	.405	.750
40	281	213	12864	294	235	25822	37742	.344	.404	.748
41	138	144	6932	157	114	13936	20328	.344	.386	.730
42	62	78	2983	37	50	5923	8682	.345	.380	.725

 

 

              As you can see, everything peaks at age 27 except on base percentage, slugging percentage and OPS, which continue to ascend slowly until age 37.  

              In fact, players do NOT hit better at age 37 than they do at age 37; that’s a statistical illusion.    There are two causes for this statistical illusion.   One is that, as players age, the best players stay in the pool whose skills are being measured, while the weaker players drop out of the major leagues, thus drop out of the pool.   At age 26 there are more than 4,000 players in the study.   At age 37 there are 567.   86% have dropped out.    

              And, of course, it is the best players who play until they are 37.    The players who are still playing at age 37 are the Willie Mayses, the Mickey Mantles, the Ty Cobbs and Babe Ruths and Stan Musials and Ted Williamses and David Ortizes and Joe Morgans and Mike Schmidts and George Bretts and Barry Bondses, plus a certain number of players who are not great players but who age exceptionally well.  

              The second reason for the illusion that older players hit a little bit better is that the floor is rising on the group.   The "floor" is the effect of defensive ability.   With the exception of Designated Hitters, each player has to have a certain level of defensive ability to stay in the lineup.   Defensive skill peaks earlier than hitting skill, and dissipates more rapidly.    A shortstop, let’s say Andrelton, might be so brilliant defensively that even if he has a .600 OPS, he can stay in the lineup.    If you are not a brilliant defensive player, you cannot stay in the lineup with a .600 OPS. 

              As players lose defensive skill in aging, they have to hit more to stay in the lineup.   All the players are being "cut off" once their OPS drops below X, with X being a different number for each player.   But the AVERAGE X increases with age.  

              As a result of these two factors—the dropping out of the weaker hitters, and the fact that the level of offensive skill required to avoid being eliminated from the sample is increasing—the average OPS of all hitters can increase and will increase with age, even if every single hitter in the study gets a little bit worse every year.    If every player loses three points off his OPS every year, but all those below a .650 OPS are eliminated from the study, and then the .650 increases by 4 points a year, then the average OPS will increase, even though every player’s OPS is declining.

              I have known THAT since at least 1980, but when I wrote about these issues in the 1980s I did not have the ability to make some of the adjustments that I needed to make.   Now I do.   That’s what this article is about.  

              We know that Cecil Fielder in 1990 was 26 years old, and we know that he hit 51 home runs that season.    We know that that is 14.9 home runs above his expectation, based on his career numbers.   It is 51 over 36.1, or 41% over expectation.    We have these numbers for all 26-year-old players.     This chart compares the performance of 26 year old hitters to their expectation, based on career performance:

 

Age	Count	G	AB	R	H	2B	3B	HR	RBI
26	4052	331943	1060892	141911	284137	48560	10409	22388	127279
26		-9543	1209	4372	4893	998	1138	528	1245
	BB	SO	SB	CS	Avg	1B	EBH	TB	GIDP
	99591	139521	23473	9602	.268	202780	81357	420679	17518
	-1539	-3324	2838	1103		2230	2663	9750	-1027
	HBP	IBB	RB	SAC	SF	OUTS	PA
	7621	5943	391348	15449	5456	824780	1189042
	133	165	3505	390	-234	-3452	0

 

              26-year-old hitters hit 10,409 triples, which is 1,138 more than expected.    We can calculate, then, that their EXPECTED triples were 9,271.   This version of the chart adds the expected number in each category:

 

Age	Count	G	AB	R	H	2B	3B	HR	RBI
26	4052	331943	1060892	141911	284137	48560	10409	22388	127279
26		-9543	1209	4372	4893	998	1138	528	1245
		341486	1059683	137539	279244	47562	9271	21860	126034
	BB	SO	SB	CS	Avg	1B	EBH	TB	GIDP
	99591	139521	23473	9602	.268	202780	81357	420679	17518
	-1539	-3324	2838	1103		2230	2663	9750	-1027
	101130	142845	20635	8499	.264	200550	78694	410929	18545
	HBP	IBB	RB	SAC	SF	OUTS	PA
	7621	5943	391348	15449	5456	824780	1189042
	133	165	3505	390	-234	-3452	0
	7488	5778	387843	15059	5690	828232	1189042

 

              We now know that the EXPECTED batting average, for this set of players, given the career batting average of each player in the sample and given the number of plate appearances that each player had, was .264.    The .268 batting average that these players had at age 26 is four points OVER expectation.   

              The overall batting average of 26-year-olds in the study is .268, and the overall batting average of 37-year-olds in the study is .269.   But the EXPECTED batting average of the 37-year-olds, given THAT set of players, was .280.    The actual batting average of the group has increased from .268 to .269, but the expected batting average, considering who the players were, has increased from .264 to .280.   This is what I did not know when I wrote about these issues in the 1980s.   I knew that this increase had occurred, but I had no way of measuring it.

              OK, continuing with the process.    26-year-old hitters hit 10,409 triple, whereas they were expected to hit a mere 9,271, the lazy bastards.    They over-achieved in the triples category, at age 26, by 12%.    We can represent that as 112; I’m sure I don’t have to explain that.   The chart below gives these numbers for each category of our study:

 

Age	Count	G	AB	R	H	2B	3B	HR	RBI
26	4052	331943	1060892	141911	284137	48560	10409	22388	127279
26		-9543	1209	4372	4893	998	1138	528	1245
		341486	1059683	137539	279244	47562	9271	21860	126034
		97	100	103	102	102	112	102	101
	BB	SO	SB	CS	Avg	1B	EBH	TB	GIDP
	99591	139521	23473	9602	.268	202780	81357	420679	17518
	-1539	-3324	2838	1103		2230	2663	9750	-1027
	101130	142845	20635	8499	.264	200550	78694	410929	18545
	98	98	114	113	102	101	103	102	94
	HBP	IBB	RB	SAC	SF	OUTS	PA
	7621	5943	391348	15449	5456	824780	1189042
	133	165	3505	390	-234	-3452	0
	7488	5778	387843	15059	5690	828232	1189042
	102	103	101	103	96	100	100

 

              OK, now we’re getting somewhere.    We now know that 26-year-old hitters overachieve in the triples category by 12%, which we represent as 112.    But at what age does the propensity to hit triples peak, and how rapidly does it decline after that peak?

              The age at which triples peak is 21, when they are 21% higher than career norms.   From age 21 to 26 they decline at a rate of about 2% per year.   After 26 they decline by more like 4% per season:

 

Age	3B
19	97
20	110
21	121
22	118
23	117
24	115
25	112
26	112
27	105
28	103
29	100
30	95
31	90
32	85
33	84
34	80
35	74
36	76
37	66
38	66
39	60
40	59

 

              Players up to age 28 hit more triples than their career norms.   From age 30 on, they hit less.  

              Of course, you would assume that this was true, but there is a difference between knowing something generally and knowing the specifics of it.   Knowing the specifics of it, we can answer questions like "How much more rapidly do catchers lose speed (lose triples) than other players?   Do outfielders lose speed less rapidly than infielders?   Do tall players lose speed more rapidly than short players?"    This chart adds doubles and home runs to the age progression chart above:

 

Age	2B	3B	HR
19	86	97	61
20	95	110	72
21	95	121	79
22	96	118	90
23	98	117	94
24	99	115	96
25	101	112	101
26	102	112	102
27	102	105	104
28	103	103	104
29	102	100	106
30	101	95	104
31	102	90	102
32	99	85	102
33	99	84	99
34	97	80	99
35	96	74	97
36	95	76	94
37	95	66	93
38	93	66	88
39	94	60	93
40	92	59	89

 

              So we can see then that the prime ages for triples are ages 20 to 28, for doubles, 25 to 31, and for home runs, 25 to 32.    This is new knowledge for me; I did not know these things with this level of precision before doing this study.   I assume that other students of the game have probably found the same things or very similar things before, but I do a poor job of following the research of others.    Let’s add runs and RBI:

 

Age	2B	3B	HR	R	RBI
19	86	97	61	91	79
20	95	110	72	95	88
21	95	121	79	97	92
22	96	118	90	99	95
23	98	117	94	101	97
24	99	115	96	102	99
25	101	112	101	103	101
26	102	112	102	103	101
27	102	105	104	103	102
28	103	103	104	101	102
29	102	100	106	102	102
30	101	95	104	101	102
31	102	90	102	100	101
32	99	85	102	99	100
33	99	84	99	96	99
34	97	80	99	96	99
35	96	74	97	94	99
36	95	76	94	91	97
37	95	66	93	91	96
38	93	66	88	87	94
39	94	60	93	87	96
40	92	59	89	85	95

 

                           

              RBI peak two years later than runs scored, as you would expect.   But at what age would you suppose the tendency to get hit by a pitch reaches its peak?   Just pointing out to you that you do not know the answer.      Grounding into a double play increases markedly with age; stolen bases decline from an early age.   You could have guessed that.   Young players hit more sacrifice bunts; veterans hit more sacrifice flies:

 

Age	SB	CS	SB Pct	GIDP	HBP	SAC	SF
19	94	110	92	90	102	100	56
20	101	106	97	84	103	112	76
21	119	109	105	88	106	107	84
22	112	102	105	90	103	108	87
23	117	113	102	91	101	106	89
24	118	111	103	93	101	105	91
25	115	109	102	95	102	104	95
26	114	113	100	94	102	103	96
27	109	105	102	98	101	102	102
28	106	108	99	99	100	100	102
29	101	99	101	99	100	99	104
30	94	97	99	104	100	98	102
31	91	92	100	103	99	96	105
32	87	91	98	107	96	94	107
33	78	85	96	107	96	97	108
34	75	82	95	111	96	93	103
35	71	79	95	113	93	93	107
36	65	77	92	112	97	96	107
37	62	70	94	113	107	93	106
38	57	64	95	115	94	88	105
39	52	63	90	119	101	92	105
40	55	73	86	118	114	93	106

 

              I probably highlighted the wrong part of the chart for GIDP.  For some reason Hit Batsmen are a young person’s trait, in general; I did not know that and would not have guessed it.    I might speculate that less experienced players occasionally fail to read a pitch, leading to more of these relatively rare events early in a career.

              Young hitters are asked to bunt more often.    You would expect that to be true, but the increase in Sacrifice Flies as players age is very interesting.   One might expect veteran players to have more sacrifice fly opportunities because they are used in more RBI situations, but the increase in Sac Flies as players age is far too large to result from RBI opportunities.   

              Let me try to explain.    Getting a fly ball when a fly ball is needed is a subset of a clutch skill, is it not?   If you can do that, you’re a clutch player.   A traditional insider, presented with this data, would say "Of course".     Of course a veteran player knows how to get the ball in the air in a situation where a fly balls means a run.   Anyone would know that.    But 99% of the old baseball accepted wisdom of this type turns out on examination not to be true or not to be meaningfully true—such as clutch hitting in general.   I’m not surprised that veteran players exceed expected sacrifice flies by 1% or 2%; that could be explained by player usage patterns and some small skill differential.   But I am VERY surprised that they exceed expectations (relative to career norms) by 5% to 7%.     That MAY indicate a clutch ability.   It may be that, in another generation, when we have the data organized to do this study, we may find that veteran players increase their batting average in clutch situations by some small amount, which we have been previously unable to document.   This may be the largest surprise of the study.

              Double plays by 41-year-olds actually exceed expectations by 32% (132), speaking of large numbers.   There’s a big change in that category as players age.    Double plays by age increase by about 2% per year, going from 84% to 119%.    Not that this is actually huge, or HUEGHE, as the Prez sez.   A player who grounds into 10 double plays a year as a 21-year-old can expect to ground into 15 as a 40-year-old.  

              Let’s see; what haven’t I done here?   Games and At Bats:

Age	Count	G	AB
19		109	103
20		105	102
21		103	101
22		101	101
23		99	101
24		99	100
25		98	100
26		97	100
27		97	100
28		98	100
29		98	100
30		99	100
31		100	100
32		102	100
33		103	100
34		105	100
35		108	100
36		110	100
37		111	100
38		113	100
39		116	100
40		118	100

 

              What the "Games" chart shows is that both young players and old players play more partial games, whereas players in their prime play more complete games.    If a player has a low number of plate appearances per game relative to his career, that causes the number of games per plate appearance to rise, which shows up as a higher number (over 100) in this chart.   Young players pinch run and are used as defensive replacements; old players pinch hit and are pulled out of the game for rest when the score is 6-2.   The "AB" column (above) just shows the share of plate appearances which result in a charged at bat.   To show REAL variation in that column you have to add a couple of decimals:

Age	Count	G	AB
19		109	102.87
20		105	101.72
21		103	101.42
22		101	100.86
23		99	100.61
24		99	100.40
25		98	100.22
26		97	100.11
27		97	99.98
28		98	99.81
29		98	99.77
30		99	99.72
31		100	99.73
32		102	99.68
33		103	99.66
34		105	99.68
35		108	99.68
36		110	99.51
37		111	99.62
38		113	100.00
39		116	99.88
40		118	100.44

 

              That’s kind of a preview of the "walks" column (BB), so let’s get to strikeouts and walks:

Age	BB	SO
19	73	115
20	82	109
21	85	108
22	90	106
23	93	103
24	95	101
25	97	99
26	98	98
27	100	98
28	102	98
29	102	98
30	103	99
31	103	99
32	104	101
33	104	101
34	104	103
35	104	104
36	105	104
37	104	106
38	101	107
39	101	108
40	97	109

 

              Walks increase with age up to the age of 36, although the increases after the age of 24 are just about 1% per year.    Strikeouts drop when a player is in his prime (25-31), but are higher both for young players and for old. 

              Now, the rate stats.    Batting average, on base percentage and slugging percentage all basically

              1) Reach maturity (100) at age 24,

              2) Are still at 100 at age 31,

              3) Increase slightly in the middle of that range, and

              4) Decline at about 1% per year after age 31.  

              On base and slugging peak a little bit later than batting average—one year later—because walks and homers peak at 36 and 29, respectively, offsetting the declines in batting average, which actually start at age 27.  

Age	Avg	OBA	SPct	OPS
19	91	89	86	87
20	97	94	93	93
21	98	96	95	95
22	98	97	98	97
23	100	99	100	99
24	101	100	100	100
25	101	100	102	101
26	102	101	102	102
27	101	101	102	102
28	101	101	102	102
29	101	101	102	102
30	100	101	101	101
31	100	100	100	100
32	99	100	99	99
33	99	100	98	99
34	98	99	97	98
35	97	99	96	97
36	96	98	95	96
37	96	98	94	96
38	94	96	92	94
39	93	96	92	94
40	93	94	90	92

 

              Tony Conigliaro from ages 19 to 22 had OPS of .883, .850, .817 and .816.   This rather suggests that he was headed toward a career OPS of. . .what?    1.015, .911, .856 and .884, by age.   Let’s say .900 to .950, but remember also that he was doing that in the middle of a pitcher’s era (1964-1967); when they lowered the mounds and clipped the toenails of the strike zone, his OPS would likely have increased a few points.  

              The last thing I wanted to do here is present aging patterns in a visual form.   Suppose that we take a typical season for an average player, a season not extreme in any fashion.    I chose this season:

Year	G	AB	R	H	2B	3B	HR	RBI	BB	SO	SB	CS	Avg	OBA	SPct	OPS
1955	144	516	72	134	20	6	16	72	60	75	10	7	.260	.340	.407	.747

             

              I think that’s actually Willie Jones, 1955, except that I modified some columns.    To illustrate what a typically aged career path would look like, we start by multiplying each column by the age/production ratio which applies.   In other words, since 22-year-olds hit 18% more triples than their career norm, we multiply the triples norm—6—by 1.18, which makes 7, so that the player hits 7 triples at age 22.   That creates this career:

Age	Year	G	AB	R	H	2B	3B	HR	RBI	BB	SO	SB	CS	Avg	OBA	SPct	OPS
17	1943	148	535	52	118	10	6	4	54	37	103	13	3	.221	.274	.301	.575
18	1944	175	532	66	125	18	6	9	59	43	96	9	8	.235	.298	.357	.655
19	1945	157	531	65	126	17	6	10	57	44	86	9	8	.237	.301	.353	.654
20	1946	151	525	68	132	19	7	12	64	49	82	10	7	.251	.320	.382	.702
21	1947	148	523	70	133	19	7	13	66	51	81	12	8	.254	.325	.394	.719
22	1948	145	520	71	133	19	7	14	68	54	79	11	7	.256	.330	.403	.733
23	1949	142	519	73	135	20	7	15	70	56	77	12	8	.260	.336	.411	.748
24	1950	142	518	73	135	20	7	15	71	57	75	12	8	.261	.339	.414	.753
25	1951	141	517	74	136	20	7	16	72	58	74	11	8	.263	.342	.419	.761
26	1952	140	517	74	136	20	7	16	73	59	73	11	8	.264	.343	.422	.765
27	1953	140	516	74	136	20	6	17	73	60	73	11	7	.263	.343	.421	.764
28	1954	141	515	73	135	21	6	17	73	61	73	11	8	.263	.344	.420	.764
29	1955	141	515	73	135	20	6	17	74	61	73	10	7	.263	.344	.421	.765
30	1956	142	515	73	134	20	6	17	73	62	74	9	7	.260	.343	.416	.759
31	1957	144	515	72	133	20	5	16	73	62	74	9	6	.259	.342	.414	.756
32	1958	147	514	71	132	20	5	16	72	62	76	9	6	.257	.340	.409	.749
33	1959	148	514	69	132	20	5	16	72	62	76	8	6	.256	.339	.405	.744
34	1960	151	514	69	131	19	5	16	71	62	77	7	6	.254	.338	.402	.739
35	1961	155	514	67	130	19	4	16	71	62	78	7	6	.253	.335	.397	.733
36	1962	158	513	66	128	19	5	15	70	63	78	7	5	.249	.333	.392	.725
37	1963	160	514	65	128	19	4	15	69	62	79	6	5	.249	.333	.389	.722
38	1964	163	516	63	126	19	4	14	68	61	80	6	4	.244	.326	.378	.704
39	1965	167	515	63	125	19	4	15	69	61	81	5	4	.242	.325	.380	.705
40	1966	170	518	61	125	18	4	14	68	58	82	5	5	.241	.320	.373	.694
41	1967	179	515	57	121	17	4	12	64	61	88	5	5	.234	.318	.353	.671

 

              Not quite realistic in several respects, of course.   One thing that is wrong with it is that it assumes that the player has the same number of plate appearances every year from ages 17 to 41.   A more realistic version adjusts the playing time for the actual playing time of the players at that age.    In other words, those 17-year-olds who were in the majors—there were 22 of them in the study—those 17-year-olds who were in the majors played an average of only 15 games apiece, whereas the 30-year-olds in the study played an average of 94 games apiece.    The 94 is the highest average for any age, so let’s say that the 94 is equivalent to 152, and set everything else proportional to that.   This, then would be the prototypically aged career:

Age	Year	G	AB	R	H	2B	3B	HR	RBI	BB	SO	SB	CS	Avg	OBA	SPct	OPS
17	1943	24	85	8	19	2	1	1	9	6	16	2	0	.221	.274	.301	.575
18	1944	26	79	10	19	3	1	1	9	6	14	1	1	.235	.298	.357	.655
19	1945	42	142	17	34	5	2	3	15	12	23	3	2	.237	.301	.353	.654
20	1946	54	189	25	47	7	2	4	23	18	29	4	3	.251	.320	.382	.702
21	1947	75	265	36	67	10	4	6	33	26	41	6	4	.254	.325	.394	.719
22	1948	92	331	45	84	12	5	9	43	34	50	7	5	.256	.330	.403	.733
23	1949	104	379	53	99	14	5	11	51	41	56	9	6	.260	.336	.411	.748
24	1950	114	417	59	109	16	6	12	57	46	61	10	6	.261	.339	.414	.753
25	1951	127	464	67	122	18	6	14	65	52	66	10	7	.263	.342	.419	.761
26	1952	137	504	72	133	20	7	16	71	58	71	11	8	.264	.343	.422	.765
27	1953	144	528	76	139	21	6	17	75	61	75	11	8	.263	.343	.421	.764
28	1954	145	532	75	140	21	6	17	76	63	76	11	8	.263	.344	.420	.764
29	1955	150	546	78	143	22	6	18	78	65	78	11	7	.263	.344	.421	.765
30	1956	152	549	77	143	22	6	18	78	66	79	10	7	.260	.343	.416	.759
31	1957	149	532	74	138	21	6	17	75	64	77	9	7	.259	.342	.414	.756
32	1958	144	505	70	130	19	5	16	71	61	74	9	6	.257	.340	.409	.749
33	1959	141	491	66	126	19	5	15	68	59	73	7	6	.256	.339	.405	.744
34	1960	134	454	61	115	17	4	14	63	55	68	7	5	.254	.338	.402	.739
35	1961	129	426	56	108	16	4	13	59	52	65	6	5	.253	.335	.397	.733
36	1962	126	410	52	102	15	4	12	56	50	62	5	4	.249	.333	.392	.725
37	1963	121	388	49	97	14	3	11	52	47	60	5	4	.249	.333	.389	.722
38	1964	115	364	44	89	13	3	10	48	43	57	4	3	.244	.326	.378	.704
39	1965	109	338	41	82	12	2	10	45	40	53	3	3	.242	.325	.380	.705
40	1966	105	320	38	77	11	2	9	42	36	51	3	3	.241	.320	.373	.694
41	1967	94	269	30	63	9	2	6	34	32	46	3	3	.234	.318	.353	.671

 

              Actually, that still understates the effects of aging, because it still ignores the players who have dropped out of the majors.    If we adjusted for games played by all players, the 37-year-olds actually would be playing only 25 games.    But we’ve done enough of this.   Thanks for reading.