23s and 34s

NOTES TOWARD A THEORY OF AGING

This effort, if it is to succeed, will need a logical, reliable and well-researched approach to the question of aging.  This article is offered as a possible first step in that direction.

               The most troubling decision made by Dick Cramer in his pioneering 1970s research on the quality of competition over time (and between leagues) had to do with his handling of age.   Dr. Cramer, to summarize as best I can, compared the strength of the American League in 1931 to the strength of the American League in 1938 by identifying all of the players who played in both leagues, and. . .I shouldn’t say “ignoring”.  He assumed a hitter’s ability was constant without regard to age.  This approach is not as troubling as it might appear.

               Still this is, of course, not true, and there is the possibility that this assumption would mark our research as unreliable, were that assumption broadly adopted.  Cramer compared the performance of every hitter who competed in two leagues, how he did in one league as compared to the other.  To do this, he basically typed an entire Baseball Encyclopedia stroke by stroke into a 1970s computer, years before personal computers.  He league-normalized everything, I think.  When comparing the 1949 season to the 1950 season, the age issue is not a matter of concern.  The difference between a 25-year-old player and a 26-year-old is not that significant, and in a group of thousands of comparisons, it is likely that the imbalance between those which favor the earlier season and those which favor the latter did not significantly affect his conclusions.  But applied over 100 seasons, applied over leagues of all levels and with that issue mixed in with a hundred others, it could hide undetected and cause mischief.  We need a better approach.

               I had this idea, this observation.  Baseball skills, as you know, peak at age 27—almost all of them.  Defensive range probably peaks earlier, but defensive reliability and position-specific defensive skills probably peak later.  I once had a meeting with an English gentleman introduced to me as the Bill James of soccer.  I asked him at what age soccer ability peaked.  “27”, he barked, hardly waiting for me to finish the question. 

               Actually, there is not too much difference between 26 and 27. There is more difference between 27 and 28 than between 27 and 26. For this reason, I usually think of the peak age as 26 and 2/3, or 26.67. 

               The shape of a player’s CAREER, now.  Most players of some stature reach the majors at age 22 or 23, and fade away in their mid-thirties.  The exceptionally talented sometimes reach the majors at age 20, and last until they are 40.  There are small numbers of teen-agers, and small numbers of players in their 40s—small, as in usually no more than two in a season, often zero. 

               What does that suggest?   It suggests that the pace of development in baseball skills occurs at essentially twice the pace of decline or decay.  By “essentially twice”, what I really mean is “EXACTLY twice.”  It appears to be almost exactly twice.  From age 20 to peak age 26.67 is six and 2/3 years; from peak age to age 40 is exactly twice that.  The number and value of 20-year-old players is similar to that of 40-year-olds. The number and value of 21-year-old players is similar to that of 38-year-olds.   The number and value of 22-year-old players is similar to that of 36-year-olds, followed by 23s and 34s, 24s and 32s, 25s and 30s, and 26s and 28s. The number and value of 23-year-old players is similar to that of 34-year-olds. The number and value of 19-year-olds is similar to that of 42-year-olds. 

               In fact, even if you get outside the range of athletic accomplishment, is there not a similar structure building a roof above all of us?   A new-born baby is 26.67 years from peak age; an 80-year old is twice that distance,  nearing the far end zone of a life. It is as if we are walking up the side of a mountain which is 26.67 miles high, but after we reach the peak the down side is exactly one-half as steep as the ascent was—individual variance, but exactly one-half, on average.

               The process of aging seems quite complex.  Suppose that we simplify the cradle-to-grave journey as a battle between development and decay, or between potential and refinement; no two terms quite capture the underlying concepts.  The things which are gained over time (skills and wisdom) are not the same as the things which are lost, and for this reason age peak attainment is quite different in different endeavors.  A writer or an artist or a politician does not peak at the same age as a sprinter or a gymnast.  Ages 15 and 50 are assumed to be at the same altitude, but having an affair with a 50-year-old woman is not at all the same as having an affair with a 15-year-old.  Some traits peak at a very early age and decline rapidly; others are acquired later and may not decline at all before age 80.  Roger Angell could still write brilliantly when he was 100. 

               I am suggesting that despite these differences, there may be some very simple rules which give shape to the balance.  There is a 2-to-1 ratio operating throughout.  Wisdom, experience and skills develop at twice the pace that the life force ebbs.  In baseball, in other sports perhaps, WES (wisdom, experience and skills) do not cease to develop, do not cease to increase, after age 27.  Rather, in sports the valuable application of WES relies upon things like balance, reflex response, motor skills and recovery speed, all of which are declining.  Accomplishment in sports is a product of the combination.  Like this: 

               Those numbers don’t EXACTLY work.  Actually, I have never been able to find the numbers that do exactly work.  Hundreds of failed attempts over a period of years.   The numbers that exactly work for our purpose

(a)    Would show 20 as more or less even to age 40,

(b)    Would show 27 as the peak,

(c)    Would show 26 as closer to 27 than age 28, and

(d)    Would show 21 as more or less even to age 38, would show 22 as more or less even to 36, would show 23 as more or less even to 34, etc. 

I’ve never been able to make it work.  Somebody reading this will glance at that problem and say “Oh, that’s easy”, and make it work in five minutes; I am sure of it.  (This issue is addressed in greater detail in the article “The Elements of Athletic Aging”, also on this site.)

               My working theory assumes that a player will perform about the same relative to his peak at age 23 as he will at age 34, that he will perform on average about the same at age 24 as he did at age 32, 22 and 36, 25 and 30, 21 and 38.  This theory is what you could call “true”.  Those relationships do in fact hold; they do in fact predict aggregate performance.  I’ll show you pages and pages of charts later on.

               The complication, which I wrote about at length in the 1982 Baseball Abstract, is that if you look at the offensive performance of ALL players, it hardly changes at all with age.  35-year-old players hit just as well in the aggregate as do 27-year-old players. 

               The reasons that is true are (1) the replacement level, and (2) the shifting composition of the population being studied.  Suppose that a player creates 6.0 runs per 27 outs and has an .800 OPS at age 27,

5.8 and .785 at age 28,

5.6  and .770 at age 29,

5.4 and .755 at age 30,

5.2 and .740 at age 31,

5.0 and .725 at age 32.  

What happens to him at age 33?

               What happens to him at age 33 is that he disappears from the data.  He loses his job; he is released, he is just not there anymore, so he has no further impact on the data.  

               Aggregate data is complicated by two other issues.  First, real players do not go from .800 OPS to .785 to .770 to .755 to .740 to .725.  Real players go from .815 to .728 to .863 to .754 to .731 to .606.   Real life is messy.  And second, the replacement level INCREASES as players age.  As players’ OPS slips a few points a year, they also are being forced to the left on the defensive spectrum.  Third basemen become first basemen.  The OPS expected of a first baseman is 35, 40 points higher than that of a first baseman.   That moves the player 35 or 40 points closer to the replacement level.  Even if there is no position move, the OPS expected of a GOOD defensive third baseman is less than what is expected of a third baseman who has lost a step. 

               As players move into their 30s, only the best are able to hold on to their jobs.  If you compare 35-year-olds to 27-year-olds, all the yannigans have been driven out of the data sample.   The combination of these factors causes AGGREGATE hitting numbers to remain the same while players age, even though each INDIVIDUAL hitter is declining.  Every hitter is declining individually, yet the average does not decline. 

Explaining now my own research

               My theory was that if you focused on a constant group of hitters, so that you didn’t have new players dropping into the group and older players dropping out, they would hit about the same at age 23 as they did at age 34, about the same 22 as at 36, about the same at 25 as at 30.  

               I studied all relevant groups, but let’s start with the 23s and 34s.  I identified all position players who were in the majors at age 23, and also at age 34.  Notes:

1)   This study was done in August, 2024, so there are no players who were aged 34 or in 2024 or 2025 in the study, and

2)   To qualify for the study, a player had to have 1000 major league plate appearances at in the three-year period ages 22 to 24, and 1000 major league plate appearances in the three-year period ages 33 to 35. 

If I included in the study players who were regulars at age 23 and had 2 at bats on the way out the door at age 34, that would introduce into the study the problem of the shifting population base.  I wanted to determine whether players who were healthy and established in the majors at age 23 were equal as hitters to themselves at age 34, without the study being contaminated by players at inherently un-equal stages of development or decline.  (Players who would or might be included in the study if it were done post-2025 include Freddie Freeman, Salvador Perez, Anthony Rizzo, Giancarlo Stanton, Nolan Arenado and Marcell Ozuna.) 

Some players who are absolutely brilliant at age 23 have been driven to the bench or driven entirely out of the game by age 34.  At age 23 Jimmie Foxx, Ben Chapman, Hal Trosky, Joe Medwick, Harland Clift, Charlie Keller, Duke Snider, Johnny Callison, Cesar Cedeno, Jeff Burroughs, Ruben Sierra, Juan Gonzalez, Nomar Garciaparra, Andruw Jones, Hank Blalock, Eric Chavez, Grady Sizemore, Prince Fielder and David Wright were brilliant players, MVP candidates every one.   By age 34 many of them were out of the game entirely, the others hanging on and getting into a game now and then.  I didn’t want to study careers after they had been shredded by injury. 

               No one was arbitrarily excluded from the study.   Every player in baseball history through 2023 who had 1000 plate appearances at ages 22-24 and 1000 at ages 33-35 was included. The three-year sample was used only to determine eligibility for the study.  Once the player was included, what was compared was only aged 23 as opposed to 34, not 22-24 as opposed to 33-35. 

               A certain number of those included were greatly diminished by injury by the age of 34, but were still in the lineup on a fairly regular basis.   Mickey Mantle, Joe Torre, Dick Allen,  Fred Lynn, Don Mattingly, Ken Griffey Jr. and Joe Mauer would be examples of that.  If you’re still in the lineup, you’re still in the study group.  

               Some players had faded badly by age 34, but on the other hand, some stars had not really come into themselves yet by age 23.  Examples of that would be Rogers Hornsby,  Yogi Berra, Ernie Banks, Roberto Clemente, Lou Brock, Joe Morgan, Mike Schmidt, Dave Winfield, Dale Murphy, Tony Gwynn, Barry Bonds, Larry Walker, Jimmie Rollins and Yadier Molina.  That is my exact theory:  that it should balance.  My premise is that since ages 23 and 34 are at the same altitude, the same distance from the peak age of 26.67, remembering that the acceleration phase is twice as powerful as the decline phase, then the number of players who are in the lineup at age 23 but not yet at full strength should almost exactly balance those who are still in the lineup at age 34 but no longer at full strength.  That is my thesis, and the data I will give you will show that this is true.  The decline phase is an almost exact mirror of the development stage, only proceeding at half the speed. 

26s and 28s

               In this study (data through 2023) there are 1,538 players who qualified for inclusion at age 26 and also qualified for inclusion at age 28. 

               This is, in a sense, a count of all the position players in baseball history who were good enough to claim a regular position and hold it for three years.  Of course it is not ALL of them; there would also be (a) players from 2024-2025, (b) players whose service was interrupted at their prime by World War II, (c) black or latin players from before Jackie Robinson, (d) players whose careers got off to an unusually slow start for one reason or another, and (e) unusual cases.  It’s not 1,538 players; it is probably 1,700 or 2,000 or something.   

               My point is, this is the neighborhood where most of the regular players live.  This is the suburb where you will find their swimming pools.  When we get to 25s and 30s, there will be fewer players, at 24 and 32, still fewer, at 23 and 34, still fewer, and at 19 and 42, finally, none.   There are three position players in baseball history who played in the majors at ages 19 and 42—Eddie Collins, Rick Dempsey and Tim Raines.  But none of the three remotely approached the 1,000-PA standard for either age.

               As the number gets less, the quality gets steadily higher.   25s and 30s are players who were good enough to hold a regular position for six years.  24s and 32s are players who held a regular position for nine seasons.  Of the 1,538 players in THIS group (26s and 28s), I think 151 are now in the Hall of Fame, which is less than 10%.  As the group narrows by requiring longer careers, this will increase to almost 100%.

               The immediate issue is comparative performance; how did these players HIT at age 26, as compared to age 28?

               836,000 plate appearances at age 26, 818,000 at age 28.  I would be most pleased to report here that there was no discernable increase OR decrease between ages 26 and 28 in the overall productivity of a constant group of hitters.  Saying that would be the strongest affirmation of my general thesis, but actually it is not true.  Their overall productivity was extremely similar, of course, but actually the players were a little bit better at age 26 than at age 28, because of larger-than-expected performance declines in the speed-related categories.  Here are the average season statistics for each group:

As a group, the 1,538 players had a 2% decrease in games and plate appearances.  A 3-point drop in batting average is essentially offset by a small increase in the walk rate, and home runs per plate appearance actually increased a little bit, but the only really meaningful changes are:

1.       A 9% decrease in stolen bases (from 13.26 to 12.01),

2.       15% decrease in triples (from 5.30 to 4.49), and

3.       A 6.1% increase in GIDP per at bat.

Of course the two batting lines above are highly similar; I just expected them to be closer than they are.   The next two little sections are just mandatory reporting of details; the meat of the report is in “23s and 34s”.

25s and 30s

               25-year-old players are predicted to be 1.67 years from their absolute peak, 30 year-olds are 3.33 years from their absolute peak, but going down the other side of the mountain.

               There are 1,016 players in the data who qualified for the study at age 25 and at age 30.  These are good players, not all great.  25% of them had 2,000 career hits.    About 15% are Hall of Famers, but Daniel Descalso is in there, and Chris Coghlan. 

               The aggregate data for 25s and 30s will look a great deal like the aggregate data for the 26s and 28s, with slightly larger divergences, but there is a critical difference hiding inside.

Essentially the same chart we saw before.   Triples are now down 23%, stolen bases down 19%.

24s and 32s

               There are 578 players who qualified for the study at both age 24 and age 32.  43% of them had at least 2,000 career hits, and 29 had 3,000, whereas there were only 6 players included who had less than 1,000.  Just a hair short of 25% are in the Hall of Fame (141/578). 

               Between ages 24 and 32 there is a 36% decline in triples, 29% in stolen bases, combined with a 16% increase in GIDP (20% per plate appearance.)   These losses are offset by increases in walks and homers, which you can’t see below because 13+ and 13- both round off to 13:

But essentially, these players (as a group) are the same at age 32 as they were at age 24. 

23s and 34s

          By now we are dealing with players who were regulars (most of them) for 12 years, from 3 or 4 years before their peak to 7-8 years after.  We’re dealing with long-term regulars, and long-term regulars are the best evidence we have about the aging curve.  There are 250 qualifying players in the data for this set of ages.  Two-thirds of them had at least 2,000 career hits, 28 of them had 3,000.   42% are in the Hall of Fame.  Here is the average performance for these players at age 23, and at age 34:

               These numbers creeping up a little bit.  The OPS(es) at 26/28 are .774 and .769; now they are .795 and .794.  Still a lot the same in that way.   But the point is not really that they are the same at these two ages.  The point is that they are different if you look at OTHER ages.  This chart gives the record of the same group of hitters at all of the ages from 23 to 34.

               The point is not really that these hitters have essentially the same OPS at 23 as at 34, or the same at 25 and 30, or the same at 26 and 28.  The point is that is ONLY true at those particular stations in life.   23 and 34, the OPS is .795 and .794.  You won’t see the pathway between those two if you don’t control the group.  If new players enter and drop out of the group every year, that will flatten the numbers out so that 26 looks about the same as 40.  If you compare the fixed group of hitters at ages 23 and 27, you can see that they are meaningfully different, 40 points difference in OPS.  They are the same at ages 23 and 34 because 23 and 34 are the same elevation in a player’s career. 

               I should make sure that everyone understands that these are not players whose first eligible season was at age 23 and whose last eligible season was at 34.  Many or most of these players were regulars at either age 22 or 35, or both.  If we focused only on players who who started at 23 and ended at 34, their end-point OPS wouldn’t be .795 or .794, as it is here; it would be more like .785. 

               Of the 250 players, 116 had better seasons at age 23 than at age 34; 134 had better seasons at age 34.  Willie Mays was the MVP at both ages.  Lou Whitaker, Johnny Damon and Vlad Guerrero were far better at 34 than at 23; Ron Santo, Ed Yost and Edgar Renteria were far better at 23 than at 34.  Among long-term regulars, it evens out.  23 balances with 34.  It won’t balance with 32, 33, 35 or 36.  It balances with 34. 

22s and 36s

               After we get past 23 and 34, the data starts to thin out to the point at which statistical reliability becomes an issue.  There are only 85 players who qualified for the study at ages 22 and 36.  They follow the general rule; they have a .788 OPS at age 22 and .792 at 36.

               80 of the 85 players in this group had 2,000 career hits.   53 of the 85 are in the Hall of Fame, and the Hall of Fame count doesn’t include Pete Rose, Barry Bonds, A-Rod, Albert Pujols, Carlos Beltran or Yadier Molina.  But the fact that the data thins out so much here is what makes 23 and 34 the best group for closer examination.  250 players is a reasonable study group.   85 is a little too small.

21s and 38s

               There are only 28 players who qualified for the study at those two ages.   All had 2,000+ hits; all except two had 2,500+.

20s and 40s

               The only three players in history who had 1,000 plate appearances at ages 19-21 AND at ages 39-41 are Ty Cobb, Ted Williams and Hank Aaron. 

Counting the Regulars

               Suppose that we say that any player who has 500 plate appearances in a season is a “regular”.  In our approach 18 balances with 44.  There is one player in baseball history who had 500 PA at age 18 and one who got 500 at age 44.  That’s trivial, but it does balance.

               In major league history there have been 10 players who got 500 PA at age 19.  There have been 56 players who got 500 PA at age 20.  This is the full chart, by age:

18 against 44 DOES balance, one each, so that is zero error.   

At age 19 there are 10 players; at age 42 there are only 6, so that’s an error of 4. 

At age 20 there have been 56 regulars; at age 40 there have been only 30, so that’s an error of 26. 

At age 21 there have been 181 regulars; at age 38 there have been only 88, so that’s an error of 93.

Marking it all out and eliminating the non-relevant lines:

The total error for the eight suggested matches is 698 out of a potential 4825, so that’s a 14.5% error.  But that’s just playing time.  Let’s count seasons of significant accomplishment, such as driving in 100 runs.  Six players in history have driven in 100 runs at age 20, 22 at age 21, 45 at age 22, 78 at age 23:

               Predicting that the number of players driving in 100 runs at age 34 would be the same as age 23, 32 the same as 24, etc., the net error of the predictions is only 20 out of a potential 617, or 3%.  

               That’s just 100-RBI seasons.  Let’s extend it to include:

200-Hit Seasons

Seasons hitting .300

Seasons with a .400 On Base Percentage

Seasons with a .500 Slugging Percentage, and

Seasons drawing 100 walks.

               The counts of .300 seasons, etc., are all based on 400 plate appearances, whereas before I used 500.  Sorry; I just didn’t stop to plan all of that out.

               Now let’s figure the Net Error of the prediction, as we did before:

Age	Total
19	6
20	58
21	132
22	304
23	478
24	741
25	952
26	1139
28	1123	16
30	1045	-93
32	736	5
34	447	31
36	228	76
38	80	52
40	26	32
42	6	0
44	2	-2
Net Error		117
Base		3810

Again, a net error of 3%.

Conclusion

               In order to make the Cramer Levels Project work, we will have to have a “standard age adjustment”, so that if a player has a .778 OPS at his peak age and a .729 OPS ten years later, we can say with confidence how much of that change is attributable to normal aging.  This seemed to me like an interesting and potentially useful observation about the normal course of aging over a long span of years, and I thought I should work it through to its end.  I hope you found the observation of some use.   This research is referenced again in “The Elements of Athletic Aging.”

 Thank you for reading.