Breaking Down The Aging Curve

Ever since I read Jeff Zimmerman’s aging curve article in December I have been thinking more about aging curves in general.  That has lead me to take a step back and start digging through players in a different way.  Jeff gave a couple of plausible reasons for the difference in aging curve, teams are developing players better prior to appearing in the majors and that they are doing a better job of identifying when they are ready.  I’ll throw another out there before I start this.  MLB has gotten younger recently and to do that you need to be pulling in more young players.  In general you would expect players first pulled up at each age point are in the farthest region of the right tail of the talent distribution and then you move left as you add more players from that group.  Maybe a larger percentage of the younger players being brought up just are not as good and won’t ever thrive at the big league level.  Anyway, let’s get to what I have started working on to see if breaking things apart can shed any light on the subject.

To start I pulled every position player year for rookies in the expansion era (after 1960) and ended up with 2,054 players and 11,585 player seasons including active players not just completed careers.  Then I broke players into age cohorts with when they played their first season with at least 300 plate appearances which I will refer to as full seasons the rest of the way.  I will be working through to see if players age differently based on what age they reach the majors and get regular playing time.  To do this I will mostly be looking at percent of peak wRC+ and WAR.  For this post I am only doing the first couple of cohorts and then I will work through more in the coming weeks.

The first cohort I broke down was the age 19 group.  Only one player amassed the 300 plate appearances necessary at age 18, Robin Yount, so there is not much to learn there except that if you can hack it at the big leagues when you are 18 you are probably really, really good.  That will be true for the 19 and 20 year-olds as well, but there are more of them.  The age 19 cohort is also small with only 8 players; Ken Griffey Jr., Edgar Renteria, Bryce Harper, Cesar Cedeno, Tony Conigliaro, Ed Kranepool, Jose Oquendo, and Rusty Staub.  This will be the only cohort small enough that I will list everybody.  Interestingly the age 20 cohort has a lot more star power as Griffey is the only Hall of Famer (I know he isn’t in yet, but he will be on the first ballot).

Of the seven 19 year-olds that have retired, the average number of full seasons played is almost 13, so they did have long careers as you would expect.    None of the players peaked in wRC+ or WAR in their first full season, which is not surprising.  The more seasons you are in the majors, the lower the probability that the first season will be the best one just because you have more opportunities to best it.  Harper actually put up a better wRC+ in year 2, though his rookie WAR was better and this year isn’t looking like a new high for him so far.  If you take their average percent of peak at each age and chart it this is what you get:
 photo 19percentofmaxchart_zps8c04fc32.jpg
The sample size here is so small I wouldn’t want to believe it too much, but we might see some improvement for this cohort early in their careers.  The peak, if there is one, looks like 25 to about 27 especially in WAR.  Then it is all decline.  Again, these are players from the ERA that showed this before, not from players in the last 10 years that are not showing improvement in Jeff’s article.

Let’s move on to a bigger group and see what happens.  The age 20 cohort includes 37 players with 10 current players.  There are Hall of Fame or near HoF players all over.  Rickey Henderson, Roberto Alomar, Ivan Rodriguez, and Johnny Bench are in along with Alex Rodriguez, Joe Torre, Andruw Jones, Gary Sheffield, Alan Trammel, Adrian Beltre, and Miguel Cabrera.  Mike Trout  is the only young guy I would assume has to eventually make it, but there are a couple others there that might eventually be that good too.  In my opinion, about a third of this group are HoF caliber or will be after their career is done.  That is 1 out of every 3 players that stick in the bigs at age 20 will be good enough to make it to Cooperstown.  Way better than the 19 year olds.  The average career length for those that are not active was over 11 years, so again most should not max out in their first year.

Only three players had their best hitting season as a rookie, but it was because all three of them had their only 300+ plate appearance season at age 20 so it was the only season in the sample.  Danny Ainge was one of the three though, so we could go see when his basketball career peaked instead maybe.  All three therefore also had their best WAR season at 20, but there was a fourth player who had his max WAR in that first full season, Claudell Washington.  Washington had 14 full seasons as a major leaguer and his best by WAR was year 1, and he had only one wRC+ better than that first year.  If we look at the chart for the age 20 cohort chart it looks way different than the 19 cohort.
 photo 20percentofmaxchart_zpse95fa760.jpg
Again, this is not a large sample, and it is overwhelmed by extremely good players.  There seems to be an increase in the first couple of seasons followed by a long, flat peak that for wRC+ goes all the way into their early 30s.  WAR is more volatile and might start declining a couple of years sooner.

I expect that this will get more informative as we get into more normal players and larger samples, but it is fun to look at elite players.  I’ll break down a couple of more age groups in the near future, and eventually try and build a regressed model for the bigger cohorts to control for the era and some of the other effects that aren’t rolled into wRC+ or WAR.

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Leo Martinic

Brian, how did you insert the graphs/visuals into the article?

Leo Martinic

Thanks a lot Brian. Good work on the article.