"He just needs another year."

If you cheer for a team that didn't quite perform up to expectations this year (and even if you cheer for a team headed to the playoffs), you've got a guy or two like this on your team. He has so much promise; it's just that he hasn't quite fulfilled it. You rationalize it by saying that he's young—well, young-ish. He just needs time.

Every year, there are a handful of guys who take that big step into stardom that we'd all assumed they would for years. After a few seasons of growing pains, Alex Gordon quietly went from disappointing prospect to a very-good-but-not-great player. It’s the tantalizing prospect of another Alex Gordon that makes some fans (and teams) hold on and hope. And a lot of times, it doesn't happen.

But when should a fan or a team give up hope for further development?

Warning! Gory Mathematical Details Ahead!
One problem with studying player development over time is that baseball presents us with a horribly biased sample. For the most part, we see only the success stories. Players who aren't developing well are often jettisoned, either to the minors or the waiver wire. Some players start with minimal skill but develop to the point where by age 27, they are fringe major leaguers. The problem is that charting their developmental course involves the shady world of "translating" minor-league statistics.

But we will make do. I isolated a group of players who had at least 100 MLB plate appearances in each season from their age 24-season through their age-31 season. I searched between 1993 and 2011, leaving me with a sample of 168 players. This adds another layer of selectivity. We know that players who debut earlier (at age 24, for instance) tend to peak a little later than their peers. This is in addition to the fact that these players were apparently developing well enough to keep a steady job over the years.

I calculated a bunch of basic stats for each player season (K/PA, BB/PA, HR/PA, OBP). Nothing incredibly inventive here. For each stat, I ran correlations from year-to-year. In other words, I ran a correlation between the age-24 seasons in the data set with the age-25 season, age 25 with 26, age 26 with 27, and so on.

There weren't any surprises in terms of stats that we once thought to be reliable suddenly becoming unreliable. What surprised me was the pattern that formed. Here are the year-to-year coefficients for OBP. Everything else that I ran had the same basic pattern.

















Notice that jump from the 25-26 correlation to 26-27? And then the drop in correlation from 28-29 to 29-30. That appeared everywhere. If you have a bad (or good) year at age 24 or 25, there's a better chance that your next season will be different than there is at age 26. At that point, things become a little more set in stone. At 29, it looks like things get a little more unstable again. My guess is that some guys start to drop off at 30, while others hold their value.

It's a simple finding, but I think it has some interesting implications for the issue of peak age. We know that certain types of players peak later and last longer based on when they debut, but I think these analyses point to a slightly different interpretation of the question. Aside from the "everyone's different and some guys are just late bloomers" argument, I think we need a slightly different conceptualization of peak age. I'd argue that instead of expecting a nice steady improvement to age 27 or so, we need to think more about a critical period of development.

To use a real-world (because baseball is a fake world) example, it is widely known that children are much quicker to learn a foreign language than are adults. For example, my wife came to the United States when she was 10. She speaks better English than I do. Her parents speak English just fine, but there are times when they have to stop and talk over a phrase in their native Russian. Developmentally, it seems that the cutoff age is about 12. Before 12, you're more likely to be able to pick up the skill. After 12, not so much.

It looks like a critical period for player development ends around 26. So, if your favorite player hasn't figured it out by then, chances are that he won't.

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Really? You guys haven't figured this out yet? Don't your PECOTA projections use age?
Any findings relating to the hypothesis that RH power batters develop later than LH batters or RH non-power batters?
I read the headline and thought..."Brandon Moss".
This is an interesting way to look at the development curve (correlations from one age to the next). I like it.

At the same time, don't these results mimic the standard aging curve, whereby there is a steep upward curve to around age 26, then a plateau (with a slight downward slope) until age 29 and then a fairly steep downward curve?

If we assume that every player has a similar curve only it shifts right or left, then we would expect the same correlations that you get.
The standard cutoff points seem to fit, but I think interpreting it as a validation of the standard peak model falls short. The last sentence that you write is the one that gives me the most trouble.

A nice, smooth, uniform, upward curve/line would have a high correlation coefficient running through it year-to-year. Straight lines have a correlation of 1.0, after all. These numbers tell me that we need to view 24-26 as more of a chaotic, malleable period. Some will take bigger jumps than others. Some will fall. At 26 though, the chaos stablizes. At 29, some start to decline, while others hold.

I think that we need to get away from the assumption that everyone follows the same curve (up, plateau, down) and embrace player development for the much more chaotic process that it is.
It's interesting that you mention Alex Gordon as a breakout player, since his 2012 hitting is almost identical to his 2008. The difference in WARP value is almost entirely in defense. Between those years of course he had two fairly horrible, injury-plagued years, and one excellent one, and those color the perceptions. We don't usually think about it like this, but the weaker correlations for young players could go both ways -- does that mean that large declines in performance (injury-related or otherwise) are more likely for younger players than those at their peaks?

Also, did you try looking at the correlations by year of experience instead of age? I'd guess that there's a similar shape since age+experience overlap to an extent, but differences might be enlightening, especially for players way ahead of or behind the curve.

(If it wasn't obvious, I'm thinking about Justin Upton as I make these inquiries. And at all times in general)

Of course I write that then refresh and see your reply to MGL, so I guess that addresses my first question!
I'd be curious to see how the players' ages and methods of entering pro-ball impact the chart, if at all. If it's indeed a particular age range where a player's most malleable, I wouldn't expect a huge difference between groupings, whereas if it's more a product of a point on a learning curve based on training, I'd expect there to be a more noticeable difference, for example, between players signed as 20+ year-olds out of college and 16 year-olds signed out of Latin America.
Dr. Carleton: I don’t quite see how your 2010 write-up shows that players who debut early "peak a little later". It did show that among players who are still in the Majors after age 31 – the earlier starters of that group tend to have later peaks. However, among those who bow out of the Majors before then – the earlier debuts tended to peak earlier. Don’t those two groups pretty well flatten the aggregate findings among all players?