Aging curves for phenoms

We are lucky enough to live in what feels like a golden age for young major-league talent, particularly position players. Mike Trout (23) and Bryce Harper (22) are the gold standard, but things get especially incredible when you consider the players forced into the second-tier by Trout and Harper's incredible standard -- names like Giancarlo Stanton (25), or Manny Machado (22). Steven Martano wrote this article laying out an absolutely terrifying lineup using only 25-and-under players, emphasizing just how many great, young players there are in MLB today. Something that's often brought up is where these wunderkinds gain their advantage. The easy answer is "just about everywhere", but for many, they're clearly physically advanced -- bigger, stronger, and more coordinated than their age-group peers.

For most 19- or 20-year-olds, a fan looks at them and projects them for some amount of growth and improvement over the next two to five years, but that was never really the case for Harper or Trout, who seemed to be finished products (physically) by their late teens. Where other 19-year-olds can be expected to improve, how much improvement can be expected from some of the best players in baseball?

Readers are probably familiar with aging curves, which aim to quantify the change in production for the average player as he ages. The most common technique used to construct an aging curve is known as the delta method, in which the analyst looks at every player's performance between one season and the next, puts the difference in performance into age buckets (e.g., plus-.040 OBP between 23 and 24, or plus-.5 percent K rate between 35 and 36), and then combines those differences across players to get the observed change as a player ages. Over at The Hardball Times in 2009, Mitchel Lichtman wrote a two-part series (part 1 and part 2) that went into great detail on the whole process, and it's great if you're looking to make an aging curve of your own or just understand the process better.

If you look at the THT article, you can see an aging curve for linear batting weights, constructed using data from 1950 through 2008, with hitters generally improving from 21 through 26, plateauing for several years, then declining from age 29 on. While research has shown a potential shift in recent years, with production beginning to decline closer to 25 or 26, this is the generally accepted average pattern.

There are certainly deviations from that basic curve, however. Some skillsets and body types appear to age better than others -- this article at FanGraphs presents a Jeff Zimmerman aging curve that shows heavy players peaking earlier and declining faster than the pool of players as a whole. Could Trout, Harper, and other excellent young players also deviate from the standard aging curve in a predictable way? It's possible that they have shifted their performance "up", so to speak, and simply have a higher starting point than their peers, and would still be expected to improve until their mid-20s. Alternately, it's possible they've shifted "horizontally" along the aging curve, and have developed faster than their peers, such that they would see their performance change from year to year like a player 2-5 years older might. Both scenarios seem at least plausible; what does the data show?

I set out to create two different aging curves, one for phenoms like Trout and Harper and one for the rest of MLB. I decided to limit myself to the post-expansion era (1961-2014), to avoid the most sudden shifts that happened to baseball in the 20th century. Step one was to define a "phenom", and I used Baseball Reference's Play Index to find any player who had garnered 8 or more WAR through his age-22 season. (That's bWAR; for the rest of the piece, I use fWAR.) This is a necessarily arbitrary dividing line, but it captures the type of player I'm looking for, who was already producing value at an above-average rate before most players debut. The full list is here, and for the most part, it looks like I would want it to, with names like Trout, Harper, and Stanton, as well as Alex Rodriguez, Ken Griffey Jr., Rickey Henderson, and more. Some look a little out-of-place in hindsight, and might not have the career numbers of the others -- Carl Crawford and Elvis Andrus are mostly seen as disappointments now, and everyone knows the tragic trajectory Tony Conigliaro's career took after his age-22 season in 1967 -- but overall, this is a list of players who generated substantial excitement among fans as they entered their mid-twenties, which is exactly the point. This is still a tiny sample to construct an aging curve with, but it will hopefully illuminate at least some general trends.

I decided to look at how two stats changed as the phenoms and non-phenoms aged, wRC+ and WAR/600. For every player, the difference between each of their seasons was calculated, weighted by the harmonic mean of their PAs in both season, and combined with the difference of every other player's change in performance at the same age.

First, the non-phenoms. I started with their age-23 season, since a) that's the age where I'm beginning to look for differences in performance, and b) many of them didn't play much or at all when they were younger than 23. Here's a table with the number of qualifying players for each age bucket.

As you can see, things get a little thin as players get older, but overall we have a very robust sample. What does the aging curve end up looking like, for wRC+ and WAR/600?

Basically as expected, with some improvement in the early 20s, a peak at age-26, and a decline from 27 onward, accelerating around age-30. The improvement is fairly muted, which suggests that for players above 22, even those making their debut in the majors (*cough* Kris Bryant *cough*), expecting substantial improvement in future seasons is probably optimistic.

What about the phenoms? First, here's the table with the sample size for each.

Three players in the phenom group had PAs in both their age-18 and age-19 season (Alex Rodriguez, Robin Yount, and Ted Simmons), which is not really enough to draw any conclusions, so I'm going to start the curves at the phenoms' age-19 season. Do they look any different?

With the much smaller sample sizes, the curves are substantially more erratic, but the same general pattern appears to be in place. Both curves peak at 25, rather than 26, but given the fluctuations it's not clear the peak wouldn't be anywhere from 24 to 27 if the sample size was 3,000 players instead of 30. Interestingly, they appear to decline somewhat more gradually than the non-phenoms; for ease of comparision, here are the charts with the non-phenoms in red and the phenoms in blue.

Indeed, it looks like my hypothesis that phenoms might have the physical traits of a 24-year-old at age-21 or -22 and would therefore stop improving sooner or decline earlier has no evidence to back it up. Again, there is substantial volatility in the phenom curve, so it's best to focus on the general trend rather than individual data points (like the inexplicable decline for phenoms at 26 and 27), but it seems clear that in these samples, the phenoms have a longer plateau than the non-phenoms. Their WAR/600 doesn't begin to decline until their age-29 season, as opposed to age-27 for the non-phenoms, and their wRC+ stays almost at peak from age-25 through age-31, compared to the single-year peak at age-26 for the non-phenoms. It appears that not only are these players great earlier than their peers, they remain great longer than their peers. They're great players! Maybe this shouldn't be a huge shock, but seeing the data laid out is always useful.

Finally, it's important to remember that aging curves are designed to describe the characteristics of the population in question as a whole, and trying to apply them directly to individual players without considering their specific traits is not a good idea. If scouting or detailed analysis suggests a 24-year-old is due for a big leap forward, trust that over the aging curve. But when considering general trends among players like Trout or Harper, who were great before they could legally drink alcohol or rent a car surcharge-free, don't think they're going to decline before their peers as a result. They tend to just be great players, and this research suggests they'll continue to be great for a very long time.

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Henry Druschel is a Contributor at Beyond the Box Score. You can follow him on Twitter at @henrydruschel.