How do prodigies age?

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These cats are a visual representation of me gazing through the window as snowfall mounts. What separates us, however, is that while these cats are likely contemplating whatever it is that cats contemplate during a blizzard, I am trying to talk myself into a false sense of hope.

“It’s going to happen*,” I say. “The Cardinals are going to get Harper or Machado.”

It almost makes too much sense. St. Louis’ payroll flexibility. The ability to upgrade a corner outfield or left infield spot overnight. The prospect of elusive consolidated value you’ve heard us blabber on about at VEB for several years on end.

*It’s probably not going to happen.

Talented free agents aren’t unheard of, but with the recent spike in pre-or-early-arbitration contract extensions, fewer premier players are hitting the open market. Furthermore, circumventing MLB’s service time system often allows teams to seize what essentially amounts to seven years of team control as opposed to six ascribed by the rulebook. That is what makes this free agent class so remarkable: it features not one but two 26-year-olds with track records and projections rivaling virtually anyone in baseball.

The underlying assumption made here is that while past free agents like Albert Pujols, for example, were already on the wrong side of 30 as teams were bidding for post-prime production, the same can’t be said for younger options like Harper and Machado, who are currently in what is considered the peak age for position players.

I wanted to test if the “phenoms” that burst onto the scene at an exceptionally young age (Harper and Machado debuted in the big leagues at 19 and 20, respectively) progressed through their careers any differently. I compiled data from every position player season (minimum 300 plate appearances) since 1988, and isolated those from hitters 21 years or younger. That comes with one caveat: I excluded any 21-and-under seasons with a negative wins above replacement total to filter out any players who were evidently overmatched and/or played for bottom-feeding teams that were willing to sacrifice wins for the sake of prospect development and MLB exposure (i.e. these weren’t necessarily prodigies that forced their way up the pipeline through raw talent alone).

From there, I calculated year-to-year changes in various prorated statistical benchmarks (fWAR/600 plate appearances, wRC+, etc.) and found the average among players within each age bracket. The graph below plots cumulative WAR for these average aging curves. For example, Matt Carpenter’s fWAR/600 went from 2.6 in 2012 to 6.0 in 2013 back down to 2.9 in 2014, resulting in a cumulative WAR of 0.3 relative to where he began.

The first thing we notice with incredibly high R² values of 97.7% and 99.2%, respectively, is that a simple polynomial equation correlates strongly with these aging curves. The surging phenoms (denoted in blue above) tend to have more productive peaks than their counterparts, but are even more so a shell of their former selves after reaching 30. Let’s also delve a little deeper into the numbers by breaking this value down into hitting (wRC+), fielding (FanGraphs’ fielding runs/150 games), and positional adjustment (to account for the fact that an average defensive catcher is more valuable than an average defensive first baseman) runs.

On all three of these polynomial trendlines as well, the phenoms appear to deteriorate more over time than everybody else. Why exactly is that? Does the longer and more intense MLB schedule take a greater physical toll on the younger stars than their still minor league peers? Or, perhaps, there is a flaw in analyzing aging curves using this methodology. Take a look not at the WAR/600 numbers as they change from year-to-year, but the raw numbers, where 4.0 fWAR is counted as four wins regardless of how that player performed the previous season.

The phenoms are more impressive both in the early stages and heights of their careers, which intuitively makes sense given how this generally more talented player pool ascended to the majors so quickly. However, the two groups essentially merge together in terms of actual, non-relative production as they grow further into their thirties. What this likely suggests is that there is a lower-bound to how poorly you can play before teams quit giving you 300-plus plate appearances to sneak into this study. There is probably a good deal of survivor’s bias in the data, particularly among the “others” category, as those who age less graciously would be out of the league once they reach that lower-bound. If all the hitters who wash out at 31 or 32 continued to receive playing time as even older players, the “other” trendlines almost certainly would not look as relatively favorable as they do.

That rationale spurs an entirely different conclusion. It’s not that the bodies of prodigies don’t hold up as well, but their superior talent level and better performance when they were younger means that teams can stomach their declining performance for longer than the average player, who by that point in their career already would have crossed the proverbial line in that sand. The lucky survivors that are an exception to the rule then skew the data in favor of the “others.”

As for how this pertains to Harper and Machado, it would be a reasonable stance to be concerned by factors specific to the individuals such as past injury histories, but their status as superstar early-bloomers shouldn’t be held against their prospective aging outlooks to the extent that some might have assumed. The tail-end of such a large contract isn’t wont to look pretty, but the hope is that these free agents would amass enough elite-caliber production and surplus value towards the beginning of the deal to justify below-market value later on. As to whether or not such a gamble is a worthwhile risk for the Cardinals, that is a far more complex conversation for another day.