Good questions.

Playing time is a function of present performance and past performance. Because of this, past performance affects the sample in a way that highlights declines. Managers are trying to identify the best players to play. A good performance in the past will keep you in the lineup even if you slump through the short term. Bad performance in the past will prevent playing in the future. To have a two-year sample you have to reach playing time minimum in both seasons. To keep this simple, let’s assume that players can have two types of seasons (good and bad), generating the following combinations of seasons in a two year sample: good-good, good-bad, bad-good, and bad-bad. We’ll get plenty of the first two types of seasons, but the latter two will happen less. The draws from year1 and year2 talent pools are not random, because the lucky-good can go from good to bad, but the lucky-bad don’t get the opportunity to go bad to good. I’ll call this phenomena the survivor effect (Fair (2005) notes something similar).

Imagine we have two players who are both true .750 OPS hitters. PlayerA hits .775 in Year1, and PlayerB hits .725 in Year1, because of normal random fluctuations. PlayerB doesn’t get the opportunity to have a Year2 to have a corresponding upward rebound. PlayerA gets to play in Year2 and his performance falls to .725. Possibly in the next round, his Year2 and Year3 won’t be recorded because he’s deemed incapable of playing (unless you’re the Braves and you build an advertising campaign around him). Thus, when we average in the change, we will be averaging in more declines that would is reflected by aging.

So why do we see any positive improvement up to the mid-20s at all (26 is where Nate Silver finds that it ends)? The survival effect ought to be less relevant when players are younger, because the aging function is steeper at this point (meaning improvements are larger and likely to overcome bad luck) and managers expect improvement and will be more tolerant of one bad year (“Tough year, kid. Hang in there.”) For older players the effect is the opposite. Being PlayerB at 36 may cause teams to disallow a bounce-back year because they observe may be a sign that his career is over.

I’m not certain the survivor effect dooms this type of analysis, but I worry about it, which is why I looked at aging using a panel data estimation method. Including a list of players who played 10 years or more allows for the smoothing of random fluctuations over time, because we don’t have to worry about players being dropped in and out of the sample. More importantly, it allows for identifying a career baseline for each player from which we can observe how he progresses. It certainly shouldn’t perform worse than the average-yearly-change method.

Of course, the downside is that players who play long enough to observe tend to be good players. What if the biological factors that make them good also make them age more slowly. This is something I looked at as best that I could. First, I looked at the very best players (those who reached the Hall of Fame) in the sample to see if they peaked later than players who just passed the bar of making the sample. I did not find any evidence of slower aging. The only possible effect I found was that HOF players tended to keep their foot-speed longer. But overall, the peaks were the same. Also, I looked to a study by Saint Onge, Rogers and Krueger (2008) that finds baseball performance is not associated with longevity among players. They all live longer than non-baseball players, but the good ones don’t live longer (or shorter) than the bad ones. If ability was affecting aging, then this might show up here. Now, these ancillary pieces of evidence are just that. But from talking with my exercise physiology colleagues, I feel that there is not much connection between ability and aging.

Are you not worried that only using players with long careers means you’ve left out players who peaked early and didn’t last long enough to make your sample?