How Do Players Age?

The last hot stove myth that I previously wrote about has to do with player aging.

Players peak at 27 and old players are worthless — Players peak at 29 — 30. And just because a guy is past his peak doesn’t mean he’s not valuable. The aging process is gradual, more like the Minneapolis Metrodome than an Egyptian pyramid. If a guy was good last year, even if he’s in his mid-30s, he’ll probably be good next year. Now, the older he gets the more dangerous long-run contracts get, but one- and two-year deals are fine.

This may not seem like much of a myth, as the conventional wisdom has long been that baseball players peak around 30. This, it turns out, is a myth of sabermetrics. Many methods have been used, aggregating performance into age-buckets, identifying the most-common (or mode) age at which players have their best season, and calculating average changes in performance from age to age. These methodologies suffer from various problems that could induce bias; therefore, I set out to conducted my own study in away that might satisfy my concerns.

I gathered a sample of major-league baseball players over 86 seasons who had significant career lengths to track performance over time. Without a career, there is no trajectory to follow. I tracked their performances over ages 24 — 35, throwing out younger and older years when only the best players typically play. Following individual players over time allowed me to set baselines for each player according to his ability, while controlling for changes in playing environments which may fluctuate quite a bit over the course of a player’s career. For example, a hitter who started his career in the mid-1980s and finished in the late-1990s might have appeared to have continuously improved, when in fact his higher offensive statistics reflected a jump in league offense. I used z-scores to measure player performance in terms of standard deviations from the league average to measure performance relative to one another.

I poked, prodded, and tortured the data, and it screamed that peak performance occurs around age 29 since the early-1920s, possibly 30 for more-recent players, not matter what changes I made. Some aspects of performance peak earlier while others peak later, but overall players tended to gradually improve until 29 and slowly declined after that. I think it’s particularly interesting that the average pitcher in the sample continues to reduce his walks until his 32nd birthday, while strikeouts peak at 24. Batters also improve in their ability to draw walks into their early-thirties, even after their hitting and power have declined. It appears that players continue improve mentally even after their physical skills are eroding. Maybe there is something to veteran know-how.

Age is often used as a reason to chastise GMs for picking up players past their prime. Though old players may not be what they once were, the evidence indicates they can still be valuable. According to my estimates, a hitter who has a .900 OPS at his peak would be expected to post around an .850 OPS at 35; a pitcher with a peak 3.5 ERA is expected to post around a 3.75 ERA at 35. Yes, age saps athletic skill, but the stock of skill being diminished is also important.

I should also note that previously, Phil Birnbaum argued that the quadratic shape of my estimated aging function could bias the peak. Certainly, this could happen. I looked into the possibility using polynomials of higher magnitudes and fractional polynomial methods that do not require symmetry. The results still hold, so I went with the more parsimonious functional form.

Update: Birnbaum offers a new critique, and I respond.

4 Responses “How Do Players Age?”

  1. Sky says:

    What are you concerns with the “calculating change in performance from age to age” method?

    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?

  2. JC says:

    Sky,

    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.

  3. John Gibson says:

    What about the skewing of the numbers that the rampant use of PEDs might have on the trends?

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