Twenty-Seven

Brian Sabean, the general manager of the San Francisco Giants, has got to go. Now that we’re well into the off-season, I’ve been dabbling in a bit of sabermetrics — what can I learn from analyzing a database of player statistics that goes back to 1871. As something of a warmup, I started to look at player performance as a function of age. After concluding I needed to look at a single cohort of ballplayers, I chose all batters who were born in 1957 (all of whom have stopped playing by now).

The graph at left is a doubly-averaged concoction. The y-axis measures Runs Created, which is an estimate of the total number of runs that a batter contributes to the team over the course of the season. What I did to produce the graph was to plot for each of the batters in my cohort RC against age and then fit a linear regression model with a quadratic term against the plot. This model generates a graph that is an upside-down parabola, the maximum of it falling at the age of the batter’s peak performance. I then took the equations for the entire set of batters, and averaged their coefficients together in turn, to produce the graph here, which is a composite look at the batting performance across the entire cohort.

The peak of the graph is at age twenty-seven. After I did my little analysis, I was gratified to read that Bill James came up with exactly that value for age of peak performance twenty-five years ago. Beyond that, players start going downhill, or as Bill James put it: “most players are declining by age 30; all players are declining by age 33.”

As Steven Rubio has pointed out, the San Francisco Giants aren’t exactly in a youth movement. This off-season they have so far signed or re-signed Ray Durham (age 35), Dave Roberts (age 34), Rich Aurilia (age 35), Bengie Molina (age 32), Pedro Feliz (age 31), the pitcher Steve Kline (age 34) and of course Barry Bonds (age 42). Sigh. With that lineup, the Giants’ winning ways (this past season their record was 76 and 85, 11.5 games out of first place in the division) are surely going to continue. It’s not even 2007 yet, and my hopes for next season are pretty dim.