Since my last posts (here and here) I have received several excellent suggestions on how to modify the model. First, I want to break down the player/age effect by different types of players. Though I discussed this below, the age-performance curves make it clear that there is not much difference in aging patterns across differently-abled players. The three classifications of players with career OPS+s of <90, >90 & <110, and >110.
Second, Skip suggested that I incorporate some higher polynomials in the estimates. While the quadratic is certainly preferred to the linear estimate, other polynomials may provide even better estimates. And he was right, because adding the cubed or third degree of age to the regression model has an interesting effect. While the R-sq. did not change much (.0086) the cubed term was statistically significant, and the estimated peak age shifted from 29 to about 27.
As you can see, adding the cube of age looks very different. (Note, adding the 4th and 5th powers did not help). I am less concerned about the different peaks and the rate of decline among the two estimates. From about 28 on, the estimates are very similar. The interesting part is the early career. In the cubed model players start just below their peak before declining, while in the squared model players improve quite a bit before they decline. I would also like to point out that this fitted prediction includes controls for the number of ABs in a season, to attempt to control for injury problems.
So which model do you like? Wade Boggs or Chipper Jones?