The impact of aging on player performance interests me, but I haven’t really done anything useful in this area. Baseball’s recent debate (really fantastic stuff) on the topic of player aging curves has motivated me to take a closer look at the affect of aging on 3pt shooting.

Ed Küpfer’s three year old post on aging is the best resource I know of on the topic, but I’m sure he’s got something more useful than what’s in that post. That said, I’d like to specifically estimate an aging curve for the 3pt shooting abilities of NBA players.

### The Data

Using Basketball-Reference.com‘s excellent Player Season Finder, I collected 3pt shooting data for players that attempted at least two 3pt shots during any season from 1999-00 to 2008-09. This resulted in a data set containing a little over 3300 player seasons.

### The Model

Individual 3pt shooting performance is more than a function of player ability and age, but in this case I’m specifically interested in estimating the affect of age. Further, I would like to estimate an aging curve for each player under the assumption that each player has their own unique aging curve.

To do this, I’ve chosen to use a multilevel model that allows the intercept and slope to vary by player, as this model allows for the estimation of a unique aging curve for each player. The aging curve is assumed to be of the form [latex]alpha + beta_{0}(age) + beta_{1}(age^{2})[/latex].

### The Results

The model fit estimates the the average player’s peak age in 3pt shooting ability is 29, and the p-values for the [latex]beta_{0}[/latex] and [latex]beta_{1}[/latex] coefficients in the model form listed above are both less than 0.01.

The estimates for each player are listed in the following spreadsheet: 3FG% Aging Estimates

In this spreadsheet you will find each player’s estimated peak age along with 3FG% estimates for each player from age 20 to 40.

With the exception of Andre Miller, most peak ages are plausible. For a player like Miller, the model suggests his 3pt shooting ability has been declining since starting his NBA career.

### Individual Players

Below you will find graphs of estimated aging curves for some player’s 3FG%. In addition to the estimated aging curve, you will see points plotted that represent the actual 3FG% for the player at the specified age.

### There is Uncertainty…

These are just estimates, and it is important to point out that uncertainty exists around these estimates. I’ve tried to simulate confidence bounds for this model without success, but even though I’m not representing the uncertainty, keep in mind that it does exist.

### Improving this Model

The debate in the baseball community suggests it’s incorrect to simply assume players have this type of aging curves. Although this type of curve appears to be a decent approximation, perhaps there are better ways to estimate the impact of a player’s age on 3FG%. Other than trying to control for other explanatory variables, trying to fit other model types might prove worthwhile.