My last post on the relationship between age and 3FG%, Brian Tung brought up a topic that I’ve wanted to look at:

… I’m not even sure that history is necessarily a good guide here, as players shoot those treys under fairly different circumstances at different stages of their careers. Who’s to say that Ariza, for example, is going to get the same looks this year as one of the primary options as opposed to last year as one of the secondary options?

Thanks to the work of Eli Witus, I’d like to see what we can say about situations like Ariza’s.

### The Goal

The goal of this study is to determine what relationship usage% has on 3FG%. For the uninitiated, usage% is the proportion of a lineup’s possessions an individual player is responsible for. See Basketball on Paper for the full details.

### Collecting the Data

To estimate this relationship, I’ve collected the number of 3pt makes and misses for each lineup from the 2006-07 to 2008-09 seasons. I also kept track of which shots were from the corner, and I’ve captured each player’s individual usage% for the season from play-by-play data.

With this data I constructed a data set that consists of how many 3pt shots were made and missed, if the shots took place in the corner, and the sum of the individual usage%s for each lineup. Lastly, the sum of the individual usage%s for each lineup were centered around one. This is done to estimate how much “more” or “less” the lineup must do relative to what the individual usage%s would indicate. For example, if the usage%s sum to 1.05, relative to one this is +0.05. Hence we would expect this lineup to take “less” of a load and increase their shooting percentages.

Lastly, I predict the effective FG% of 3pt shots of each lineup based on the likelihood that each player in the lineup attempts a 3pt shot and their probability of making these 3pt shots, where the difference between making a corner and non-corner 3pt shot are taken into account. (These predictions are made conditional on knowing some player in the lineup took a 3pt shot.)

### Fitting the Model

I’ve chosen to fit this model with a linear regression, so like Eli’s efficiency study, I’m using the difference between the predicted effective FG% of 3pt shots and the actual effective FG% of 3pt shots as the response variable and the relative difference from one of the summed usage%s as the predictor.

In 2008-09, the estimated coefficient for usage% is 0.131 with a p-value < 0.01. 2007-08, the estimated coefficient for usage% is 0.087 with a p-value of 0.06. In 2006-07, the estimated coefficient for usage% is 0.046 with a p-value of 0.33. When fit to all three seasons of data, the estimated coefficient for usage% is 0.09 with a p-value < 0.01. A 95% confidence interval for this coefficient is (0.039, 0.142).

### Interpreting the Results

Using the model fit to all three seasons of data, the estimated coefficient suggests that for each 0.01 increase in the sum of the individual player’s usage%s we expect the lineup’s effective FG% on 3pt shots to increase by 0.09%.

At the player level we would estimate that each 0.01 decrease in a player’s usage% would increase the effective FG% of their 3pt shots by 0.45%.

In Ariza’s case, we would estimate that a change from using 16.3% of his lineup’s possessions to 21.8% (a net -5.5%) would decrease his effective FG% of 3pt shots by 2.5%. The actual estimated change from last year with the Lakers and this year with the Rockets is -1.7% on corner 3pt shots and -3.4% on other 3pt shots.

### Future Work

Even though we have some evidence to suggest an increase in usage% will decrease a player’s effective FG% on 3pt shots, we know that age and other factors affect 3FG%. Thus in the future I would like to determine how much confidence we have in out of sample predictions when taking into account usage%, age, etc. The goal of this study was to present the estimates from in-sample data, but more work needs to be done to determine how useful this is for making predictions about the future in a new season.