During Kobe’s “hot streak,” I’ve been writing that he’s actually inefficient compared to Andrau Gasnum, the Lakers’ superb tw0-man post presence. I’ve said that he should give up some shots until his efficiency equalizes with Gasnum’s. Adrian the Canadian was quick to send me a Sloan Sports Analytics Conference paper arguing that teams might equalize offensive efficiency too much already. The author (Brian Skinner) uses some network theory for unknown reasons (it’s not related to his point), but the paper boils down to a comparison of the marginal cost and benefit of changing shot selection from one player to another.
Assume that players’ efficiency decreases as they take more shots (due to more defensive attention, fatigue, etc.). Imagine you are Kobe. Giving Andrau Gasnum one of your shots has the following marginal benefits:
- higher efficiency on all your other shots
- higher efficiency of this specific shot (since Gasnum is more efficient than you).
The marginal cost:
- lower efficiency for Gasnum on all his other shots.
If the benefits exceed the costs, shifting shots is the smart move. Skinner argues in the paper above that these costs might be less than the benefits at extreme values, but that the costs will overtake the benefits long before efficiency equalizes (which is the point that teams might aim for).
I think he’s technically correct — I was wrong in my earlier posts to say that the Lakers should shift shots to Gasnum until the efficiencies are exactly equal. For example, if Kobe gives all his shots to Gasnum and, in doing so, equalizes their efficiencies, there will be no gain on that individual shot (efficiencies are now equal) and no gain in Kobe’s efficiency on other shots (he has none left). Meanwhile, the shot will lower Gasnum’s efficiency on ALL other shots. The right point to stop shifting shots will surely happen even sooner than this.
However, Skinner’s examples depend heavily on the functional form that he assumes for the shot attempt/efficiency relationship and on teams’ starting points (he assumes teams start from the point where all efficiencies are equalized). He has no data — just a model. In his example with Ray Allen, he assumes that the less efficient player (Kobe in our case) does not improve his shooting percentage when he gives up a shot to the more efficient player (Gasnum). Kobe might take bad shots no matter what since he’s more macho than smart, but this completely eliminates one large marginal benefit of shifting shots away from him!
So, while I agree with Skinner that efficiency should not be equalized completely, I still think there are opportunities to improve efficiency by shifting shots and bringing efficiencies closer together. In the Lakers’ case, Kobe has taken at least 28 shots in all four of his 40 point games! Gasnum didn’t shoot nearly as many. An increase in Kobe’s efficiency would affect a ton of shots, while a decrease in Gasnum’s would affect far fewer, suggesting that the benefits outweigh the costs for the Lakers. (Again, all of this depends on the true relationships between efficiency and shot volume.) The lesson is a two parter: (1) teams shouldn’t equalize efficiencies exactly, but (2) there’s probably some benefit from bringing efficiencies closer together when they are way out of whack.