Comprehensive NBA Free Throw Modeling

Enough predictors to tighten up the posterior distributions

Previously, we modeled how well players shoot free throws using a simple hierarchical Bayesian binomial model. How well a player shot depended both on what we’ve seen them shoot so far this season, as well as learning across players hierarchically.

Then we incrementally added in their position, since it makes more sense to assume guards shoot like guards if you don’t know anything else about them.

Here, we take it one step further. Actually 5 steps further, just dumping in the next easiest features into the model.

This was partially inspired by our friend who has a solid NBA analysis newsletter

The Model

Incrementally improving on our free throw modeling, we added the following position-specific features:

• Height

• Experience

• Draft Position

• Weight

• International vs US

The Players

Here’s the posterior broken out by position:

Height: Smaller is Better, But Tons of Uncertainty

The estimate for the effect of height is negative, but the uncertainty is huge. Notably, it’s reasonably certain for guards.

Posterior estimate for the impact of height on free throw shooting

Broken out by position, plotting our estimate of the effect of height on top of the raw data:

Posterior estimate for the impact of height on free throw shooting by position

Experience: More → Better

This isn’t to say more experience makes you better. But if all you know is a player’s position and number of years in the NBA, you know more than nothing.

Posterior estimate for the impact of experience on free throw shooting

Draft Position: Another Obvious Effect

Probably don’t need much commentary on this one.

Weight: Heavy Forwards Struggle

I’m curious what your thoughts on weight are. I’ll hold off on my interpretation, but if you leave a comment, I promise to engage.

International vs US

It doesn’t matter.

Top Shooters

Look how much we’ve tightened up our estimates.

Bottom Shooters

Looking Ahead

I’m so thankful for everyone that DM’d me over the last few weeks.

I probably won’t be posting any more free throw modeling for a bit. I have some really off-the-wall ideas that I’ve been modeling, and I want to share that next, I think.