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How many games for FT% to stabilize?
Posted: Mon Nov 21, 2016 4:28 pm
by hoopthinker
How many games or FTA better is the optimal sample to predict the true FT% of a player?His true free throw skill?
Does anyone know/has done any research on that?
Re: How many games for FT% to stabilize?
Posted: Mon Nov 21, 2016 10:25 pm
by Mike G
Depends what the definition of is is.
Some players seem to be notably better on the 2nd shot than they were on the 1st.
Some are consistent from year to year, while others are not; or vary over the course of a season.
The chance of a given player making a given shot? Probably a different formula for every player, but I'd guess after 100 FTA in a given season, you pretty much know.
Re: How many games for FT% to stabilize?
Posted: Mon Nov 28, 2016 8:42 pm
by Nate
hoopthinker wrote:How many games or FTA better is the optimal sample to predict the true FT% of a player?His true free throw skill?
Does anyone know/has done any research on that?
More is always better.
If you assume that a players' FT% is fixed, and all the FTA are independent trials (both of which seem like reasonable assumptions) then it looks like a classic statistics question, so it's pretty straightforward. Modelling it as a normal distribution should work pretty well.
We know that the variance is less than or equal to 0.25 shots made squared per shot, so the confidence interval is roughly proportional to 1 divided by the square root of the sample size. (You get some extra confidence for players whose FT% is close to 0 or 1, but it's not going to be a huge difference.)
Re: How many games for FT% to stabilize?
Posted: Mon Nov 28, 2016 11:55 pm
by Mike G
More is always better.
Well, what if it isn't? What if FT shooting indeed fluctuates on a large scale?
It may well be that a player's latest 100 or 50 or 20 FTA are a better indicator than any hundreds taken earlier.
This could be tested if you had a player's log of FTA.
Re: How many games for FT% to stabilize?
Posted: Tue Nov 29, 2016 11:20 am
by Nate
Mike G wrote:More is always better.
Well, what if it isn't? What if FT shooting indeed fluctuates on a large scale?
It may well be that a players latest 100 or 50 or 20 FTA are a better indicator than any hundreds taken earlier.
This could be tested if you had a player's log of FTA.
That's true - there could be sample bias or something. Let's suppose that players don't have a fixed FT% - for example, if a player played with a significant injury or if there's some unpredictable age-related trajectory for FT performance. Then it might be a bad idea to include a veteran's rookie year performance, or a player's injured FTAs in the FT% estimate.
That said, the OP's question is about how to best "predict the true FT% of a player," which implicitly assumes a 'true FT%' for each player.