## Saturday, March 3, 2012

### Value of the 3 pointer

In a basketball overall rating system, how much should the 3 point shot be valued? The easy answer is "3 points", and that's the way I've done it for a long time, but it actually doesn't quite work.

Ratings that incorporate all the box score stats will give you credit for scoring points, and then remove credit for missing shots. In the Tendex system, developed by Dave Heeren back in the 1980's (or maybe before, I read his books in the 80's) a player taking 10 shots and making 6 of them will get a credit of 8 - 12 points scored minus 4 missed shots. A player taking 10 3 pointers and making 4 of them scores an identical 12 points on the same number of shots, but he misses 6 so his credit is only 6. Further compounding the imbalance is that if these two players are playing each other, 1 on 1, and all missed shots are rebounded by the defender, the guy taking two pointers will get 6 rebounds, putting him up to 14 credits, while the 3 point shooter only gets 4 boards (and 10 credits).

Not all of the statistical systems work that way. The Wages of Wins system gives .032 for a 2 pointer and double that, .064 for the 3 pointer. So these players are getting even credit for the points and missed shots, but even still they are out of balance when you consider the rebounds.
Let's try an experiment. One team shoots 50%, taking only 2 pointers. Assume no free throws are taken, no turnovers from either team, and rebounds are split at a league average rate (27/73) between the offensive and defensive teams. What shooting percentage would a team have to shoot from 3 pointers to tie the score?

If you said 33.3%, then you are wrong. That only works if every rebound is by the defensive team. The actual answer is about 30.5%. When the teams score, then they are giving the ball to the other team 100% of the time. When they miss, they get the ball back 27% of the time. So if you can score the same number of points per shot, and do so while missing more shots, then you are going to get more shot attempts than the other team, and score more points overall.

In light of this, as the starting point for my win shares formula I will now add 0.9 for every three pointer to balance out the formula. For offense it is (PTS + 3pt made *.9 - (fga-fg) - (fta-ft)*.5)