We talked a few weeks back about valuing a rebound in some form or fashion. We can’t really continue that conversation without talking about expected value. Expected value is a little different than points per possession.
Points per possession simply takes your points and divides by possessions so any offensive rebounds are factored in there or sometimes they’re not depending on what possessions formulas you’re using. If you’re using one that separates out offensive rebounds as different possessions than you end affecting your points per possession every time you get an offensive rebound.
Expected value doesn’t take that into consideration. Let’s start with this, take the value of each shot in the game – 1, 2, 3 – and multiply that by your shooting percentage for each of those. Let’s use last year’s national champion Villanova Wildcats as an example:
0.779 FT% x 1 = .779 expected pts per free throws
0.558 2PT% x 2 = 1.179 expected pts per two-point shot – don’t forget to subtract the three-pointers from your field goal numbers
.401 3PT% x 3 = 1.203 expected pts per three-point shot
First, you can tell why they shot so many three-pointers, it gave them the best bang for their buck. But now let’s take this a step further and look at where they got their points overall:
559 pts on free throws – 16.1% of their points
1,512 pts on two-point shots – 43.7% of their points
1,392 pts on three-point shots – 40.2% of their points
3,463 pts overall
When you take that percentage times each of their expected values above, you can see the approximate value of a scoring possession:
.779 x .161 = .125
1.179 x .437 = .515
1.203 x .402 = .484
That gives you a total expected value of 1.124 pts per scoring possession. The next step is to determine how an offensive rebound can affect this expected value when factoring in defensive fatigue and the shots you get off said rebound.