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Thursday, February 26, 2004

Rebounding 2’s vs. 3’s

Here’s what I have come up for offensive rebounding percentages (OR%) for each type of missed shot. This is based on all games involving at least one D-1 team played between January 1 and February 21.

3 point shot: 21.0% (21% of missed 3 pointers are rebounded by the offense)
2 point shot: 41.1%
Free throw: 20.3%

Keep in mind these are NCAA-wide averages. Individual teams will be better or worse than these percentages depending on their personnel and who they play against.

If you question the validity of the numbers (which you should), just watch a few games with this in mind and see if it’s believable.

I was going to post a bunch of statistical mumbo-jumbo on the meaning of this, but I will refrain for now.

The one thing I’ll point out is this: The results give the 3 point shot an interesting symmetry. They’re worth 50% more than the made 2 pointer, but then they’re also about ½ as likely to be rebounded by the offense. This makes it a little easier to understand shot selection. If your team’s brickmeister is jacking up a lot of perimeter shots, he becomes a drain on the offense. Sure, there are nights when he’s hitting and everything’s great. But over the long haul he’s going to miss too often to help the offense. However, the closer he gets to the hoop, the less his bricks hurt, because there's a better chance points will be scored on a put-back. You can also look at it from the defensive perspective in the same light.

For those with too much time on their hands, the methodology for how I came up with the percentages is described below.

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From the box score we know the following:

A team’s missed free throws
A team’s missed 2 point FGA’s
A team’s missed 3 point FGA’s
A team’s offensive rebounds*
Opposing team’s defensive rebounds*

*Team rebounds – the rebounds that go out of bounds before being controlled by a player - throw a monkey wrench into this. In the “official box score,” team rebounds are recorded as both offensive and defensive. Unfortunately SportsTicker, the purveyor of college basketball box scores, dumbs down the official box score and lumps team rebounds into one category. So for every game, I made the assumption that team rebounds go to the offense as often as normal rebounds (about 1/3 of the time).

Things we can’t tell from the box score:

1) How many offensive rebounds occurred on FT’s, 2’s or 3’s.

2) How many FT misses had rebounds – some misses will occur on the front end of a 2 or 3 shot foul.

I am trying to solve for (1). To get around (2), I took Team A’s offensive rebounds + Team B’s defensive rebounds and subtracted the missed 2’s and 3’s by Team A. The remaining number yields the number of missed free throws that were rebounded. In some cases, due to the team rebound assumption, the number of remaining rebounds was greater than the number of missed free throws. Corrections were made for this.

So now to figure out what’s mentioned in (1). I assumed a 2 pt OR% and a FT OR% for all games. The 3 pt OR% can be calculated from the total offensive and defensive rebounds for all games after the first two are assumed.

With the assumed values I went back and computed the theoretical rebounds for each team in each game. This was done taking 2 pt. OR% x 2 pt. misses + 3 pt. OR% x 3 pt. misses + FT OR% x “reboundable” FT misses. From this I took the difference between the theoretical rebounds and actual rebounds and called this the rebounding error. I averaged this error over all games. The numbers presented at the beginning of this post represent the values of OR% for each shot that minimized the rebounding error. If you have any more questions, e-mail me. I could go on, but I think I’ve covered the main points here.

Posted on 02/26 at 11:13 AM
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