## Thursday, February 23, 2012

### 3PT Attempt Percentage

Ken Pomeroy recently made a couple of blog postings concerning defense, and specifically a statistic he calls the "3 Point Attempt Percentage" (3PA%).  He defines this statistic as the "percentage of field-goal attempts that are from three-point range."  Ken Pomeroy thinks this is a better measure of defense than 3PT%.  His reasoning is that most teams only take 3 point shots when they are relatively unguarded; the effect of defense is not to make these shots harder, but to cut down on the number of opportunities.  Hence the claim that it's really how many 3 pointers your opponent takes that reveals the quality of your 3PT defense.  Near the end of the second posting he says:
People that are unaware of 3PA% (which is to say nearly everyone) are missing a very telling statistic that explains a lot of how defense works.
This is a strong statement and worthy of a little research to see whether it is true (at least so far as predicting outcomes is concerned).

3PA% is similar to Effective Field Goal Percentage, one of Dean Oliver's Four Factors.  I have previously considered the Four Factors and concluded that they didn't add any predictive value to my models, but 3PA% captures a slightly different slice of information.

When I recently looked at derived statistics, one of the derived statistics was pretty close to 3PA%:

(Ave. number of 3PT attempts by the opposing team)
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(Ave. number of FG attempts by the opposing team)
This isn't quite the same statistic, because it is using game averages rather than cumulatives, but it is close.  This statistic turned out to have no predictive value, but a couple of statistics based upon 3PT attempts did have value:

(Ave. number of 3PT attempts by the opposing team)
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(Ave. number of turnovers)

(Ave. number of 3PT attempts by the opposing team)
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(Ave. number of rebounds)
Note that these statistics are relating the number of 3PT attempts by the opponent to a statistic for the defending team.  I'm not entirely sure what these statistics are capturing, but I don't think it is 3PT defense.  (The latter might be indirectly saying something about how a team defends against the three pointer, from how it is positioned to rebound effectively or not after a taken three pointer.)

That aside, I modified my models to generate four new statistics:  the 3PA% for the home team in previous games, the 3PA% for the away team in previous games, the 3PA% for the home team's opponents in previous games, and the 3PA% for the away team's opponents in previous games.  I then tested the model both with and without these statistics:

Model   Error      %Correct
Base Statistical model  11.0672.7%
Base Statistical model + 3PA% statistics 11.0572.7%

There's a very small improvement in RMSE with the added 3PA% statistics.  So at least for my model, the 3PA% statistics don't seem to add any significant new information.