Rating 3pt Statistics with the Colley Matrix Method
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Taking into account opponent strength is one area I continually question when studying all forms of NBA statistics, whether it be at the team, 5-player unit, or individual player level. Having the ability to quantify this is something I want to get a handle on, so I’ve spent time studying methods the BCS uses to rank college football teams. More specifically, I have studied the Colley Matrix Method created by Wes Colley.
I feel I have a strong understanding of how the method works, so my first application will be to a team’s 3pt shooting statistics. I’m still studying how to quantify the uncertainty in the method, so while I have a belief as to how to measure this uncertainty I will leave that for a future time until I’ve got a firmer grip on what I believe to be true.
The Method for Rating 3pt Shooting Statistics
To setup the Colley matrix, I create 60 “teams”: one “team” for each team’s offensive 3pt shots attempted, and one team for each team’s defensive 3pt shots faced.
So an offensive team’s “wins” are the number of 3pt shots made, and the number of offensive team’s “losses” are the number of 3pt shots missed. The reverse is true for defensive team’s “wins” and “losses”.
In addition to the Colley matrix, the b vector is created using the win-loss information as outlined above.
Solving for the Ratings
To solve for the ratings (the r vector), one must solve:
r = C-1 x b
Solving this equation gives you the ratings for each team.
Below are the offensive and defensive ratings using data from all games of the 2008-2009 season played on or before December 23rd:
Using These Ratings
One noteworthy aspect of the Colley Matrix Method is that the mean rating is 0.5. Thus you can interpret these ratings in terms of “against 0.500 level competition”. This means the log5 method can be used to calculate expectations for any given matchup.
For example, suppose the Boston Celtics play the Golden State Warriors. What % of 3pt shots should we expect the Celtics to make? The Warriors?
Applying the log5 method:
The Celtics Expectation Is
0.4544 x (1-0.5323) / ( 0.4544 x (1-0.5323) + (1-0.4544) x 0.5323) = 0.423 = 42.3%
The Warriors Expectation Is
0.3941 x (1-0.6070) / (0.3941 x (1-0.6070) + (1-0.3941) x 0.6070) = 0.296 = 29.6%
Future Work with the Colley Matrix Method
Applying the Colley Matrix Method to team level 3pt shooting statistics is mainly just to help show how this might be applied to other areas of basketball statistics. I am most interested in applying this to 5-player unit level statistics, with the ideal goal of using those to extract each player’s impact.
Where would you like to see the Colley Matrix Method applied?