Dec 26 2008

# Rating 3pt Statistics with the Colley Matrix Method

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.

The Results

Below are the offensive and defensive ratings using data from all games of the 2008-2009 season played on or before December 23rd:

Offensive Ratings

Rank Team Rating Rank Team Rating Rank Team Rating
1 SAS 0.4681 11 ATL 0.4437 21 MEM 0.4167
2 PHX 0.4664 12 OKC 0.4430 22 MIA 0.4100
3 NOH 0.4627 13 TOR 0.4425 23 UTA 0.4081
4 POR 0.4586 14 ORL 0.4423 24 DAL 0.4014
5 BOS 0.4544 15 CHA 0.4386 25 WAS 0.3994
6 DET 0.4522 16 DEN 0.4349 26 GSW 0.3941
7 LAL 0.4504 17 NYK 0.4334 27 SAC 0.3824
8 HOU 0.4495 18 IND 0.4235 28 LAC 0.3813
9 CHI 0.4456 19 CLE 0.4229 29 MIN 0.3783
10 NJN 0.4450 20 MIL 0.4191 30 PHI 0.3642

Defensive Ratings

Rank Team Rating Rank Team Rating Rank Team Rating
1 ATL 0.6070 11 DET 0.5883 21 TOR 0.5611
2 BOS 0.6070 12 PHI 0.5847 22 CHA 0.5603
3 NYK 0.6066 13 UTA 0.5820 23 OKC 0.5588
4 HOU 0.6028 14 LAC 0.5800 24 MIA 0.5538
5 DAL 0.6016 15 LAL 0.5794 25 MEM 0.5462
6 MIL 0.6002 16 SAS 0.5715 26 POR 0.5405
7 CHI 0.6001 17 IND 0.5690 27 MIN 0.5370
8 DEN 0.5939 18 WAS 0.5683 28 GSW 0.5323
9 ORL 0.5935 19 PHX 0.5643 29 SAC 0.5119
10 CLE 0.5891 20 NOH 0.5641 30 NJN 0.5117

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?