You may already be familiar with my marginal scoring metric, PSAMS (if not, see here). The basic idea with that metric is that I try to take into account the volume and type of shots (inside, mid-range, 3-pt, and free throws) for each player and calculate an "adjusted" scoring metric. For example, I give more credit to players who generate a high volume of inside shots and debit players who don't. I take into account the fact that some players are responsible for taking more than their fair share of mid-range shots (which tend to be lower efficiency), while others take less, thus placing the burden of taking those bad shots on their teammates. And so on...
The approach I took previously was simply to compare each player to the league average at his position. Of course, that doesn't really take into account the specific dynamics of each team. Some teams might need certain players to take more mid-range shots, while other teams have an overall lower number of those shots. Also, I didn't take into account opponent strength.
One way to address this issue is to use "adjusted" versions of each scoring type, as I did previously for inside scoring. In that article, I combined inside scoring and free throw attempts, but here I'm going to focus just on inside scoring. I'll save free throws, mid-range, and 3-pt shots for subsequent articles, and eventually combine them all back together to get a fully adjusted version of PSAMS.
Short aside. I know what you're thinking. This is really horrible nomenclature. The adjusted version of PSAMS in full is "Adjusted Position- and Shot-Adjusted Marginal Scoring". We can take out the "Position", because there's no need for it now. So, it becomes "Adjusted Shot-Adjusted Marginal Scoring". I think I will just call it "Adjusted Marginal Scoring" (AMS), or maybe as an homage to Apple, I will call it "The new Adjusted Marginal Scoring". I'm open to suggestions, believe me.
Back to the live broadcast...
Hopefully, by now, you are familiar with how the "adjustment" is made using a regularized version of linear regression. If not, no big deal, I suggest you just read my Advanced Stats Primer to get up to speed on the background. For the current analysis, I setup two separate regressions where the dependent variable is: 1) the number of inside shots taken per 100 possessions *at the team level*; or 2) the FG% of inside shots *at the team level*. For each regression, a player will have an offensive and defensive rating. Once I have those ratings, I then calculate the adjusted marginal scoring in the same way that I did here. The only difference now is that I ignore positional differences and simply compare to the overall league averages (you see, in theory, the adjustment should already have accounted for positional difference). I should mention that the league average inside shooting rate and FG%, respectively, determined by the regression was 28.5 (shots per 100 possessions) and 61.50%. I should also mention that the data used are from the past "2.5 seasons" spanning 2009-10 through games completed on March 20, 2012.
Here are three sets of ratings tables, respectively, for total (offense+defense), offense, and defense. I've made it so that positive ratings are better on offense and defense, which I hope is more intuitive (note this is a change from the previous articles in which negative defensive ratings were better). It's just a cosmetic change. Only players with more than 3000 possessions played are shown. (Note that some teams may be listed incorrectly, due to recent trades. The ratings are not affected, however.)
Total Marginal Adjusted Inside Scoring
(O/D)INSR=marginal number of inside shots taken/allowed by offense/defense per 100 possessions. (Positive ratings are better in both cases.)
(O/D)INS%=marginal field goal efficiency (in %-points) on inside shots taken/allowed by offense/defense. (Positive ratings are better in both cases.)
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Offensive Marginal Adjusted Inside Scoring
Go to Google Spreadsheet
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Defensive Marginal Adjusted Inside Scoring
Go to Google Spreadsheet
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