[82games] Adjusted Plus/Minus Ratings

Discussion in 'NBA General' started by durvasa, Jan 10, 2007.

  1. durvasa

    durvasa JBB Rockets Fan

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    Explaining adjusted Plus/Minus Ratings

    Ratings for every player in the 05/06 season

    A very interesting piece explaining the idea behind adjusted +/- ratings, with results from this method for every player last season.

    This is a concept that I think can be potentially very useful for understanding and summing up a player's total contribution to his team in terms of impacting point differential. I say "potentially" because there are limitations (many of which he discusses), and I think there's scope for improvement in the manner in which the ratings are calculated. One example he highlights in the article is for the Detroit Pistons. They were a strange team last year. They had an extremely rigid rotation thanks to a dominating starting 5 who rarely got injured. While it's obvious that their starting-5 as a unit was dominant, it's much more difficult to figure out just based on +/- numbers how individuals contributed to that dominance because of the nature of their rotations.
     
  2. Shapecity

    Shapecity S2/JBB Teamster Staff Member Administrator

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    Very good article and analysis. I prefer this to PER and really validates LeBron James for being the clear cut choice for MVP last season. Most of the top ranked players are two-way threats, and this formula accounts for defensive impact on a game.
     
  3. AirJordan

    AirJordan JBB JustBBall Member

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    Derrik Martin first for Toronto? The guy sleeps on defense and is crap on offense.
     
  4. Shapecity

    Shapecity S2/JBB Teamster Staff Member Administrator

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    <div class="quote_poster">AirJordan Wrote</div><div class="quote_post">Derrik Martin first for Toronto? The guy sleeps on defense and is crap on offense.</div>

    Martin only played in 9% of the minutes for the entire 2005-2006 season. It's not a significant amount of playing time to determine his true rating. My guess is he played a lot of garbage minutes, and padded his stats.
     
  5. durvasa

    durvasa JBB Rockets Fan

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    I've been thinking a bit about these ratings, and I wanted to try to explain them as I understand them.

    The idea is to determine a number (the rating) for every player in the league. First of all, what does this number signify? Well, let's take a concrete example.

    Suppose you have the following matchup:

    <div class='codetop'>CODE</div><div class='codemain'><br/>Tm 12 3 4 5<br/>Rockets AlstonMcGrady Battier HayesYao<br/>KnicksMarbury CrawfordRichardsonFrye Curry<br/></div>

    In theory, what you could do is sum up the difference between total ratings of each unit, and that will tell you what the point differential will be (per 100 possessions). Actually, this model assumes a "home court advantage" term that you'd also throw in there to give a slight advantage to the home team. To keep it simple for this discussion, I'll assume that's zero.

    Here were their ratings last year (as determined by the method which I'll attempt to describe below):

    <div class='codetop'>CODE</div><div class='codemain'><br/>PlayerRating<br/>R1Alston-0.13<br/>R2McGrady +7.83<br/>R3Battier +6.0<br/>R4Hayes +9.18<br/>R5Yao +7.83<br/>K1Marbury +7.57<br/>K2Crawford-1.01<br/>K3Richardson-1.06<br/>K4Frye-1.40<br/>K5Curry -8.26<br/></div>

    So, if the two teams were matched up against eachother, these ratings tell us that we could expect the following margin (point differential per 100 possessions):

    <div class='codetop'>CODE</div><div class='codemain'><br/>Margin = (R1 + R2 + R3 + R4 + R5) - (K1 + K2 + K3 + K4 + K5)<br/> = (30.71) - (-4.16) = +34.87<br/></div>

    In other words, based on the calculated ratings, the Rockets lineup would absolutely blowout the Knicks lineup. There are roughly 90 possessions in a 48 minute game, so per 48 minutes that would amount to the Rockets lineups beating the Knicks lineup by 31 points.

    Note that the ratings for every player is "normalized". What this means is that the average player's rating is set to 0. Consequentially, you could also think of the ratings in the following way. If a player on the court played with perfectly "average" teammates, and he faced an average opponent, then the margin of victory would end up being equal to that player's rating. For example, if Yao had perfectly average teammates, and played a perfectly average opposing lineup, then his team would outscore the other team by about 7.8 points per 100 possessions.

    Alright, so how the hell are these ratings calculated anyways, you might be wondering. It's done using a statistical technique called a linear regression. Last season, tens of thousands of "observations" are made -- each observation consists of stint during a game between substitutions. For every observation, you record the players on each side, and the margin (point differential per 100 possessions). For example, let's suppose that we observed the above matchup in one game last year, it lasted 12 possessions, and the Rockets outscored the Knicks by 4 during the stint. So for this observation, we'd record +33.3 points per 100 possessions as the margin. Likewise, you do this for every observation last season:

    <div class='codetop'>CODE</div><div class='codemain'><br/>+33.3 = H + (R1 + R2 + R3 + R4 + R5) - (K1 + K2 + K3 + K4 + K5) + e1<br/>-12.7 = H + (R1 + R6 + R3 + R7 + R8) - (K1 + K2 + K6 + K4 + K7) + e2<br/>...<br/></div>

    I just showed a couple up above as an example, but as I said there are literally tens of thousands of such observations over the course of an entire season. What the regression does is it finds values for all those ratings (R1, R2, ..., K1, K2, ..., etc.), including the "home court advantage" term H, such that the overall error (technically, sum of the squares of e1, e2, ...) is minimized.

    Alright. That's it for now. If I can think of more stuff to bore you with, I'll be sure post it!
     

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