As some of you know, I often lurk on the APBRmetrics message board looking for interesting research the statheads are doing. Well, I came across something interesting tonight. Board member DSMok1 posted some very interesting research he had done for his blog.
The jist of his research was this: he wanted to create a predictive model of future results based on past results. The most common and trusted statistical method for taking past data to make predictive results is called Bayesian analysis. So DSMok1 took the data for the NBA and used Bayesian analysis to come up with predictive rankings and power rankings. One of the best parts about these results is that, unlike John Hollinger's power rankings which rely on just what happened in the last ten games to give the results a component that compensates for changes in quality over the length of the season, DSMok1's results use a function that weighs every game, but uses a gradual function to make it so the most recent result is weighted the most heavy and the first game of the season is weighted the lightest. DSMok1 explains it like this:
The basic concept is this: between each game, apply a transformation that increases the standard deviation by a fixed amount. Thus, if the current game has a standard deviation of 12, then the previous game would have a standard deviation of 12 + a, and the next a standard deviation of 12 + 2a, etc… This has the effect of weighting each game 1/(12)^2, then 1/(12+a)^2, then 1/(12+2a)^2, and so on. That can be restated as a weighting of the form b, b-c, b-c^2, b-c^3, etc. In this case, b would be 1/144, and c would be… ugly. (24a + a^2)/[144*(144+24a+a^2)], I believe. Anyway, moving along…
Adding the "penalty factor" depreciates the value of the older samples. The choice of how much depreciation to use requires the empirical work. To do this, I compiled last year’s NBA data and this year’s NBA data, adjusted all of the games for opponent, location, and rest, and set to work. I created a framework using the above methods to create the Bayesian-updated projection for each game, based on the games so far that season.
The numbers also take into account the strength of the opponent from each game. So now, I'm sure you're all curious as about the results of this analysis. Well, here they are:
So the Bulls come in at 5th in the big cluster of 6 teams cluttered tightly at the top of the league. The top 6 is Miami, San Antonio, Orlando, Lakers, Bulls, and Boston in that order, but outside of the top 2 (Heat and Spurs), there's hardly a significant difference between the teams.