Rating the Ratings

1995

There are a number of different statistics people use on the rec.sport.basketball.pro newsgroup to support all the woofing that goes on. I'm not so much interested in the woofing, but in these statistics and whether they make any sense. At all. So I'm going to look at a few and discuss some of their features and what they contribute to our knowledge of the game. I will do this in no particular order, just so you don't think I'm playing favorites....

Team Points per Possession -- Tony Minkoff posts this every so often for teams, using Doug Steele's raw stats. All it does is divide the team's points scored and allowed by the number of possessions used by the team. Fortunately, Minkoff uses a good definition of possessions. I believe his formula is FGA - OR + TO + 0.4 * FTA. Basically, this means that a team has possession until the other team has possession -- this is so obvious it's hard to say. Other definitions do not subtract the offensive rebounds. This implies that a team shooting the ball, then getting the offensive board has two possessions. By defining possessions the way he does, Minkoff essentially says two opposing teams in a game have an equal number of possessions with which to win the game, just as each baseball team has 27 outs with which to win the game. Defining possessions the other way doesn't give this nice feature. Anyway, this rating is simple and essentially states a fact about a team, removing the illusion caused by fast vs slow paces. It is a fundamental tool for evaluating teams' abilities to score or prevent scoring.

Minkoff Player Rating -- My understanding of this stat is that it takes a linear regression of minutes per game against each per minute stat, then uses those coefficients to compute the number of minutes "earned" through a players statistical performance. This may be modified by weighting it with actual minutes per game. This is one of the most interesting player stats I have seen and I have seen a lot. The concept of rating players by how much time they deserve is very innovative and conceptually simple. I am not convinced that linear regression is a great tool for a game as complex as basketball (I know, I know, Dickie V. calls it a simple game.) I think this may be why the stat is fudged by weighting the actual minutes per game along with it. For what it is, this rating is quite good, but it does have the limitation that it serves no other purpose other than to woof. It is a rating. It ends all debate by hiding it behind one number.

Tendex (and all linear weights) -- Tendex was created by Dave Heeren, a real sportswriter in Florida (for what that is worth). It basically consists of adding a player's positive stats and subtracting his negative stats, sometimes weighting each of these by some amount. Doug Steele has his version. This, like the Minkoff Player Rating, is pretty much just a rating, ending all debate. It has an analogous form in baseball analysis, called the Linear Weights method. Bill James argued against it a lot because he had an alternative method and, well, there tends to be a proliferation of people in this world who think you can always add things up and get the true answer. Tendex has the weakness in that there is no good theory for what the weights on all the stats should be. Some people say that offensive rebounds should be weighted heavily, some say no. Some say they should be weighted the same as defensive rebounds, some say no. Some say assists are the same as blocks, some say no. There is no good theory to guide us on what the weights should be because a linear weight model of basketball is not a good model of the game.

Norris Power Ratings -- This is essentially a filter, as known to statisticians or mathematicians. Kalman filters are common if anyone out there has heard of them. It essentially takes the score of games, the location, and tries to "learn" how good a team is based pretty much on these two facts. Traditional filters also have information like how much variability a team has. Norris' does things a different way, but uses pretty much the same information, making me think he has a filter in a different formality. My congratulations to him if it is a filter. These have proven successful in predicting physical processes, even complex ones. I believe Norris' does pretty well, too. Basically a lot of information is wrapped up in the scores of games and the home-road thing. It ignores the details, which is a problem when, say Michael Jordan returns to the Bulls in midseason, but otherwise it does pretty well. This is probably a good thing for all you gamblers out there, but don't blame it on me if you lose to Vegas -- they use the best filter of all.

Jon Moser's Player Efficiency Rating -- I have only seen this a few times, but it appears to divide a player's points scored by the number of shots taken, essentially. I may be mistaken on this. Obviously it ignores rebounds and assists and maybe turnovers. It does what it says it does and doesn't say anything more. I don't think he claims it says more. That is good.

Finally, I want to add that Doug Steele's stats, which are the basis for a lot of the numbers we see posted are deficient in one slight area. Most public sources of stats do not include team turnovers, incurred on 5 second calls or 24 second calls, usually. This is an increasing source of error as 24 second calls continue to rise with a slower paced game. It is still minor and Doug sometimes gets them, but I have compared his numbers with official NBA stats and his always have too few team turnovers. This, I will reiterate, is no fault of Doug's. Doug does good work. I just wish he would show us his individual defensive stats, too.