Sunday’s New York Times Magazine had a fascinating article about sports and data analysis by Michael Lewis. Lewis is the author of the 2003 best-seller Moneyball, which profiled a new breed of baseball analysts who revolutionized how major-league baseball players were valued (or undervalued) in the 1990s. In Sunday’s article Lewis does the same thing for the NBA, focusing in particular on Houston Rockets forward Shane Battier.

Battier is mediocre at best in every traditional measure of performance: points, assists, rebounds, blocked shots, steals, and so on. He even lacks athletic ability. “He can’t dribble, he’s slow and hasn’t got much body control,” according to Houston general manager Daryl Morey. Yet he’s one of the most valuable players in the NBA, measured by the fact that when he’s on the floor, his team wins, and when he’s not, they don’t. The subtle reasons for this, and how the Rockets came to discover and measure them, make for a great read.

In one statistical measure of Battier’s effectiveness, he’s clearly in the same league as perennial all-stars. Lewis explains,

One well-known statistic the Rockets’ front office pays attention to is plus-minus, which simply measures what happens to the score when any given player is on the court. In its crude form, plus-minus is hardly perfect: a player who finds himself on the same team with the world’s four best basketball players, and who plays only when they do, will have a plus-minus that looks pretty good, even if it says little about his play. Morey says that he and his staff can adjust for these potential distortions — though he is coy about how they do it — and render plus-minus a useful measure of a player’s effect on a basketball game.

I won’t be coy. Here’s how I would extract the individual “plus-minus” metric for Player X (NBA teams, take note):

1) Put every point scored and every player substitution from all NBA games in a season into a online database. Make sure each score and substitution is recorded in order, with a time stamp.

2) Calculate the average number of points scored and allowed per minute while Player X is in the game. The difference between them is the net impact, or the plus-minus.

3) Subtract the contribution of the other players in the game, averaging them by time spent in the game. For example, if Player X’s team averaged a 1-point gain per minute while he was in, but the other four players have a combined average of 0.9 points gained per minute, then Player X gets credit for 0.1 point per minute. Similarly, subtract the contribution of the five opposing players. The result is Player X’s individual plus-minus.

This recipe contains a chicken-and-egg problem. To calculate Player X’s individual metric, we have to know the other players’ individual metrics, which in turn requires knowing Player X’s. The circular dependency can be solved by doing the calculation iteratively. That is, calculate each player’s metric by assuming all other players have a metric of 0 (a neutral impact on the game). Plug those results back into the formula to get a second, better set of results. Keep repeating the calculation until the numbers stop changing.

TrackVia doesn’t do this out of the box, of course, but it does have a very powerful custom logic capability. So if any NBA teams are interested in trading data analysis tools for season tickets, let’s talk!