During tourney-time, I played with some stats on how efficient teams were on offense and defense. In order to best evaluate this, one should look at how well a team does per possession, as opposed to per game or per minute. For instance Billy Tubbs’ Lamar team averaged 79.1 points per game last season, good for 15th nationally. But they used around 80 possessions per 40 minutes, the fastest pace in the nation. They averaged .963 points per possesion, which ranked 242nd nationally and partially exposes why they lost 18 of 29 games this year.

Across college basketball, teams average .994 points per possession. So Lamar’s offense was 3% less efficient than the average college team. And the average college team isn’t getting close to thinking about getting to the NCAA Tournament with something other than an automatic bid.

So how does one compute possessions?

Before I go any further, I have to recommend reading Dean Oliver’s Basketball on Paper. He does some creative stuff with basketball statistics. The only problem is that he deals with NBA statistics, but the concepts apply to the college game. You’ll learn a lot about the game after having read it. I’ll be refering to this book more in the future.

Commercial over.

The most common formula for estimating possesions is (FGA – OR) + TO + (Y * FTA),

where FGA = field goal attempts, OR = offensive rebounds, TO = turnovers, Y = some number between zero and 1, and FTA = free throw attempts.

Going through the three terms in the formula, a possession can end by:

1) a shot not rebounded by the offense. An offensive rebound would continue the possession. This is captured by the term FGA-OR.

2) a turnover. (duh.)

3) Free throws – sometimes.

The only mystery here is what Y should be. First off, I’ll clear up why Y needs to be there. We don’t know how many possesions are used up by free throws, that’s why. In the ideal situation, if every trip to the line resulted in two free throws, then we could multiply free throws by one half and be done with it. However, technical fouls, the "and one" situation, missing the front end of the 1 and 1, and shooting 3 shots resulting from a 3-point attempt all deviate from the ideal situation. Oliver estimates that Y should be .4. John Hollinger in Pro Basketball Prospectus estimates it to be .44. From the data I’ve seen for college hoops, .44 is more accurate so I’ve been using that.

So that’s how possesions can be estimated, and using possesions, folks can get a better understanding of which teams do good things on offense and defense.

You might wonder why offensive rebounds are treated as continuing a possesion, rather than starting a new one. I’ve seen two good reasons. First, by including them each team’s possesions can reasonably be assumed to come out equal for each game. Second, getting and preventing offensive rebounds are skills. So if some teams do those skills better than others, it makes sense to attach those skills to a team’s offensive or defensive ability.