Making the little ones count: Introducing Free Throw+

All college basketball teams are unique, but some are more unique than others. If we could quantify uniqueness (don’t tempt me), Wisconsin would certainly be near the top.

The Badgers, darlings of the tempo-free community for years, are not only the slowest team in the country on a possessions-per-game basis; they are No. 1 in turnover percentage. But the number that really jumps out is their free-throw shooting. Wisconsin shoots an ungodly 81.8 percent from the line as a team. That is the best percentage of 2011 by a wide margin—and the best percentage of the past decade.

But free-throw percentage is only part of it. Wisconsin attempts merely 26.79 free throws per 100 possessions, good for 297th in Division I. While the Badgers might be extremely good at finishing off opponents from the free-throw line, they do not get there often over the course of the game.

This is symptomatic of a larger problem with the two main free-throw-related statistics: free-throw percentage and free-throw rate. Each tells a piece of the story of how a team performs at the stripe—and each is incomplete without the other. How do we reconcile them?

To fix this problem, I’ve created a new stat I am calling Free Throw+ (assist to Luke Winn for the name). FT+ represents how many points a team gains at the free-throw line over the course of the game (or 100 possessions). I am indebted to the contributions of Michael James and my friends in the Harvard Sports Analysis Collective for helping me come up with the framework for it.

The first step was calculating two new statistics: Free Throws Made Per 100 Possessions and Free Throws Attempted Per 100 Possessions. I then multiplied FTA/100 Poss by .475, the generally agreed-upon conversion factor for free-throw attempts into possessions. This produced an estimate of the possessions (out of every 100) that a team spends at the free-throw line. I multiplied this by the offensive rating of the team to estimate the expected points a team would score on those possessions, if not fouled.

This table for Wisconsin will help illustrate the calculations.

Free Throw+ represents how many extra points a team gets by being fouled and shooting free throws, rather than simply playing offense. The significance of FT+ can be explained by showing the ten worst teams in terms of FT+ so far this year.

As you can see, several very good teams rank very poorly in terms of FT+. This shows FT+ is not necessarily a red flag. Teams like Pittsburgh, Washington and Kansas rank poorly in FT+ because of their combination of poor free-throw shooting (none shoots better than 67 percent) and efficient offenses. For these teams, the opportunity cost of a trip to the free-throw line is fairly high: They do not convert especially well from the stripe, but they do score efficiently from the floor.

But San Diego State? That’s another story. All of the other elite teams in this table get to the line effectively. (Pitt does it especially well.) Not only does San Diego State not shoot free throws well, but the Aztecs do not get to the line often. This double whammy is certainly cause for SDSU’s concern. A poor FT+ caused by a combination of poor free-throw shooting and an inability to get to the line can indicate trouble.

This analysis of FT+ has only just begun, and it is far from a finished statistic. Two important factors are lacking. Ignored is the effect of getting the opponent into foul trouble, another added bonus of getting to the line often that does not depend on making free throws. Also, as I mentioned earlier, teams that are good at shooting free throws can salt games away at the end more easily when they are ahead. This important quality is not accounted for in FT+ presently.

Additionally, there might be simultaneous causality: Better squads lead games late more often and thus get to the line frequently because of intentional fouls. This bias does not concern me as much, as the best teams blow out opponents fairly often and as such do not get this added benefit always. Plus, more average teams play closer games, in which they may benefit from intentional fouling. This really only seems to be a source of bias for the worst teams in college basketball.

I certainly intend to continue looking into FT+ and FT+ per-game, including analysis of previous years. I welcome any thoughts you might have on the stat or its interpretation.