# Making The Little Ones Count: Introducing Free Throw Plus

By John Ezekowitz

This post can also be found at College Hoops Journal

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 also are number one 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 not only the best percentage of 2011 by a wide margin, but also the best percentage of the past decade.

But free throw percentage only tells a part of the story. Wisconsin only attempts 26.79 free throws per 100 possessions, good for 297th in Division-I. While the Badgers may be extremely good at closing games 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 stats: free throw percentage and free throw rate. They each tell a piece of the story of how a team performs at the stripe, but are both 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.

What I first did was calculate two new stats: 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 gave me an estimate of the number of 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 that a team would score on those possessions if they had not been fouled. This table for Wisconsin will help illustrate the calculations:

Thus FT+ represents how many extra points a team gets by getting 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, a number of very good teams rank very poorly in terms of FT+. This shows that 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 shoot better than 67%) 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 and 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). San Diego State not only does not shoot free throws well, they also do not get to the line often. This double whammy is certainly cause for concern for SDSU. A poor FT+ caused by a combination of poor free throw shooting and an inability to get to the line can indicate trouble for a team.

This analysis of FT+ has only just begun and it is far from a finished stat. It also leaves out two important factors which must be noted. It ignores 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 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 may be simultaneous causality: better teams lead games late more often, and thus get to the line more often because of intentional fouls committed by the other team. This bias does not concern me as much as the best teams blow out opponents fairly often and thus do not get this added benefit all of the time, and 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 would welcome any thoughts you might have on the stat or its interpretation. The full 2011 FT+ rankings through February 1st can be found right here.

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## 5 Comments

• What does the 3.74 FT+ for Pittsburgh mean? They are losing 3.74 points per 100 possessions from their FT’s? If so, why is it a positive numbers.

• Wait, I see now. The way that table of ten was sorted was confusing.

• jezekowitz says:

Sorry about the sort. No team in my sample actually lost points by going to the free throw line (which makes sense). The average so far this year is 6.27 with an sd of 1.27.