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# A stat is born

 (Graphic by David Schutz/Globe Staff)
February 27, 2011

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In basketball, success at free throws is measured by two standard statistics: “free-throw percentage,” or how good a particular player or team is at scoring on free throws, and “free-throw rate,” the rate, compared with all team possessions, at which a team’s players attempt free throws.

But John Ezekowitz wanted to know exactly how much free throw points matter in the bigger picture, so he devised a new statistic. He called it “free throw plus,” or FT+.

What he found is, the impact of free throws very much depends on the team. The Oklahoma City Thunder has, by far, the highest FT+ in the NBA. Its players shoot free throws more often than any other team (15.5 percent of possessions as of earlier this month, when the numbers in the chart were run) and, once at the line, its players score 83 percent of the time, the league’s highest rate. The Celtics rank 27th for FT+.

“A low free throw plus is not necessarily a bad thing,” says Ezekowitz. “It could mean that the opportunity cost of going to the free-throw line for a team is high because their regular offense works so well. Teams with low FT+ numbers are susceptible in close games, however, because FT+ identifies teams that are both bad at getting to the line often and bad at sinking free throws.”

To calculate FT+, Ezekowitz, with fellow members of the Harvard Sports Analysis Collective, first calculated two new statistics: “free throws made per 100 possessions” and “free throws attempted per 100 possessions.” The next step was to multiply free throws attempted per 100 possessions by .475, the accepted conversion factor for free-throw attempts into possessions. This showed how frequently a team goes to the free-throw line. Then, he took that number and multiplied it by the team’s “non-free-throw offensive rating” to estimate “the expected points that a team would score on those possessions if they had not been fouled.”

• February 27, 2011 cover