Crediting Basketball’s Three-Pointers

The adoption of the three-point field goal in basketball changed the game. Initially, its impact was limited, but in recent years, shooting three-point baskets has had a significant effect on game strategy and outcome.

Many sports fans can’t resist the lure of quantifying performance–ranking teams, rating players, and keeping various statistics. Now, statistician Thomas P. Ryan asks how best to credit three-point field goals so that the resulting numbers say something useful about how a game was played.

In the current issue of Chance, Ryan offers a new, improved formula for calculating field-goal percentage–a statistical performance measure that he describes as a composite field-goal percentage. He claims that calculating this particular quantity generates numbers that would better capture what happened in a game than is now possible.

Before 1987 in college basketball, box scores recapping a game simply gave the field-goal percentage, reflecting the proportion of two-point field-goal attempts that were successful. With the advent of the three-point shot, a new category was added to the box score: the three-point field-goal percentage.

The trouble, says Ryan, is that the two field-goal percentages, taken together, don’t always let you to “see” what happened in a game. It’s often hard to tell which team had the better shooting performance.

Ryan cites a game between North Carolina State and Clemson, which took place on Jan. 15, 2002. N.C. State defeated Clemson 80 to 79. Yet Clemson’s overall field-goal percentage was 61.2 percent, and N.C. State shot just 49.1 percent. Moreover, Clemson had a sizeable rebounding advantage, 32 to 20, made five more free throws, and had five more turnovers. Why did Clemson lose?

One important factor is reflected in the respective three-point field-goal percentages: 48.4 percent for N.C. State and 41.7 percent for Clemson. That’s not enough, however. “We also need to know the relationship between the number of three-point field goals attempted and the number of two-point field goals attempted,” Ryan contends. Indeed, N.C. State attempted more three-pointers than twos (31 versus 26), whereas Clemson settled for far more twos than threes (37 versus 12).

“This helps us see why N.C. State won, but it would be easier to see that if we used a more appropriate field-goal percentage,” Ryan says.

Ryan proposes the following formula:

C = (a + 1.5b)/N, where a is the number of two-point field goals made, b is the number of three-point field goals made, and N is the total number of field-goal attempts.

Applying that formula to the Clemson-N.C. State game, N.C. State’s composite percentage was 62.2 percent and Clemson’s was 66.3 percent. That’s much closer to what happened in the game than was indicated by the box score differences, Ryan remarks. “The proper statistics essentially show that it was an even game–which it was,” he adds.

The new statistic also corrects for the downward trend in team field-goal percentage calculated for a full season, evident after 1987. “Does this mean that the ability to shoot a basketball is in recession?” Ryan asks. “Obviously, that is not the case.”

For example, Missouri holds the National Collegiate Athletic Association (NCAA) Division I record for team shooting: 57.2 percent. The record was set in 1980, before the advent of the three-point field goal. In 2002, a highly regarded Kansas team shot “only” 50.6 percent for the year yet was the best in the country. The team’s composite field-goal percentage, 55.1 percent, would be a better reflection of its superior performance, Ryan argues.

Ryan insists that the composite field-goal percentage is also important for properly rating individual shooting performance, not only at the high school and college level but also in professional basketball. “It would undoubtedly be easier to evaluate players and teams at all levels if the composite field-goal percentage were used,” he concludes. “College recruiters and rating services would have an easier time rating high school players if they used the composite percentage to gain better insight into how well, for example, ‘shooting guards’ actually shoot.”

Ryan has proposed his new statistic to the NCAA, but so far the organization has taken no action. He hasn’t given up, however. “Let’s apply our statistical skills to try to improve our understanding [of] and insight into the game of basketball,” he declares. “Surely there is much that can be done.”