The Three Point Revolution: An Economic Approach to Analytics

Mar 29, 2016

Basketball is changing; NBA players are shooting more three-pointers than ever before. Through 66 games in the 2015-2016 season, NBA teams are averaging 23.8 three-pointers per game, up from 22.4 three-pointers per game a season ago and from 18.0 three-pointers five seasons ago. This increase in three-point shooting has been accompanied by the rise of basketball analytics. Basketball analytics is the management of structured historical data, the application of predictive models that utilize that data, and the use of information systems to inform decision makers and enable them to help their organizations in gaining a competitive advantage on the field of play.

One useful approach to analyzing the rise of three-point shooting involves looking at field goal attempts in terms of expected value.

The expected value can be thought of as the long-run average value of repetitions of an experiment. The expected value can be calculated by multiplying each of the possible outcomes of an experiment by the likelihood that each outcome will occur and summing all of those values.

During the inaugural season of the three-point line (1979-1980), teams made an average of 48.8% of their two-point field goal attempts, and 28.0% of their three-point field goal attempts. Thus, the expected values of a two-point and three-point shot in 1980 were, respectively:

.488*2 + .512*0 = .976

.280*3 + .720*0 = .840

During the 2014-2015 season, teams made an average of 48.5% of their two-point field goal attempts, and 35.0% of their three-point field goal attempts. Thus, the expected values of a two-point and three-point shot in 2015 were, respectively:

.485*2 + .515*0 = .970

.350*3 + .650*0 = 1.050

All else equal, on average, taking a three-point shot now has a higher expected value than a two-point shot. While the expected value of a two-point shot has remained relatively constant over the last 35 years, the expected value of a three-point shot has increased as players have become more proficient three-point shooters.

However, expected values do not tell us that all players should only take three-point shots. This analytic tool only measures the probability-weighted average of all possible values and does not take into consideration specific in-game circumstances, such as player abilities, team attitudes towards risk, or opposing team defensive schemes.

In this case, expected values give us some insight into the recent trend of increased three-point shooting and perhaps why teams have gone from averaging 2.8 three-pointers a game in 1980 to 23.8 three-pointers a game in 2015. Expected values can also help explain why the three-point proficient Golden State Warriors, currently attempting 30.9 three-point shots per game–roughly seven more than the league average–are the favorites to win a consecutive championship. 

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