Stat of the week: 1.047, the expected value of any Brewer field-goal attempt.
Each season since 2010-2011, three-point attempts per game have gone up in the NBA, reaching an all-time high this year at 33.7 (
Steph Curry is largely credited with jump-starting the three-point revolution in the NBA. He ranks third all-time in three-pointers made, and has played seven seasons fewer than the two players, Ray Allen and Reggie Miller, with more (Land of Basketball.com, “NBA All-Time 3-Pointers Made Leaders,” 02.02.2020). He made NBA executives question their long-held offensive beliefs—the conventional wisdom that said driving into the paint for an easy bucket was the best way to score.
However, three-pointers are worth 50 percent more than a bucket in the paint. Using the simple idea of expected value, a team that shoots 30 percent from beyond the arc and 40 percent from the field otherwise would average .303 = 0.90 points for every three attempted and .402 = 0.80 points for every two-pointer attempted. Seemingly ignorant of this simple math, coaches and teams kept three-point attempts down since the three-point line was introduced in 1979, as low as 17 per game as recently as the 2006-2007 season.
Is Vassar keeping up with the revolution, or do the Brewers need to shoot more threes? This year, they’ve shot a 34.9 percent clip from beyond the arc and 48 percent from the field otherwise. That puts their expected value for threes at .349(3) = 1.047 and their expected value for two-pointers at .48(2) = .96. Indeed, it seems like they should continue to increase their three-point attempts. Yet, we have neglected to look at free throws in this experiment, and free throws are far more likely to occur on two-point possessions. The Brewers are making an excellent 74.4 percent of their
It’s optimal for all of your shots to have the same expected value; this means you don’t need to take any more of either kind of shot at the expense of the other. This in mind, the Brewers should just keep doing what they’re doing. Shooting optimally and with a record of 13-6, the rest of the Liberty League should watch out for our Brewers!
[Correction: An earlier version of this article included calculations that omitted the necessary parentheses. The parentheses have been added.]