# A Better Statistic

A Better Statistic

According to NBA rules, a made shot from behind the designated arc surrounding the basket, known as the 3-point line, is worth 3 points. A field goal made from within this arc is worth 2 points. A 3-point shot is worth 1.5 times more than a 2 point shot. Charles Barkley can do that math. In essence, the NBA is stating that a 3-point shot is 1.5 times more difficult than a 2-point attempt. The problem with this statement is that for every NBA season for the last 30 years that was absolutely false. In 2016, The league average 3-point percentage was 35.4%, while the league average percentage on 2 point shots was 49.1%. Meaning, the expected value on the average 3-point shot was 1.062 (3 *.354) while the expected value on the average 2-point shot was .982 (2 * .491). Furthermore, the average 3 point shot was not 1.5 times harder than the average 2-point shot.

The rise of “effective field-goal” percentage as an important metric in evaluating a player’s offensive value is built on the fact that a 3-point shot is 1.5 times more valuable than a 2-point shot. If player A shoots 1000 3-pointers and zero 2 pointers while shooting 34.4%, his “effective field goal percentage” comes out to 51.6%; meanwhile, if Player B shoots 1000 2 pointers and zero 3-pointers while shooting 51%, his effective field goal percentage is 51%. “Effective field goal percentage” implies that Player A is more valuable to his offense than Player B is to his. However, my new statistic: “Difficulty-Adjusted Field Goal Percentage” portrays how Player A is significantly easier to replace than Player B, due to scarcity and league averages. Player A’s Difficulty-Adjusted Field Goal Percentage comes out to 47.7%, while Player B’s Difficulty-Adjusted Field Goal Percentage remains 51%.

“Effective Field Goal Percentage:”

(FGM + (0.5*3PM)) divided by (FGA)

(FGM + (Yearly Difficulty Coefficient*3PM)) divided by (FGA)

Let me explain myself. The “Yearly Difficulty Coefficient” signifies how much more difficult the average 3-point shot was for the given season. Let’s take 2015–16 season for example. I discovered that the average 3 point shot attempt was 1.387 times harder than the average 2 point shot. Discovery explained:

Expected value on 2 point shot = (Shooting percentage on 2 point attempts in 2016) * (2)

(.491) * 2 = .982

In order to make the expected value of the average shot from beyond the arc equal the expected value of the average 2 point shot you must discover the “true value of an outside shot”:

(3-point shooting percentage) * (“True value of outside shot”) = .982

(.354) X = .982

X = “True value of an outside shot” = 2.774

2.774/2 = 1.387

Concluding that the average 3-point shot in 2015–16 season was 1.387 times more difficult than the average 2-point shot.

Soooo. If you’re still with me, that means that the 2015–16 “Difficulty Coefficient” is equal to .387. Making the 2015–16 “Difficulty-Adjusted Field Goal Percentage” formula:

(FGM + (.387*3PM)) / FGA

“Difficulty-Adjusted Field Goal Percentage” provides front offices with a better idea of how valuable a player’s shooting is for an offense compared to “Effective Field Goal Percentage” For example, a GM will have an easier time finding a player who can shoot at least 34.4% from 3-point land than they will finding a player who shoots at least 51% from inside the arc. (During the 2015–16 NBA season, only 55 qualified players shot 51% or better from inside the arc, while 106 qualified players shot at least 34.4% from 3-point territory.)

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