The NBA playoffs are about to begin. Sports announcers and writers again will hype the game, especially long shots from outside the three point arc. The common refrain I hear is that teams should take more 3 pointers because they are worth 50% more than 2 pointers.

This statement while factually correct is just plain wrong.

A great example is Ben Cohen’s Wall Street Journal article. To explain why teams should be taking more 3s he quotes Golden State Warriors president of basketball operations Bob Myers saying “The idea that 3 points is 1.5 more times than 2 sounds simple, but it took a lot of time” for NBA teams to understand.

The idea that NBA basketball teams made a mental mistake until the Golden State Warriors’ Steph Curry came along and showed them the value of a three pointer is mistaken. The mistake comes from not understanding expected value. I talked about expected value in my post about risk (read it here or here).

In simple terms, when dealing with any risky situation, which includes taking a shot in basketball, the key idea is to know **both** the chance success will occur (the shot goes in) and the payoff (how many points are scored). When the chance is multiplied by the payoff we get the “expected value” of a situation.

When a basketball player shoots for two points, they are typically much closer to the basket. Being closer improves the chance the shot goes in. NBA.com’s stats page at the end of the 2018 season shows the average team made 55.6% of shots from two point range. This means when the typical NBA team puts up a two point shot the coach expects that shot will boost the team’s score by 55.6% X 2 points = 1.11 points.

Being outside the three point arc makes the shot more difficult since it is farther away. Because it is more difficult an extra point is awarded. Being more difficult also reduces the chances the ball goes in. NBA.com’s stats page also shows the average team made 36.4% of shots from three point range. This means the expected value is 36.4% X 3 points = 1.09 points.

For the typical NBA team it is not a simple trade-off. Currently, for most teams taking a three results in almost the exact same expected points as taking a two.

However, not all teams are average. The reason why Golden State loves the three is that Steph Curry is well above average. His lifetime 3 point percentage is currently 43.6%. While the typical NBA teams expects 1.09 points when their player shoots the three, Golden State expects 43.6% X 3 points = 1.31 points when Curry throws up a long range shot.

While an extra 0.2 points doesn’t seem like much, NBA teams take a lot of shots every game and that small advantage snowballs into a winning formula for Golden State. Golden State wins by taking long range shots. However, this doesn’t mean every basketball player and team should start taking shots from center court. Being a consistent scorer down low to the basket can be a better strategy than being an inconsistent scorer from way outside.

So what should anyone from NBA coaches to weekend warriors do with this information? It is pretty simple. Don’t just count the points made. Count the number of shots too. With both numbers it is easy to calculate the percentage of shots made in 2 and 3 point range. Plug those two percentages into the expected value formula and it should be pretty obvious what kinds of shots you or any team you follow should take.

You’re missing an important point. Teams are encouraged to shoot from 4 feet in where to success rate is very high and worth as much or more than 3-pointers. That high conversion rate skews the expected value of 2-pointers. From 5 feet to the 3 point line has a lower expected value than 3-pointers and when compared to midrange jumpers 12-20 feet, it’s not even close. The math is not that complicated and the NBA has it right.

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