The Game Theory behind the Deep 3 in the NBA
https://fansided.com/2018/07/31/nylon-calculus-game-theory-deep-3/
This article was a fascinating read on the game theory behind shooting the deep 3 in basketball. In basketball, a player can shoot from anywhere on the court. A made basket counts for 2 points normally or 3 points if it is shot from behind the 3-point arc. In this age of basketball, teams try to be as efficient as they can in terms of shot selection. The result is that efficient players nearly exclusively shoot from right under the basket for an easy 2, or from right behind the 3-point arc for a relatively easy 3. It doesn’t make sense to shoot a long 2 or 3 because those shots are worth the same as shooting it closer, but they are harder to make. With this in mind, lets talk about why a player would ever shoot a deep 3 – which is a 3 point shot from significantly behind the 3-point arc – when it is the hardest shot to make in a game.
The article simplifies the strategies each team has during a possession to the following: the offense can either take the ball to the rim for an easy 2, shoot right behind the 3-point arc for a regular 3, or launch a deep 3; and the defense can either press up to half-court to defend the deep 3, stick a balanced defense around the arc to defend the regular 3, or pack the paint to defend the easy 2. The resulting payoff matrix looks like the following, where a green circle corresponds to a wide open shot, a yellow circle to an average shot, and a red circle to a tightly contested shot:
The article proceeds to show what this payoff matrix looks like for some of the most elite shooters in the NBA. To do this, the author makes a few assumptions. The first assumption (which is based on an academic paper by Sandy Weil) is that tight defense reduces a player’s shooting efficiency by 12%. The second assumption is based on the first and says that an open shot increases a player’s shooting efficiency by an equivalent 12%. Based on these assumptions and the strategies posed above, we get the following payoff matrices for Steph Curry and James Harden, arguably the two best shooters currently in the NBA:
The payoff matrices show the expected amount of points each player would receive given their strategy on offense and the opposing team’s strategy on defense. It is apparent from the matrix that shooting a regular 3 for these players is a dominated strategy – that is, there is always each player always has a better strategy than shooting a regular 3, and one of those strategies is shooting a deep 3. This is only a good strategy when the defense decides to pack the paint to defend the easy 2. This leaves the offensive player wide open to take a deep 3. For most players, shooting the deep 3 might not actually yield a higher payoff than a regular 3. But for elite shooters like Steph Curry and James Harden that are capable of taking such a difficult shot, an open deep 3 yields a much better payoff than shooting a regular 3 for 2 out of the 3 strategies the defense can employ.
This article ties into the topic of Game Theory and Mixed Strategies we learned in class. In fact, the article computes the mixed strategies of the payoff matrices for both players and finds that for Steph Curry (the better shooter of the two), the equilibrium is at 40% deep 3’s and 60% runs to the rim, while for James Harden the equilibrium is at 38% deep 3’s and 62% runs to the rim. This was very surprising to me because the conclusion the article found was for these shooters to either take very efficient 2’s or very inefficient 3’s. This is contrary to popular belief, especially in the basketball world, but it makes sense if you really think about it. Sure shooting a 3 is easier the closer you are. But for players like Steph Curry and James Harden, shooting from 1 foot behind the arc and shooting from 10 feet behind the arc doesn’t make a huge difference. The thing that makes the biggest difference is how tightly the defense is guarding them. So it makes sense that to get a more open shot, a player can sacrifice a few feet, and this will have a positive impact on the player’s payoff. So the next time you see an elite shooter launch a deep 3 in a crucial part of the game, remember that it was probably a smarter move than it looks like.