Optimizing Pick-up Basketball (Shot Selection)
By: Tony Tao
Tags: Analytics, Sports, Basketball

One of my favorite hobbies is pickup basketball. One question I often ask myself is whether shot selection actually makes a difference in pickup basketball games, and how much of a difference. We all know that trying to shoot over someone much taller is bad, and an open layup is good in basketball. Let’s run a simulation to try to figure that out.

The data set I’m pulling is pretty primitive, and is the Woollen Gymnasium data set ( Powell, Adam (2005). University of North Carolina Basketball. Mount Pleasant, S.C.: Arcadia Publishing. ISBN 0–7385–4150–8). The only thing we are going to be using is the scoring probabilities, and extrapolating that this data fits the average pick up game.

This is how pickup basketball games are scored:

Field goals are 1 point and shots beyond the arc are 2 points.

Based on data, the probability of making a 1 point shot is: 42%. The expected value of shooting a 1 point shot is therefore 1 point x 0.42 = 0.42.

The probability of making a 2 point shot is: 28%. The expected value of shooting a 2 point shot is therefore 2 point x 0.28 = 0.56.

The probability of making a layup (closest shot to the basket) is 60%. The expected value of a layup is therefore 1 point x 0.60 = 0.60.

A team turns the ball over before attempting the shot 10% of the time.

The offense shoots a 2 point shot 33% of the time and a 1 point shot 67% of the time.

The simulation i’m running assumes that on each possession, the team either attempts to shoot the ball or turns it over. In this simulation if the team doesn’t turn it over, they will attempt to shoot the ball. Fouling has been removed from the simulation, but since both team can foul, it probably does not drastically affect the takeaways from this simulation. We don’t make any assumptions on the distribution of shots among the team.

This bring us to our first hypothesis in 1 point / 2 point games. What if your strategy was to take only layups or 2 point shots since these shots give the highest return? Also, this gives you options. If you are a big player, it’s probably good to try to make a lot of layups and if you are a smaller player, you can use quickness to get open for 2 point shots.

We shall test this hypothesis using a simulation. Let’s run 1 million games where the player only takes 2 point shots on their possession:

Your probability of winning a game to 7 increases by ~2.66%

Your probability of winning a game to 11 increases by ~3.68%

Your probability of winning a game to 15 increases by ~4.42%

Your probability of winning a game to 21 increases by ~5.02%

Next we will run 1 million games where the player only takes high percentage layups:

Your probability of winning a game to 7 increases by ~ 4.96%

Your probability of winning a game to 11 increases by ~ 5.89%

Your probability of winning a game to 15 increase by ~6.67%

Your probability of winning a game to 21 increases by ~7.76%

In conclusion, a good strategy to follow is: Only take layups or shots beyond the arc with layups being preferred in a 1 point / 2 point game. In a game to 11 you are 3.68% to 5.89% more likely to win the game given equal skill and the opposing team takes a wider array of shots. Although in reality, if you forgo shooting mid range shots, this may affect your scoring probability on layups and 2 point shots. The world is messy…