Pick up basketball: Should you shoot more 2 pointers or 3 pointers when you play winners’ take?

The NBA basketball season just started last week, and the three point shot is having its moment. Despite some high profile doubters, the Warriors are the reigning NBA champions due to very impressive three point shooting. Also, the total number of three pointers taken in the NBA has steadily risen over the past 35 years.

Is it better to take a three pointer or a two pointer? The theory behind this is pretty simple, and can be done without a spreadsheet. Because a three pointer is worth 50% more than a two pointer, if a team can hit three pointers with at least 2/3 the percentage that they hit two pointers, then they would be better off taking more three pointers.

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Okay, now moving on to something useful: how this applies to pick-up basketball.  In pick-up basketball, one wrinkle that people play with is that 3 pointers are worth 2 points and 2 pointers are worth 1 point.  This essentially makes the three pointer worth double the two pointer, and makes the three pointer the optimal shot if the three point percentage is at least 1/2 the two point percentage.

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Another wrinkle in pick-up basketball is that people often play winner’s take, which means when you make a basket you get to keep possession, and thus likely get another shot opportunity. How might this affect the relative values of the two and three point shots? A quick thought about the problem suggests that playing winner’s take make you want to take more two point shots, because two points shots have a higher percentage and will result in getting the ball back more frequently. But how much?

We add in a column for “Point value of the next possession”. Here we’ll take the simple  approach and assume two pointers and three pointers are shot with the same frequency in the next possession. Now the value of the two pointer is worth more than the three pointer:

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We find that the three pointer percentage needs to be 37.5%, or about 63% the two point shooting percentage to be even, up from 50% previously.

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Okay, I’m guessing no pick-up basketball player in the history of pick-up basketball is tracking their shooting percentages closely enough to detect the difference between 30% and 37.5% shooting. But let’s complete the analysis by looking at the range of different two and three point shooting percentages in a data table. Here the data table output is the Expected points per shot of the two pointer minus the points per shot of the three pointer – when the box is red, the two pointer is better, and yellow if the three pointer is better. One interesting finding is that the ratio of the equivalent three point percentage required relative to two point percentage seems to rise as two point percentage increases…so if you have DeAndre Jordan on your pickup team, keep passing it to him!image

Here’s the spreadsheet: Pick-up Basketball – 2 or 3 Pointer

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