APBRmetrics

[Ed Küpfer]

Here's a question: if a team is trailing in the latter part of a game, what strategy would be more likely to produce a comeback? There are lots of ways to answer that. Here's the simplest:

Assume that there's only two strategies available to the team:

• Chucking up three pointers quickly and fouling the opposing team as soon as they gain possession. Call this the 3 Point Strategy.
  
• Shooting two pointers quickly and fouling the opposing team as soon as they gain possession. Call this the 2 Point Strategy.

Neither of these are very realistic, but I didn't want to complicate matters. Of the two, most of you will probably guess that the comeback is most likely using the chuck-a-three. But it's fun to put some numbers to these types of questions. To that end, I created a spreadsheet which calculates the comeback probability, based on a few variables:

1. The number of points the team is trailing by.
   
2. The team's 3 point shooting accuracy.
   
3. The team's 2 point shooting accuracy.
   
4. The opposing team's free throw shooting accuracy.
   
5. Possessions remaining in the game. This variable depends in turn on three other variables:
   1. The time remaining in the game.
      
   2. The number of seconds into the shot clock at which point the team shoots.
      
   3. The number of seconds into the shot clock at which point the team fouls.
      

The spreadsheet, which I'm calling the Comeback Probability Toy, assumes that both of the strategies require the team to shoot the ball at a given point in the shot clock, the same on each possession; and for the team to foul at a certain point, the same in each possession. The Toy allows you to change these values to whatever you want.

Example scenario: a team down 5 points with 30 seconds remaining. The team shoots 50% on 2-pointers, 33% on 3-pointers. Their opponents shoot 70% on free throws. Team will chuck a shot 5 seconds into the shot clock, and will foul one second after opponents gain possession. What is the probability of a comeback? The Toy says the 2 Point Strategy results in a comeback less than 1% of the time, while the 3 Point Strategy works about 4% of the time.

How about: down 2, 30 seconds left, same shooting percentages, same shooting and fouling times? The Toy says the 2 Point Strategy results in a comeback 10% of the time, while the 3 Point Strategy works 16% of the time.

Of course, reality is more complex, and nobody would ever opt to use an all-two- or all-three-point strategy. I have to make it clear that the probabilities produced by the Toy rely heavily on the assumptions built into it, and these assumptions bear little resemblance to what happens in an actual game. But I am not trying to model reality here. I am trying to coontrast two reductio ad absurdum strategies in order to have a baseline for comparison.

You can download the Comeback Probability Toy at my Yahoo page, in the files section.
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ed