An Elam Ending Win Probability Calculator


Despite the muted enthusiasm (and questionable judgment) surrounding this year's NBA All Star game, most would agree that bringing back the Elam Ending this year was a good call.

The Elam Ending is a fairly radical departure from the traditional rules of basketball, although one that strives to preserve what we all like about basketball, while preventing the slow, boring endgame situations that the traditional rules encourage.

While I'm still skeptical that the NBA will ever adopt the Elam Ending outside of exhibition situations, that didn't stop me from coding up an Elam Ending win probability calculator. Feel free to use this as you follow along to tonight's All Star Game.

Link: Elam Ending Win Probability Calculator

Methodology

We don't have a robust data set of actual Elam Ending games to pull from, so to create win probabilities, we have to do the next best thing: simulate them [1].

Each possession is modeled independently, with the following assumptions:

Simulated outcome of each possession
PointsProbability
0 points50.5%
1 point3.1%
2 points32.5%
3 points13.7%
4 points0.2%

These probabilities reflect the actual point frequency for all possessions from the pre-Covid 2019-20 NBA season. Each game state is simulated 10,000 times to estimate win probability.

To specify game state for the Elam Ending, you need to know three things:
  • Distance to Target Score: How far away the leading team's score is from the established target score that determines the end of the game.
  • Leading Team Scoring Margin: How many points the leading team is ahead by
  • Possession: Whether the leading team has possession or not
Currently the calculator goes up to a "distance to target score" of 24 points, corresponding to the All Star Game rules for the 4th quarter. A typical Elam Ending starts with a much lower target score (usually 8 points).

One use of this tool, particularly if the NBA wants to get serious about the Elam Ending, is to see how well Elam Ending win probabilities line up with actual NBA win probabilities in similar situations. For example, a team with a 5 point lead with 3:30 left in the game has an 88% win probability. For the corresponding Elam Ending situation, a team would have an 87% win probability. A pretty good agreement, at least for this spot check.

I'm also sharing the (poorly documented, likely inefficient) R code I used to create the simulations. Here's the gist

Footnotes

[1] When building a win probability model, always use actual games and game results whenever possible. The game is not played on a spreadsheet (or in RStudio, or on a Jupyter notebook, etc.) and you never know what sins of omission you are making when crafting your simulation assumptions.

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