Quick confession: my initial impressions of “traditional points” was that they seemed pretty arbitrary and so I opted for a categories league for the inaugural season of Ottoneu Basketball. But a few weeks into the season, I was curious about how traditional points compared to some basic empirically based point values. Spoiler alert: quite well, somewhat to my surprise.
To investigate, I took player game-level logs for every game through 11/05/21. I then constructed a simple binary outcome measure: 0 if loss, 1 if win. I then conducted what is called a probit panel regression (grouped by team). The probit regression yields coefficients that measure the marginal increase in the probability of winning based on a one unit increase in each category: PTS, REB, AST, STL, BLK, TOV, FGM, FGA, FTM, and FTA. There were nearly 3,000 observations.
Because of the correlation between these statistics (i.e., multicolinearity) as well as the relatively small sample size (i.e., micronumerosity), I decided to run separate probit regressions for each category along with MP to control for the impact of playing time of the counting statistics.
Here are the coefficients from the separate probit panel regressions (most were statistically significant):
- PTS: 0.0219
- REB: 0.0258
- AST: 0.0360
- STL: 0.0840
- BLK: 0.0573
- TOV: -0.0313
- FGM: 0.1127
- FGA: -0.0513
- FTM: 0.0736
- FTA: -0.0273
To convert these to point values (except for FGM, FGA, FTM, and FTA), I used the PTS coefficient as a numeraire. That is, I divided each coefficient by 0.0219. Here were the resulting point values (rounded to the nearest integer in parentheses):
- PTS: 1.00 (1)
- REB: 1.18 (1)
- AST: 1.64 (2)
- STL: 3.83 (4)
- BLK: 2.61 (3)
- TOV: -1.43 (-1)
To convert the last four categories, I ran FGM and FGA simultaneously as well as FTM and FTA together and then used the coefficient for FGM as a numeraire and multiplied by two (to match traditional points). This yielded:
- FGM: 2.00 (2)
- FGA: -0.91 (-1)
- FTM: 1.31 (1)
- FTA: -0.48 (0)
If you’re familiar with traditional points schedule, these rounded values will look very familiar. With just a couple of exceptions, they are nearly identical: BLK is 3 instead of 4, TOV is -1 instead of -2, and FTA is 0 instead of -1 (and in case of the latter, it’s just a few hundreds away from rounded down to -1). These deviations can possibly be attributed to the small sample size; that is, it’s within the realm of possibilities that with additional data, the adjusted coefficients will match even more of the categories.
So for those looking for something analogous to FGPts for basketball (i.e., something with an empirical basis), I think traditional points compares very favorably; they’re just rounded to the nearest integer. But they convey the relative importance of each statistic on the marginal probability of winning.
EDIT: I was a little imprecise in my original writeup. The probit coefficients themselves are not the marginal probabilities; the marginal probabilities are a function of the probit coefficients.