Empirical Basis for Traditional Points

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.

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Fantastic work dude, this was something I was thinking about but didn’t have a chance to explore! Always enjoy your analyses, keep’em coming!

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Nicely done, thanks for this write up!

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So I was curious to see how this analysis held up with a complete season. As before, I ran a series of probit regressions with wins as the outcome and each statistic as a covariate along with minutes played for PTS, REB, AST, STL, BLK, and TO. For FGM, FGA, FTM, and FTA, I ran the pairs together without minutes played.

Here’s what I came up with (regular season only). First the probit coefficients (all were statistically significant):

PTS: 0.0225
REB: 0.0274
AST: 0.0454
STL: 0.0599
BLK: 0.0610
TO: -0.0343
FGM: 0.1270
FGA: -0.0624
FTM: 0.0772
FTA: -0.0549

To convert to points, I used PTS as the numeraire and divided PTS, REB, AST, STL, BLK, and TO by it. For FGM, FGA, FTM, and FTA, I used FGA as the numeraire and divided those coefficients to yield point values. Here are the raw points, followed by what it is rounded to the nearest integer (traditional points in parentheses):

PTS: 1.00 => +1 (+1)
REB: 1.22 => +1 (+1)
AST: 2.02 => +2 (+2)
STL: 2.66 => +3 (+4)
BLK: 2.71 => +3 (+4)
TO: -1.52 => -2 (-2)
FGM: 2.04 => +2 (+2)
FGA: 1.00 => -1 (-1)
FTM: 1.24 => +1 (+1)
FTA: -0.88 => -1 (-1)

As you can see, the results are similar to what was found midseason: traditional points nearly perfectly capture the marginal probability of each stat towards winning. The exceptions are the defensive statistics: STL and BLK. These only contribute +3 points to winning rather than +4. But that’s a pretty minor difference.

As I said in my initial post, I just played categories this past season because the points schedule seemed sort of arbitrary. But it’s really not: there’s convincing empirical evidence that they line up with the marginal probabilities associated with wins.

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