Home Win Probability Using SRS

November 12, 2013

One of my favorite rating systems for NBA teams is the Simple Rating System (SRS). A team’s SRS rating is made up of two things: average margin of victory and strength of schedule. The rating is denominated in points above or below average, where zero is average.

These ratings can be used to estimate the probability that home team A will defeat visiting team B. Let me explain how I went about the process of converting SRS ratings into win probabilities.

I started by looking at all regular season games from 1976-77 through 2012-13 in seasons that ended in an odd number (i.e., 1976-77, 1978-79, etc.).

For each game I computed the difference between the home team’s SRS and the visiting team’s SRS.* In other words:

dSRS = hSRS – vSRS

* I should note that I used the team’s SRS at the end of the season, not the team’s SRS when the game was played.

I then built a logistic regression model using a home win indicator as the dependent variable (1 = home win, 0 = home loss) and dSRS as the independent variable. That model yielded the following equation for expected win probability:

p = 1 / (1 + e-(0.616591 + 0.166622 × dSRS))

For example, if the 2012-13 Miami Heat played the San Antonio Spurs in Miami, its win probability would be:

dSRS = 7.03 – 6.67 = 0.36
p = 1 / (1 + e-(0.616591 + 0.166622 × 0.36)) = 0.663

To test this model, I looked at all regular season games from 1976-77 through 2012-13 in seasons that ended in an even number (i.e., 1977-78, 1979-80, etc.).

I created “buckets” of games by rounding the SRS difference to the nearest one, then computed the actual and expected home winning percentage within each bucket. Here are the results for the buckets that contained at least 250 games:

dSRS Games Actual Expected
-11 306 0.206 0.229
-10 376 0.239 0.259
-9 435 0.278 0.293
-8 577 0.341 0.328
-7 631 0.385 0.366
-6 752 0.370 0.405
-5 901 0.425 0.446
-4 938 0.506 0.488
-3 1114 0.530 0.529
-2 1142 0.572 0.570
-1 1291 0.607 0.611
0 1248 0.646 0.649
1 1288 0.686 0.686
2 1147 0.733 0.721
3 1093 0.745 0.753
4 937 0.811 0.783
5 887 0.794 0.810
6 754 0.837 0.834
7 630 0.849 0.856
8 582 0.878 0.875
9 436 0.890 0.892
10 380 0.895 0.907
11 306 0.931 0.921

I was satisfied with the out-of-sample results, so I rebuilt the model using all regular season games from 1976-77 through 2012-13 and obtained the following win probability formula:

p = 1 / (1 + e-(0.613230 + 0.167546 × dSRS))

And here are the results for that model across all seasons:

dSRS Games Actual Expected
-14 251 0.131 0.150
-13 307 0.189 0.173
-12 478 0.205 0.198
-11 594 0.224 0.226
-10 725 0.263 0.257
-9 904 0.291 0.290
-8 1208 0.330 0.326
-7 1394 0.371 0.364
-6 1551 0.393 0.403
-5 1839 0.450 0.444
-4 2018 0.495 0.486
-3 2223 0.524 0.528
-2 2386 0.567 0.569
-1 2525 0.604 0.610
0 2443 0.640 0.649
1 2504 0.687 0.686
2 2400 0.725 0.721
3 2208 0.740 0.753
4 2011 0.795 0.783
5 1837 0.801 0.810
6 1545 0.844 0.835
7 1388 0.851 0.856
8 1205 0.885 0.876
9 904 0.894 0.893
10 729 0.909 0.908
11 600 0.928 0.921
12 484 0.934 0.932
13 308 0.929 0.942
14 254 0.945 0.951

For example, in a matchup where the home team has a +2 advantage in SRS, the home team would be expected to win 72.1 percent of the time, a figure that is slightly less than the actual result of 72.5 percent.

Now as I mentioned earlier, I used end-of-season results when calculating the difference in SRS, but you can use this within the current season with some minor modifications.

Based on some work by Tom Tango that is summarized a here, I’ve found that a team’s SRS within season should be adjusted as follows:

aSRS = (G × SRS + 12 × 0) = (G × SRS) / (G + 12)

In other words, I am adding 12 games of league average performance (SRS = 0) in order to get a better estimate of the team’s “true” talent level.

For example, tonight the New Orleans Pelicans (G = 7, SRS = 2.85) are playing the Los Angeles Lakers (G = 8, SRS = -4.91) in Los Angeles. In order to calculate the Lakers win probability, we first have to adjust each team’s SRS:

LAL aSRS = (8 * (-4.91)) / (8 + 12) = -1.96
NOP aSRS = (7 * 2.85) / (7 + 12) = 1.05

Next compute the SRS difference:

dSRS = -1.96 – 1.05 = -3.01

Finally, plug this number into the win probability formula:

p = 1 / (1 + e-(0.613230 + 0.167546 × (-3.01))) = 0.527

So we would estimate that the Lakers have about a 52.7 percent chance to win tonight.

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