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Friday, August 21, 2020

NBA Playoffs: Comparing Simulation Output vs SRS Model

Originally, I ran my play-by-play NBA simulator on this year's playoffs to estimate each team's chances, and then separately simplified those results to an SRS model so each team could easily be directly compared.

But if I run that SRS model back through the simulator, how would the predictions change?

The original projections were:


SeedConferenceTeamRound 2Conf FinalsFinalsChampion
1EastMIL84.4%49.2%34.4%22.4%
8EastORL15.6%3.1%0.9%0.3%
4EastIND18.3%4.1%1.4%0.4%
5EastMIA81.7%43.6%28.8%17.5%
3EastBOS65.0%32.2%11.0%4.8%
6EastPHI35.0%10.3%2.4%0.7%
2EastTOR83.0%51.5%20.0%10.1%
7EastBKN17.0%5.9%1.2%0.3%
SeedConferenceTeamRound 2Conf FinalsFinalsChampion
1WestLAL62.5%28.2%13.6%5.4%
8WestPOR37.5%12.5%4.1%1.1%
4WestHOU44.3%23.8%11.0%4.4%
5WestOKC55.7%35.5%19.7%9.4%
3WestDEN46.3%12.8%4.7%1.5%
6WestUTA53.7%19.6%8.4%3.0%
2WestLAC60.6%43.6%26.3%13.5%
7WestDAL39.4%24.0%12.3%5.2%

The SRS model then gave these relative ratings:

TeamMMultMatrix Rank
MIA3.741
MIL3.722
LAC3.113
OKC2.324
TOR2.055
DAL1.766
LAL1.447
HOU1.098
BOS0.619
UTA-0.1810
DEN-2.1811
POR-2.3712
PHI-3.1213
IND-3.5114
ORL-3.6815
BKN-4.1016
So I then have to run these ratings through Log5, converting the expected margin of victory to a probability using a standard deviation of 13.47 in NBA, and then simulating each round again (or I can do the math explicitly).

For example, take the LAC/DAL series. The original simulation output had:
  • LAC single game win probability: 54.88%
  • Average MOV: 1.65
  • Over a 7 game series, this is equivalent to: 60.57% series win probability
Now let's take the above ratings. We have to invert the first calculation:
  • LAC rating - DAL rating = 3.11 - 1.76: 1.35 average MOV
  • Normal distribution; mean = 0, standard deviation = 13.47, x = 1.35: 53.99% LAC single game win probability
  • Over a 7 game series, this is equivalent to: 58.67% series win probability
    • The full math on this is at the end of this post
Running this through the playoff bracket gives the following probabilities:

SeedConferenceTeamRound 2Conf FinalsFinalsChampion
1EastMIL88.5%48.1%32.1%19.9%
8EastORL11.5%1.8%0.4%0.1%
4EastIND12.0%2.0%0.5%0.1%
5EastMIA88.0%48.0%32.1%20.0%
3EastBOS72.8%33.9%11.0%4.7%
6EastPHI27.2%7.0%1.0%0.2%
2EastTOR84.1%54.6%22.3%11.5%
7EastBKN15.9%4.5%0.5%0.1%
SeedConferenceTeamRound 2Conf FinalsFinalsChampion
1WestLAL73.2%34.9%17.0%7.0%
8WestPOR26.8%6.7%1.8%0.4%
4WestHOU42.1%22.8%10.6%4.1%
5WestOKC57.9%35.6%19.3%9.0%
3WestDEN37.3%8.3%2.3%0.5%
6WestUTA62.7%20.7%8.2%2.6%
2WestLAC58.7%43.5%26.4%13.6%
7WestDAL41.3%27.6%14.4%6.2%
This gives the strange phenomenon where the Bucks are barely more likely to reach the conference finals than the Heat, yet the Heat are slightly more likely to make the Finals and win it all, as the Bucks are marginally more likely to win their first round series, and the Heat are only the slightest of favorites in each game over the Bucks. 

Nevertheless, we get different results! Directionally they're almost the same (same picks in the first and second round), but there are large differences in magnitude in these early rounds.

SeedConferenceTeamRound 2Conf FinalsFinalsChampion
1EastMIL4.1%-1.0%-2.3%-2.5%
8EastORL-4.1%-1.3%-0.5%-0.2%
4EastIND-6.3%-2.1%-0.9%-0.3%
5EastMIA6.3%4.5%3.3%2.5%
3EastBOS7.8%1.7%-0.1%-0.2%
6EastPHI-7.8%-3.3%-1.3%-0.5%
2EastTOR1.0%3.0%2.4%1.4%
7EastBKN-1.0%-1.4%-0.7%-0.2%
SeedConferenceTeamRound 2Conf FinalsFinalsChampion
1WestLAL10.6%6.6%3.4%1.6%
8WestPOR-10.6%-5.8%-2.3%-0.7%
4WestHOU-2.2%-1.0%-0.4%-0.3%
5WestOKC2.2%0.1%-0.4%-0.4%
3WestDEN-9.0%-4.5%-2.3%-1.0%
6WestUTA9.0%1.0%-0.1%-0.4%
2WestLAC-1.9%-0.1%0.1%0.1%
7WestDAL1.9%3.6%2.1%1.0%
Calculating Series Probability

Neutral court makes this calculation much easier - we can just calculate each possible outcome (winning in 4, 5, 6, or 7 games).

Take our LAC/DAL example: 53.99% LAC win probability in any game. We just have to calculate the following outcomes, multiplied by the number of possible combinations for each series:
  • Win in 4: WWWW, 8.5%, 1 possible outcome
  • Win in 5: WWWLW, 3.91%, 4 possible outcomes
    • Think of it as 4 Choose 1 (nCr calculation): there are 4 places (games 1, 2, 3, 4) to put the 1 loss
  • Win in 6: WWWLLW, 1.8%, 10 possible outcomes
    • 5 Choose 2 = 10
  • Win in 7: WWWLLLW, 0.83%, 20 possible outcomes
    • 6 Choose 3 = 20


=6!(3!(63)!)
= 20
OutcomeG1G2G3G4G5G6G7Win SeriesCombosTotal ProbSeries Prob
Win in 454%54%54%54%8.50%18.50%58.67%
Win in 554%54%54%46%54%3.91%415.64%
Win in 654%54%54%46%46%54%1.80%1017.99%
Win in 754%54%54%46%46%46%54%0.83%2016.55%

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