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:

Seed | Conference | Team | Round 2 | Conf Finals | Finals | Champion |

1 | East | MIL | 84.4% | 49.2% | 34.4% | 22.4% |

8 | East | ORL | 15.6% | 3.1% | 0.9% | 0.3% |

4 | East | IND | 18.3% | 4.1% | 1.4% | 0.4% |

5 | East | MIA | 81.7% | 43.6% | 28.8% | 17.5% |

3 | East | BOS | 65.0% | 32.2% | 11.0% | 4.8% |

6 | East | PHI | 35.0% | 10.3% | 2.4% | 0.7% |

2 | East | TOR | 83.0% | 51.5% | 20.0% | 10.1% |

7 | East | BKN | 17.0% | 5.9% | 1.2% | 0.3% |

Seed | Conference | Team | Round 2 | Conf Finals | Finals | Champion |

1 | West | LAL | 62.5% | 28.2% | 13.6% | 5.4% |

8 | West | POR | 37.5% | 12.5% | 4.1% | 1.1% |

4 | West | HOU | 44.3% | 23.8% | 11.0% | 4.4% |

5 | West | OKC | 55.7% | 35.5% | 19.7% | 9.4% |

3 | West | DEN | 46.3% | 12.8% | 4.7% | 1.5% |

6 | West | UTA | 53.7% | 19.6% | 8.4% | 3.0% |

2 | West | LAC | 60.6% | 43.6% | 26.3% | 13.5% |

7 | West | DAL | 39.4% | 24.0% | 12.3% | 5.2% |

The SRS model then gave these relative ratings:

Team | MMult | Matrix Rank |

MIA | 3.74 | 1 |

MIL | 3.72 | 2 |

LAC | 3.11 | 3 |

OKC | 2.32 | 4 |

TOR | 2.05 | 5 |

DAL | 1.76 | 6 |

LAL | 1.44 | 7 |

HOU | 1.09 | 8 |

BOS | 0.61 | 9 |

UTA | -0.18 | 10 |

DEN | -2.18 | 11 |

POR | -2.37 | 12 |

PHI | -3.12 | 13 |

IND | -3.51 | 14 |

ORL | -3.68 | 15 |

BKN | -4.10 | 16 |

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:

Seed | Conference | Team | Round 2 | Conf Finals | Finals | Champion |

1 | East | MIL | 88.5% | 48.1% | 32.1% | 19.9% |

8 | East | ORL | 11.5% | 1.8% | 0.4% | 0.1% |

4 | East | IND | 12.0% | 2.0% | 0.5% | 0.1% |

5 | East | MIA | 88.0% | 48.0% | 32.1% | 20.0% |

3 | East | BOS | 72.8% | 33.9% | 11.0% | 4.7% |

6 | East | PHI | 27.2% | 7.0% | 1.0% | 0.2% |

2 | East | TOR | 84.1% | 54.6% | 22.3% | 11.5% |

7 | East | BKN | 15.9% | 4.5% | 0.5% | 0.1% |

Seed | Conference | Team | Round 2 | Conf Finals | Finals | Champion |

1 | West | LAL | 73.2% | 34.9% | 17.0% | 7.0% |

8 | West | POR | 26.8% | 6.7% | 1.8% | 0.4% |

4 | West | HOU | 42.1% | 22.8% | 10.6% | 4.1% |

5 | West | OKC | 57.9% | 35.6% | 19.3% | 9.0% |

3 | West | DEN | 37.3% | 8.3% | 2.3% | 0.5% |

6 | West | UTA | 62.7% | 20.7% | 8.2% | 2.6% |

2 | West | LAC | 58.7% | 43.5% | 26.4% | 13.6% |

7 | West | DAL | 41.3% | 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.

Seed | Conference | Team | Round 2 | Conf Finals | Finals | Champion |

1 | East | MIL | 4.1% | -1.0% | -2.3% | -2.5% |

8 | East | ORL | -4.1% | -1.3% | -0.5% | -0.2% |

4 | East | IND | -6.3% | -2.1% | -0.9% | -0.3% |

5 | East | MIA | 6.3% | 4.5% | 3.3% | 2.5% |

3 | East | BOS | 7.8% | 1.7% | -0.1% | -0.2% |

6 | East | PHI | -7.8% | -3.3% | -1.3% | -0.5% |

2 | East | TOR | 1.0% | 3.0% | 2.4% | 1.4% |

7 | East | BKN | -1.0% | -1.4% | -0.7% | -0.2% |

Seed | Conference | Team | Round 2 | Conf Finals | Finals | Champion |

1 | West | LAL | 10.6% | 6.6% | 3.4% | 1.6% |

8 | West | POR | -10.6% | -5.8% | -2.3% | -0.7% |

4 | West | HOU | -2.2% | -1.0% | -0.4% | -0.3% |

5 | West | OKC | 2.2% | 0.1% | -0.4% | -0.4% |

3 | West | DEN | -9.0% | -4.5% | -2.3% | -1.0% |

6 | West | UTA | 9.0% | 1.0% | -0.1% | -0.4% |

2 | West | LAC | -1.9% | -0.1% | 0.1% | 0.1% |

7 | West | DAL | 1.9% | 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
- Win in 7: WWWLLLW, 0.83%, 20 possible outcomes

C(n,r)=C(6,3)

=6!(3!(6−3)!)$$=\frac{6!}{(3!(6-3)!)}$$$$\frac{}{}$$$$\frac{=\; 20}{}$$

Outcome | G1 | G2 | G3 | G4 | G5 | G6 | G7 | Win Series | Combos | Total Prob | Series Prob |

Win in 4 | 54% | 54% | 54% | 54% | | | | 8.50% | 1 | 8.50% | 58.67% |

Win in 5 | 54% | 54% | 54% | 46% | 54% | | | 3.91% | 4 | 15.64% | |

Win in 6 | 54% | 54% | 54% | 46% | 46% | 54% | | 1.80% | 10 | 17.99% | |

Win in 7 | 54% | 54% | 54% | 46% | 46% | 46% | 54% | 0.83% | 20 | 16.55% |