**avg:** 316.06 •
**sd:** 126.19 •
** top 16/20:** 0%

# | Opponent | Result | Game Rating | Status | Date | Event |
---|---|---|---|---|---|---|

89 | Carleton College-GoP** | Loss 0-13 | 678.33 | Ignored | Feb 8th | Stanford Open 2020 |

126 | Chico State** | Loss 1-13 | 522.43 | Ignored | Feb 8th | Stanford Open 2020 |

284 | San Jose State | Loss 11-12 | 306.9 | Feb 8th | Stanford Open 2020 | |

61 | Washington University** | Loss 2-13 | 824.4 | Ignored | Feb 8th | Stanford Open 2020 |

76 | Puget Sound** | Loss 2-10 | 747.71 | Ignored | Feb 9th | Stanford Open 2020 |

203 | Cal Poly-SLO-B | Loss 2-10 | 223.79 | Feb 9th | Stanford Open 2020 | |

85 | Humboldt State | Loss 0-1 | 707.34 | Feb 9th | Stanford Open 2020 |

The uncertainty of the mean is equal to the standard deviation of the set of game ratings, divided by the square root of the number of games. We treated a teamâ€™s ranking as a normally distributed random variable, with the USAU ranking as the mean and the uncertainty of the ranking as the standard deviation

- Calculate uncertainy for USAU ranking averge
- Model ranking as a normal distribution around USAU averge with standard deviation equal to uncertainty
- Simulate seasons by drawing a rank for each team from their distribution. Note the teams in the top 16 (club) or top 20 (college)
- Sum the fractions for each region for how often each of it's teams appeared in the top 16 (club) or top 20 (college)
- Subtract one from each fraction for "autobids"
- Award remainings bids to the regions with the highest remaining fraction, subtracting one from the fraction each time a bid is awarded

There is an article on Ulitworld written by Scott Dunham and I that gives a little more context (though it probably was the thing that linked you here)