**avg:** 498.92 •
**sd:** 66.99 •
** top 16/20:** 0%

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

354 | California-Santa Cruz-B | Win 9-7 | 770.66 | Jan 20th | Pres Day Quals | |

211 | San Diego State | Loss 6-11 | 533.44 | Jan 20th | Pres Day Quals | |

230 | California-Davis | Loss 3-13 | 415.39 | Jan 20th | Pres Day Quals | |

334 | California-Santa Barbara-B | Loss 8-9 | 456.39 | Jan 20th | Pres Day Quals | |

298 | Southern California-B | Loss 7-10 | 330.48 | Jan 21st | Pres Day Quals |

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)