Probabilistic Algorithm FAQ

What is the probabilistic algorithm?

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

What is the uncertainty of the mean?

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 team’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.

Is there a longer explanation of all this?

There is an article on Ultiworld written by Cody Mills and Scott Dunham that gives a little more context (though it may have been the thing that linked you here!).