1) The Ken Pomeroy simulation.
https://dl.dropbox.com/u/241759/bracket_simulation.htm
Ken Pomeroy has set up his statistics in a simple way to find point margin (see one of my way old posts). For several reasons that I have mentioned on this site, I do not agree with his % chance of win statistic, and so instead I stick to Dean Oliver's (the one I learned in statistics class). Simply, in excel, I tell it to look at the normal distribution of the expected outcome of the two teams. Assuming a standard deviation of 10.9 points (which is roughly what we find from most teams in Pomeroy ratings, and the number found by the LRMC paper), we tell the computer:
=Normdist(x, 0, 10.9, 1)
where X is the expected point margin.
Then, we tell the computer to create one random tournament. For each game, the computer generates a random number between 0 and 1. If the value surpasses the better team's win%, (i.e., if it chose .91 while the better team's win% was .9) -- the worse team moves on.
Then by setting up a macro, I record the number of times each team makes it to which round. Then we simply divide the number of times each team makes it to any given round and divide it by the total number of trials to get % chance that a team will make it to whichever round of the tournament.
where X is the expected point margin.
Then, we tell the computer to create one random tournament. For each game, the computer generates a random number between 0 and 1. If the value surpasses the better team's win%, (i.e., if it chose .91 while the better team's win% was .9) -- the worse team moves on.
Then by setting up a macro, I record the number of times each team makes it to which round. Then we simply divide the number of times each team makes it to any given round and divide it by the total number of trials to get % chance that a team will make it to whichever round of the tournament.
2) The LRMC simulation
http://dl.dropbox.com/u/241759/lrmc_montecarlo.htm
This uses the same computer program, but different statistics.
Unfortunately, the LRMC does not post anything that we can convert to point margin or win probabilities. So we have to estimate point margin from each team's ranking. I took Jeff Sagarin's predictor rating of all 347 teams by ranking, and used the LRMC's ranking order. While this certainly has some inaccuracies, I should say that this method was by far my best for the vast majority of the tournament. Then, we just convert his numbers into a win probability by subtracting one rating from another (this gives us predicted point margin).
This uses the same computer program, but different statistics.
Unfortunately, the LRMC does not post anything that we can convert to point margin or win probabilities. So we have to estimate point margin from each team's ranking. I took Jeff Sagarin's predictor rating of all 347 teams by ranking, and used the LRMC's ranking order. While this certainly has some inaccuracies, I should say that this method was by far my best for the vast majority of the tournament. Then, we just convert his numbers into a win probability by subtracting one rating from another (this gives us predicted point margin).
Hope that answers any questions!
Looks good to me. One of your posts caused me to want to use the point spread distribution like you have to simulate wins as opposed to some clunkier methiods I had based on the history of the tournament.
ReplyDeleteStill didn't help me to have better picks in my office pool.