tag:blogger.com,1999:blog-35971090.post22277477466257131..comments2014-09-29T15:57:01.630-04:00Comments on The Hoover Street Rag: CCHA Tournament OddsGeoffhttp://www.blogger.com/profile/09461267960136260783noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-35971090.post-25818701543275722492009-03-11T17:32:00.000-04:002009-03-11T17:32:00.000-04:00@chriscamzz: Not really. There's a 9% chance tha...@chriscamzz: Not really. There's a 9% chance that the winner has to take some path we haven't identified here. For example, we're assuming that Notre Dame will have to beat UNO, OSU, and Michigan to win the title, when in reality Notre Dame could end up playing Alaska, OSU, Northern, or Western in the semifinal and Miami, Alaska, OSU, or Northern in the title game. Unlikely paths to the championship are where the extra 9% is.Geoffhttp://www.blogger.com/profile/09461267960136260783noreply@blogger.comtag:blogger.com,1999:blog-35971090.post-81570661224438380802009-03-11T12:24:00.000-04:002009-03-11T12:24:00.000-04:00Right, I totally forgot about the re-seeding. Tha...Right, I totally forgot about the re-seeding. That does make it a lot more complicated and probably would make Notre Dame benefit the most.<BR/><BR/>It shouldn't require much more probability theory, each matchup is independent so the probability of Northern and UNO advancing is just the product of their individual probabilities of advancing. Each team's chance of winning next round would be the sum of Prob(winning a matchup)*Prob(that matchup occurs) for all possible matchups.<BR/><BR/>It does however require a decent amount of combinations. There are 16 choices of semifinal teams. After that though, there are only 8 possible finals teams and you already have the probability of each one occuring. Basically, all the hard work is in the semifinal round.Jeffhttp://www.blogger.com/profile/16503024815470017220noreply@blogger.comtag:blogger.com,1999:blog-35971090.post-46836152625676864432009-03-11T08:40:00.000-04:002009-03-11T08:40:00.000-04:00looks like there's a 9% chance no team wins the fi...looks like there's a 9% chance no team wins the final......chriscamzzhttp://www.blogger.com/profile/17325223485003352715noreply@blogger.comtag:blogger.com,1999:blog-35971090.post-18299829682380487852009-03-11T07:56:00.000-04:002009-03-11T07:56:00.000-04:00I'd try to do something like that, but my limited ...I'd try to do something like that, but my limited knowledge of probability makes that unwieldy. To know the true chances, I'd have to figure out the chances of Michigan playing each team in the next round, which means I'd have to figure out the probability of things like "What if Northern and UNO both advance?" If you total up the last column right, there's a 9.5% chance that some other path is needed for any of these teams to win the title. My gut tells me Notre Dame probably benefits the most from a fuller analysis, since they'd get first crack at any weaker seed advancing, with the effects trickling down to Michigan.<BR/><BR/>There's also the effect that re-seeding has on the field. For example, Michigan can't play Northern in the next round. If Michigan and Notre Dame advance, no lower seed can be left in the field, so they have to play Notre Dame. If Notre Dame fails to advance (I know, good one), then Michigan is the top remaining seed and must play UNO, the lowest remaining seed. Maybe I can find a method to mitigate the pain of figuring out all the possible combinations.Geoffhttp://www.blogger.com/profile/08568289556977038048noreply@blogger.comtag:blogger.com,1999:blog-35971090.post-52876663052096488902009-03-11T01:32:00.000-04:002009-03-11T01:32:00.000-04:00I have a suggestion for the advancement probabilit...I have a suggestion for the advancement probabilities. Instead of assuming the hardest possible schedule, you should use all possible schedules with your previous calculations and get the total probability.<BR/><BR/>For example, Michigan's chances of winning the next round would be .5640*.6986 + (Prob Michigan beats Northern)*.3014<BR/><BR/>It probably wouldn't change any of the numbers by more than a few percentage points. Although Miami, Alaska and Ohio St would be candidates for change.Jeffhttp://www.blogger.com/profile/16503024815470017220noreply@blogger.com