![]() ![]() Indicating the probability that seed i beats seed j, where is some measure of “strength” of seed i (decreasing in i), and k is a scaling factor that effectively determines the range of resulting probabilities. More precisely, let P be a 16×16 matrix with entries A reasonably simple starting point is to assume that all games are independent, with each outcome’s probability depending only on the teams’ seeds. My goal in this post is to describe a means of more accurately evaluating and comparing these and other bracket scoring systems.įirst, we need a way to model the probability of correctly picking any particular game. One of the more amusing common suggestions is a progression based on the Fibonacci sequence, with games in each round worth 2, 3, 5, 8, 13, and 21 points, respectively. Intuitively, then, it seems like this doubling system might be over-weighting the importance of later rounds, and perhaps a better system involves less extreme increases in points per game from one round to the next. Also, assuming all of the teams are evenly matched– or equivalently, assuming that you make all of your picks by flipping a fair coin– then the expected number of points scored decreases by exactly half with each round.īut teams aren’t evenly matched, and you don’t make your picks by flipping coins. For example, each round of games is potentially worth the same number of points (32). ![]() This “doubling” system has several reasonable mathematical motivations. ![]() 32 points for correctly picking the champion.16 points for each correct pick in the two Final Four games,.8 points for each correct pick in the fourth round of 8 teams,.4 points for each correct pick in the third round of 16 teams,.2 points for each correct pick in the second round of 32 teams,.1 point for each correct pick in the first round of 64 teams,.It was a come-from-behind victory for my bracket, moving from 14th place to 7th to 1st… over the span of the last three games in the 63-game tournament.īut should I have won? Our pool used the common bracket scoring system of assigning: During the 2015 NCAA men’s basketball tournament, I won our office pool by (1) picking then-undefeated Kentucky to lose– although earlier than their actual Final Four loss to Wisconsin– and (2) picking Duke to win the championship game. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |