Comments on: Boston versus the field http://arbitrarian.wordpress.com/2008/04/19/boston-versus-the-field/ Anything but arbitrary. Tue, 23 Jun 2009 01:22:44 +0000 http://wordpress.com/ hourly 1 By: rapidadverbssuck http://arbitrarian.wordpress.com/2008/04/19/boston-versus-the-field/#comment-200 rapidadverbssuck Sun, 20 Apr 2008 13:36:28 +0000 http://arbitrarian.wordpress.com/?p=133#comment-200 Drew, I did the original odds analysis in a very lazy way. I just found the chance of each team beating each of the other teams, and normalized those odds to sum to zero. Since this isn't actually how the playoffs are played (obviously), it's pretty poor analysis. However, your comment encouraged me to actually do a more thorough analysis, which I've posted. In this second analysis, I predict the most likely winner of each round, and then each team's probability of beating an Expected Value version of their second round opponent, and so on to the title. Thanks for your interest and your pushing me a little on the analysis. I need to be kept honest. Drew,
I did the original odds analysis in a very lazy way. I just found the chance of each team beating each of the other teams, and normalized those odds to sum to zero. Since this isn’t actually how the playoffs are played (obviously), it’s pretty poor analysis. However, your comment encouraged me to actually do a more thorough analysis, which I’ve posted. In this second analysis, I predict the most likely winner of each round, and then each team’s probability of beating an Expected Value version of their second round opponent, and so on to the title. Thanks for your interest and your pushing me a little on the analysis. I need to be kept honest.

]]> By: Drew http://arbitrarian.wordpress.com/2008/04/19/boston-versus-the-field/#comment-198 Drew Sat, 19 Apr 2008 16:21:24 +0000 http://arbitrarian.wordpress.com/?p=133#comment-198 David, Can you give a little more insight into how you calculated each team's probability of winning the championship? The probability of a team winning the championship should be equal to the product of the probabilities of the given team winning each round given the team makes it to that round. Taking your round-by-round win probabilities for the Celtics versus the most likely opponents and adjusting them upward a bit to account for the potential of facing weaker opponents (except for the first round, since the opponent is known) , I get roughly a 35% chance of them winning the championship, which intuitively seems much more reasonable than 78%. Looking at it another way, the fact that you're giving Boston a 77.5% chance of winning the title and a 85.1% chance of winning round 1, this implies that the Celtics have a ridiculous 91.1% chance of advancing through the next three rounds given they make it past Atlanta. I've been a fan of your recent analyses (and graphics), but this just doesn't seem to add up. Is there something that I'm missing? David,

Can you give a little more insight into how you calculated each team’s probability of winning the championship?

The probability of a team winning the championship should be equal to the product of the probabilities of the given team winning each round given the team makes it to that round. Taking your round-by-round win probabilities for the Celtics versus the most likely opponents and adjusting them upward a bit to account for the potential of facing weaker opponents (except for the first round, since the opponent is known) , I get roughly a 35% chance of them winning the championship, which intuitively seems much more reasonable than 78%.

Looking at it another way, the fact that you’re giving Boston a 77.5% chance of winning the title and a 85.1% chance of winning round 1, this implies that the Celtics have a ridiculous 91.1% chance of advancing through the next three rounds given they make it past Atlanta.

I’ve been a fan of your recent analyses (and graphics), but this just doesn’t seem to add up. Is there something that I’m missing?

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