Deslok
03-12-2007, 04:36 AM
Ok, so I had a little free time this afternoon and crunched a few numbers about the brackets. I found and entered into a spreadsheet the Pomeroy ratings and the Sagarin ratings(predictor) for each team in the tourney. I then looked at all the 1 seeds and ranked them 1,2,3,4... did the same for the 2 seeds, and so on.
If you add up the rankings of the top 12 teams in each region and average them for each region(I chose the top 12 figuring that statistical discrepencies between the low major teams would have relatively insignificant impacts on the difficulty of each bracket, indeed, a 13+ seed winning is perceived as making a bracket "easier" so perhaps having worse low seeds makes a bracket tougher? Anyway, no school lower than 12 is going to have a prayer of a Final Four run, so that's where I drew my line).
Average ranking of East region teams:
Pomeroy: 2.75 Sagarin: 2.75
Average ranking of South Region teams:
Pomeroy: 3.08 Sagarin: 2.91
Average ranking of Midwest region teams:
Pomeroy: 2.33 Sagarin: 2.25
Average ranking of West region teams:
Pomeroy: 1.91 Sagarin: 2.08
In both cases, you get the West is toughest, followed by Midwest, then East, and South is easiest.
If you are really looking at best teams with shots at going to the Final Four, perhaps you want to break things off at the 6 seed(because anyone worse than Duke isn't headed to the Final Four, while Duke is of course going all the way). If you just average out the top 6 it comes out:
East top 6 Pomeroy: 2.83 Sagarin: 2.83
South top 6 Pomeroy: 3.00 Sagarin: 2.67
Midwest top 6 Pomeroy: 2.33 Sagarin: 2.33
West top 6 Pomeroy: 2.00 Sagarin: 2.16
Again, West is toughest, then Midwest, and then the vote is split between the East and South between the rankings. As a final number check, I looked at the overall top 20 teams in each rating(figuring its a wide open tourney, so lets say 20 teams have a chance of winning it all, again, just a number I tossed out to use). If you break the top 20 down by region you get:
East: per Pomeroy 4 per Sagarin 4
South: per Pomeroy 4 per Sagarin 3
Midwest:per Pomeroy 5 per Sagarin 8
West: per Pomeroy 7 per Sagarin 5
A split vote at the top, with Pomeroy rating the West toughest, and Sagarin rating the Midwest toughest(the large margin for the Sagarin rating can slightly be negated by noting that teams 21 and 22 would be in the West).
While I'd love to say this shows how easy UNC's road is, one of the things I found interesting was that they have a number of opponents who they are unlikely to ever see who are considered the worst of that seed rating(Wash St is the worst 3, USC is the worst 5, Vandy is the worst 6, Texas Tech is the worst 11, and GW is the worst 12). But since that will actually make it easier for the tough teams to come up against UNC(Texas and Georgetown in particular), it really doesn't do UNC any favors. Whereas the West has pretty much the best seeds at 5,6,7 and 8, which means all 4 top seeds will have their work cut out for them just making the Sweet 16.
Anyway, I'll probably crunch some more numbers as I usually have my students do a program running simulated tourneys to see how many times each ends up winning. And we'll see how it goes.
If you add up the rankings of the top 12 teams in each region and average them for each region(I chose the top 12 figuring that statistical discrepencies between the low major teams would have relatively insignificant impacts on the difficulty of each bracket, indeed, a 13+ seed winning is perceived as making a bracket "easier" so perhaps having worse low seeds makes a bracket tougher? Anyway, no school lower than 12 is going to have a prayer of a Final Four run, so that's where I drew my line).
Average ranking of East region teams:
Pomeroy: 2.75 Sagarin: 2.75
Average ranking of South Region teams:
Pomeroy: 3.08 Sagarin: 2.91
Average ranking of Midwest region teams:
Pomeroy: 2.33 Sagarin: 2.25
Average ranking of West region teams:
Pomeroy: 1.91 Sagarin: 2.08
In both cases, you get the West is toughest, followed by Midwest, then East, and South is easiest.
If you are really looking at best teams with shots at going to the Final Four, perhaps you want to break things off at the 6 seed(because anyone worse than Duke isn't headed to the Final Four, while Duke is of course going all the way). If you just average out the top 6 it comes out:
East top 6 Pomeroy: 2.83 Sagarin: 2.83
South top 6 Pomeroy: 3.00 Sagarin: 2.67
Midwest top 6 Pomeroy: 2.33 Sagarin: 2.33
West top 6 Pomeroy: 2.00 Sagarin: 2.16
Again, West is toughest, then Midwest, and then the vote is split between the East and South between the rankings. As a final number check, I looked at the overall top 20 teams in each rating(figuring its a wide open tourney, so lets say 20 teams have a chance of winning it all, again, just a number I tossed out to use). If you break the top 20 down by region you get:
East: per Pomeroy 4 per Sagarin 4
South: per Pomeroy 4 per Sagarin 3
Midwest:per Pomeroy 5 per Sagarin 8
West: per Pomeroy 7 per Sagarin 5
A split vote at the top, with Pomeroy rating the West toughest, and Sagarin rating the Midwest toughest(the large margin for the Sagarin rating can slightly be negated by noting that teams 21 and 22 would be in the West).
While I'd love to say this shows how easy UNC's road is, one of the things I found interesting was that they have a number of opponents who they are unlikely to ever see who are considered the worst of that seed rating(Wash St is the worst 3, USC is the worst 5, Vandy is the worst 6, Texas Tech is the worst 11, and GW is the worst 12). But since that will actually make it easier for the tough teams to come up against UNC(Texas and Georgetown in particular), it really doesn't do UNC any favors. Whereas the West has pretty much the best seeds at 5,6,7 and 8, which means all 4 top seeds will have their work cut out for them just making the Sweet 16.
Anyway, I'll probably crunch some more numbers as I usually have my students do a program running simulated tourneys to see how many times each ends up winning. And we'll see how it goes.