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  1. #1
    Join Date
    Feb 2007
    Location
    Partly Orlando, FL partly heard Sandpoint, ID

    Bracket breakdown numbers

    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
    Midwester 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.

  2. #2
    Join Date
    Feb 2007
    Location
    Partly Orlando, FL partly heard Sandpoint, ID
    Always nice to reply to oneself, but since I'm just crunching numbers for my own amusement... what the heck.

    Ok, so I entered in stats from Ken Pomeroy's site(specificially using the offensive and defensive effeciency stats combined with the tempo stat to simulate games between opponents using some random number generation). I simulated 1000 tournaments using this format, and here's the results I came up with(alas, I'm sure the formatting will be messed up, and by the stats, the wrong team wins too many times ):

    Team Total Wins Avg Wins #Champs
    UNC 2747 2.747 135
    Florida 2657 2.657 100
    Ohio St 2504 2.504 84
    Kansas 2316 2.316 82
    Texas A&M 2061 2.061 68
    Georgetown 2245 2.245 67
    Wisconsin 1923 1.923 47
    UCLA 1992 1.992 41
    Memphis 2051 2.051 40
    Pitt 1631 1.631 27
    Maryland 1541 1.541 23
    Indiana 1244 1.244 20
    Duke 1409 1.409 19
    Texas 1539 1.539 19
    Notre Dame 1377 1.377 17
    Oregon 1497 1.497 16
    Louisville 1185 1.185 15
    S. Illinois 1291 1.291 14
    Virginia Tech 1161 1.161 13
    Georgia Tech 1109 1.109 13
    Washington St 1475 1.475 13
    Tennessee 1507 1.507 13
    Kentucky 902 0.902 12
    Arizona 877 0.877 12
    Butler 1128 1.128 10
    Villanova 925 0.925 8
    Virginia 1382 1.382 8
    Creighton 947 0.947 8
    Michigan St 946 0.946 7
    UNLV 735 0.735 7
    Vanderbilt 1114 1.114 5
    Xavier 882 0.882 5
    USC 979 0.979 4
    BC 1070 1.07 4
    Illinois 785 0.785 4
    Arkansas 789 0.789 3
    BYU 726 0.726 3
    Nevada 726 0.726 2
    Gonzaga 588 0.588 2
    Davidson 463 0.463 2
    Purdue 726 0.726 2
    Stanford 560 0.56 2
    Texas Tech 562 0.562 1
    Winthrop 487 0.487 1
    Marquette 643 0.643 1
    Wright St 333 0.333 1
    E. Kentucky 72 0.072 0
    George Wash 611 0.611 0
    Holy Cross 410 0.41 0
    Central Conn St 122 0.122 0
    Jackson St 35 0.035 0
    VCU 475 0.475 0
    Niagara 108 0.108 0
    Long Beach St 378 0.378 0
    Weber St 160 0.16 0
    Albany 339 0.339 0
    Oral Roberts 414 0.414 0
    North Texas 127 0.127 0
    Texas A&M CC 256 0.256 0
    Miami OH 380 0.38 0
    New Mexico St 347 0.347 0
    Penn 255 0.255 0
    Old Dominion 572 0.572 0
    Belmont 202 0.202 0

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