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We are back for another year of algorithm based fun. For the complete rankings and information on how they are calculated, please visit the website: http://math.bd.psu.edu/faculty/rutte...sRankings.html
For games played through 10/10/10
Yes, Quinnipiac is ranked above OSU as the started the season ranked a little higher.
I have added another page to the website this year describing the uncertainty in the rankings: http://math.bd.psu.edu/faculty/rutter/CurrentD1Unc.html
Since I use a statistical model to estimate a teams quality rating, there is some degree of uncertainty in the estimates. Very rarely are these estimates of uncertainty reported, but they do contain some interesting information. Here is the Top 10 from that page:
The table is sorted by Percent Top 8. This is determined by looking at simulations of all 33 teams' quality ratings and ranking them over 10,000 times. Percent Top 8 is the percentage of times these simulated rankings have that team in the top 8, the same number of teams that make the NCAA tournament. The 25th and 75th percentile represent the innerquartile range of all the simulated rankings, that is the middle 50% of the rankings. So, for at least half the time, Merychurst was ranked between first and sixth.
Can the Percent Top 8 column be used to predict the probability that a team will be in the top 8? Yes, IF the team played an infinite number of games against all of the other teams and the true quality rating did not change over time. That is a big "if." In reality, the teams play a finite number of games against a subset of all the teams, and the Percent Top 8 calculation does not take into account future opponents.
You will note that Ivy league teams have the widest spread of rankings, as they have not played any games yet and their ratings are based on last season's results. These results will improve over time as more games are played. For example, in 2008-2009, Wisconsin finished ranked number 1 with an interquartile range of [1,2] and a 100% of being in the top 8.
For games played through 10/10/10
Code:
Team Rating 1 Mercyhurst 1.7743 2 Minnesota 1.4368 3 Wisconsin 1.2998 4 Quinnipiac 1.1193 5 Ohio State 0.9929 6 Boston College 0.9259 7 Harvard 0.6314 8 UMD 0.5116 9 Cornell 0.5085 10 Providence 0.4357
I have added another page to the website this year describing the uncertainty in the rankings: http://math.bd.psu.edu/faculty/rutter/CurrentD1Unc.html
Since I use a statistical model to estimate a teams quality rating, there is some degree of uncertainty in the estimates. Very rarely are these estimates of uncertainty reported, but they do contain some interesting information. Here is the Top 10 from that page:
Code:
Team 25th 75th Percent Top 8 1 Mercyhurst 1 6 86.8 2 Minnesota 2 7 82.5 3 UMD 2 10 70.4 4 Wisconsin 3 10 69.0 5 Quinnipiac 3 10 67.0 6 Boston College 4 12 57.8 7 Ohio State 4 12 57.4 8 Harvard 5 18 43.7 9 Cornell 6 19 39.4 10 Princeton 10 25 21.1
Can the Percent Top 8 column be used to predict the probability that a team will be in the top 8? Yes, IF the team played an infinite number of games against all of the other teams and the true quality rating did not change over time. That is a big "if." In reality, the teams play a finite number of games against a subset of all the teams, and the Percent Top 8 calculation does not take into account future opponents.
You will note that Ivy league teams have the widest spread of rankings, as they have not played any games yet and their ratings are based on last season's results. These results will improve over time as more games are played. For example, in 2008-2009, Wisconsin finished ranked number 1 with an interquartile range of [1,2] and a 100% of being in the top 8.
, however this must make OnMaa very happy as he has been lobbying for the Q!
Nice work.
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