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WWR Rankings
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The Iterative Method See the paper for a complete description of the Iterative algorithm. A few clarifications on how we apply the developed algorithm: For all posted rankings (in 2010), w1, w2, w3, w4 all are set to 1. The scoring parameter is set to infinity (raw difference of scores is used). Learning Parameter Values off the Current Season To produce rankings for week 9 (the week starting on Oct 25, 2010), the weeks 1-8 are used to determine edge weights, and weeks 7 and 8 (games played from Oct 11, 2010 through Oct 24, 2010) are used to measure the accuracy of the rankings for every combination of parameter values (home win, away loss, date, ranking). The last two weeks are used to analyze the rankings since we expect team ability to change over the season and we want the rankings to reflect the current abilities of the teams. Two weeks are used to measure accuracy so that every FBS team will have played at least one game that contributes to the accuracy measurement. Process We also follow the BCS standard for dealing with teams prohibited from post-season play. The teams and their results are used to produce the rankings but then the teams in question are removed from the rankings. Games between FBS and FCS schools are used to generate the rankings and all FCS schools that are involved in a game with a FBS school are ranked. This year, the rankings contain 195 teams. The FCS schools are removed from the rankings before the rankings are posted. The problem with using FBS vs FCS games in the ranking is that few FCS schools play more than one or two FBS schools making them poorly connected in the graph. Summed Weights, Normalized Weights, Raw Rankings On many occasions, multiple parameter (home win, away loss, date, ranking) value combinations produce the same accuracy for a given week (although each parameter value combination may differ in which games are correctly predicted). In these cases, each parameter value combination that produces the highest accuracy is used to produce a team weight and ranking as described in the paper. We use three distinct methods, Summed Weights, Normalized Weights, Raw Rankings, to combine these rankings into one final ranking for the week. A final team weight is determined and this value is used to rank the team. The final team weight is determined as explained below for each method. Summed Weights
A final team weight is found by summing a team's weight produced by each parameter value combination previously identified. Since certain parameter combinations may produce larger team weights than others, this method may give more or less weight to a particular ranking. Normalized Weights A final team weight is found by summing a team's normalized weight produced by running each parameter value combination previously identified. The normalized weights range from 0 to 1. This preserves the distance between teams within a ranking, but does not allow rankings that produce large team weights to to be over represented. Raw Rankings A final team weight is found by summing a team's numeric rank produced by each parameter value combination previously identified. This method gives each set of rankings equal weight but does not preserve the distance between teams in a given ranking. How well were Week N games predicted? This data represents how well these rankings predicted Week N games. Note that we follow the BCS convention of saying Week N rankings are produced the day after Week N-1 games have been completed. Week N rankings can then be evaluated by finding the accuracy of predicting Week N games. All: All games played during Week N.
Top 70: Games played during Week N that involved a team ranked in the Top 70. 70 is choosen since ESPN lists 35 bowl games to be played after the 2010-2011 season. Top 70 (Both): Games played during Week N were both teams were ranked in the Top 70 Top 25: Games played during Week N that involved a team ranked in the Top 25. Top 25 (Both): Games played during Week N were both teams were ranked in the Top 25 Since the BCS only releases that Top 25 each week, only the latter two accuracies can be calculated for the BCS Computer rankings. Note that the accuracy of WWR rankings is produced before FCS schools and teams prohibited from post-season play have been removed from the rankings. |