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College Football Ranking ComparisonSaturday, October 25, 2003 (80 Rankings)Kenneth Massey has made a remarkable thing - has collected about hundred ranking systems of College Football teams. And having assumed, that as behind everyone ranking authors stand and all of them are equal and are the experts as though armed with mathematics. And time so that is naturally simple to calculate certain average ranking, for example, by summing ranks of teams. Well and as consequence in his compilation of ranking system are located according to a degree of the consent with average ranking. I have decided to look who has the best ranking system. The criterion the most simple is better the one who makes mistakes less. I hope that my e-rating certainly the best :)). The amount of mistakes is shown in the table in column Err. But mistakes are different. One - when 35-l team loses 36-th and other - when 10-I team lose 90-th team. To estimate WEIGHT of a mistake take a difference of places of teams. WEIGHT = the RANK of the WINNER - the RANK of the DEFEATED On the other hand the place in the table matters also where the mistake is accomplished. One - were mistaken at the top of the table for example 5-th a have lost 10-th team and other when 95-th team has lost 100-th. Let's define the IMPORTANCE as the sum of estimations of rank of teams which we shall define simply the N - Rank. In a result we shall receive IMPORTANCE = 2*N - the RANK of the WINNER - the RANK DEFEATED And than VALUE of MISTAKE = WEIGHT " IMPORTANCE Here again we come to a problem of an ESTIMATION of RESULT. As result for the given object of ranking it is natural to take which number of participants it has outstripped. Or the number of participants a minus a rank of the given participant. As some teams meet teams not included in 1À division number of 1 A teams we increase on 1 - 117+1. In the elementary case it is possible to count, that the ESTIMATION of RESULT is equal to RESULT. In this case the formula for VALUE of a mistake will be so VALUE of MISTAKE = (Result of the Winner + Result Defeated) * (Result of the Winner - Result Defeated) Result of the winner = Number of Participants + 1 - the Rank of the Winner Result defeated = Number of Participants + 1 - the Rank Defeated
E-Rnk - Ranking by this method
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