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It is the next version of a rank of ranks. 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. As has truly noticed by Kenneth Massey models of an estimation of validity of ranks much. Probably as much how many models of ranks. More or less the general structure probably is fair ESTIMATION of the MISTAKE = IMPORTANCE of MISTAKE * SIZE of MISTAKE Here: IMPORTANCE of MISTAKE = SIZE of MISTAKE = ESTIMATION of DEFEATED RANK - ESTIMATION of WINNER'S RANK It results in beautiful expression: ESTIMATION of MISTAKE = In the previous version the elementary estimation of the RANK of participants was used 1. RANK ESTIMATION = N - RANK However it is only one of possible elementary arithmetic expressions. To look as influence various estimation models of the RANK, I used one another expressions 2. RANK ESTIMATION = N / RANK - gives more "attention" to the top rank The size of a mistake is submitted by a difference of estimations of ranks. If we as an estimation of a rank take the number of teams of below given rank (N - R) that will turn out, that the SIZE of a mistake is identical to a case the 10 th team wins 1-st and when the 110-th team) wins at 101. Something prompts me that it is incorrectly. If as an estimation of a rank to take N/R that the Size of a mistake will be N / RL - N / RW = N * (RW - RL) / RW*RL For pair RW = 1 and RL = 10 VM = N * (1-10) / 10 = 0,9 * N For pair RW = 101 and RL = 110 VM = N * (101 - 110) / (101 * 110) = 0,0009 N It is more similar to the truth The importance of a mistake it is submitted by the sum of estimations of ranks If as an estimation of a rank âîçìåì the number of commands (teams) of below given rank (N - R) it will turn out is simple that the IMPORTANCE of a mistake is identical to a case when 51-I a command (team) win against 50-th and when 101-I lose 1-st. Something and in this case prompts me that it incorrectly. Let's look, that turns out if as an estimation of a rank to take N/R. For pair RW = 51 and RL = 50 IM = N * (51 + 50) / (50 * 51) = N / 50 For pair RW = 100 and RL = 1 IM = N * (100 + 1) / (100 * 1) = 1 * N And it is more similar to the truth too :) And so the estimation of a rank as N/R has advantage before N - R. And how do you think? 22 November 2003 I'll Update this table as soon as Kenneth Massey update his COMPILATION/ Wait a moment :)) You can see that MASSEY'S CONSENSUS RANKING is not the first. But let's wait for complete data So, we have three rank - lists. I do not know that with them to do. Therefore has gone on the worn way simply summed ranks. Also that has turned out. Sum Rnk Links ABR M-12 RM RN-R RN/R CorrBest 13 Sagarin-Elo SE 122 7 4 2 957 15 Rothman RTH 124 13 1 1 978 23 Greenfield GRN 123 8 10 5 968 25 Wilson WIL 123 8 3 14 972 27 Sports TSR 124 13 2 12 968 30 Dolphin DOL 114 3 20 7 963 31 McMurry MMY 125 19 8 4 965 33 Bihl BIH 124 13 12 8 967 35 SportsDoc SD 124 13 16 6 971 37 Self SEL 127 29 5 3 978 46 Slots SLT 93 1 6 39 1000 52 Bobcat BOB 124 13 30 9 957 55 CPA Retro CPR 115 4 7 44 964 56 McCormick MCK 104 2 11 43 967 60 Massey BCS MB 127 29 9 22 968 62 Rudacille RUD 128 38 14 10 973 66 Bowl Champ Series BCS 126 26 22 18 957 74 Ashburn ASH 129 46 15 13 973 76 Massey COMP CONS 125 19 28 29 966 76 Massey MAS 129 46 19 11 967 82 Wolfe WOL 123 8 29 45 943 83 Montgomery MGY 127 29 23 31 965 85 Anderson AND 128 38 32 15 954 88 Fleming FMG 124 13 42 33 969 89 Billingsley BIL 126 26 39 24 923 91 ARGH ARG 127 29 45 17 953 95 DeSimone DES 123 8 66 21 902 95 WAJL10 WAJ 127 29 38 28 957 104 Sorensen SOR 121 6 27 71 975 106 Coffey COF 127 29 37 40 954 108 CPA CPA 116 5 35 68 962 112 Sagarin SAG 134 72 13 27 974 114 Mease MEA 128 38 26 50 943 116 E-Rating E31 127 29 21 66 959 116 Wobus WOB 127 29 33 54 947 118 Random Monkeys RM 128 38 18 62 958 118 Hermrats HER 131 62 36 20 960 123 Dwiggins DWI 125 19 62 42 948 123 Sauceda SAU 134 72 17 34 976 124 Maurer MAU 128 38 67 19 955 125 Reese RSE 128 38 55 32 926 126 Whitlock WLK 129 46 44 36 960 133 Craig CRD 125 19 31 83 951 136 Imes IMS 129 46 74 16 920 137 Ranma RAN 125 19 71 47 936 137 New York Times NYT 127 28 51 58 938 140 Armstrong ARM 125 19 34 87 959 143 PerformanZ PRZ 131 62 40 41 969 151 Suni SUN 125 19 48 84 940 151 Maas MAA 130 52 24 75 962 151 Matthews MAT 130 52 25 74 973 153 Pigskin PIG 127 29 68 56 951 153 BoCaDuck BCD 129 46 61 46 910 158 Boyer-DeSimone BD 130 52 54 52 948 161 Born BRN 130 52 72 37 940 163 Dolphin Pred DP 133 68 57 38 963 164 Dunkel DUN 123 8 76 80 948 164 Bassett BAS 134 72 43 49 957 165 Claassen CLA 130 52 41 72 958 166 Eck ECK 134 72 64 30 911 166 Krueger KGR 140 87 56 23 956 168 Colley COL 130 52 47 69 944 175 Welch WEL 130 52 58 65 930 176 Kiser KIS 128 38 49 89 949 184 Gindin GRS 130 52 59 73 948 184 Elrod ERD 135 79 79 26 928 188 Marsee MAR 132 65 75 48 943 191 Howell HOW 134 72 60 59 942 196 Colton CTN 135 79 53 64 942 198 MJS MJS 132 65 70 63 913 199 Tellshow TSW 135 79 85 35 932 201 Rager RAG 133 68 63 70 943 201 UCS UCS 134 72 52 77 948 203 Congrove CGV 140 87 91 25 894 208 Mark MRK 134 72 50 86 911 209 Flyman FLY 130 52 69 88 920 211 Palm PSR 130 52 65 94 921 214 Laz LAZ 142 92 46 76 963 216 BMC BMC 128 38 86 92 926 217 P-Rating P10 132 64 93 60 865 220 CSL CSL 129 46 78 96 916 225 Pankratz PFZ 137 84 90 51 921 228 135 79 82 67 907 228 E-Rating ER 141 90 77 61 955 234 Moore MOR 133 68 87 79 933 234 Markov MKV 145 93 84 57 945 236 Holland HOL 132 65 80 91 916 237 Dokter DOK 147 94 88 55 941 246 Stephens-Sabey SS 137 84 81 81 917 246 Reid REI 152 97 96 53 883 247 Solecismic SOL 133 68 89 90 924 247 Daniel DAN 135 79 73 95 919 262 Hatch HAT 139 86 94 82 907 263 Matschke MKE 140 87 83 93 945 265 Kambour KAM 149 95 92 78 928 277 YourLinx YL 149 95 97 85 887 282 Gupta GUP 141 90 95 97 900
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