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 =
                           ESTIMATION of WINNER'S RANK  + ESTIMATION of DEFEATED RANK

SIZE of MISTAKE = ESTIMATION of  DEFEATED RANK  - ESTIMATION of WINNER'S RANK

It results in beautiful expression:

ESTIMATION of MISTAKE =
                        ESTIMATION of RANK DEFEATED ^ 2 - ESTIMATION of WINNER'S RANK ^ 2

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?

6 December 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 and POTEMKIN'S CONSENSUS are different

Difference between Massey's CONSENSUS and Potemkin's CONSENSUS in the first case absolute values of ranks are used and in the second the relative arrangement of ranks is taken into account.

 RM        Links       ABR  Mist RN-R RN/R CorrBest N-R + N/R
 
    1      Slots       SLT    100    7   50    1,00   57
    2    McCormick     MCK    104    2   15    0,98   17
    3     Dolphin      DOL    125   27    1    0,95   28
    4    CPA Retro     CPR    127   10   71    0,96   81
    5      Ranma       RAN    129   70   48    0,93   118
    6   Sagarin-Elo     SE    130    8    6    0,96   14
    7      Palm        PSR    131   69   92    0,92   161
    8 New York Times   NYT    131   53   84    0,94   137
    9     WAJL10       WAJ    132   46   51    0,96   97
   10      Bihl        BIH    133   14   69    0,96   83
   10    DeSimone      DES    133   75   44    0,90   119
   10     Dunkel       DUN    133   81   83    0,95   164
   13    Dwiggins      DWI    134   89   72    0,93   161
   13The Sports Report TSR    134    3   18    0,96   21
   15       BMC        BMC    135   92  102    0,92   194
   15       CPA        CPA    135   43   95    0,95   138
   15     Flyman       FLY    135   72   76    0,91   148
   15     Fleming      FMG    135   35   55    0,97   90
   15      Imes        IMS    135   68   77    0,94   145
   15    Matthews      MAT    135   18   45    0,97   63
   22     Bobcat       BOB    136   19   85    0,97   104
   22      Craig       CRD    136   40   78    0,95   118
   22      Kiser       KIS    136   56   80    0,95   136
   22   Montgomery     MGY    136   16   10    0,97   26
   22     Rothman      RTH    136    1    4    0,98    5
   22    Sorensen      SOR    136   23   66    0,97   89
   28   Billingsley    BIL    137   58   63    0,92   121
   28     Coffey       COF    137   33   54    0,96   87
   28     Colley       COL    137   54   65    0,94   119
   28   Massey COMP    Cons   137   31   57    0,96   88
   28     Gindin       GRS    137   52   29    0,95   81
   28   Massey BCS      MB    137    6   21    0,96   27
   28     McMurry      MMY    137    9    2    0,96   11
   28    SportsDoc      SD    137   28   73    0,96   101
   28      Suni        SUN    137   30   28    0,97   58
   28     Wilson       WIL    137    4   82    0,97   86
   39   Greenfield     GRN    138   11   13    0,97   24
   39      Jones       JON    138   55   42    0,93   97
   39     Massey       MAS    138   20   26    0,97   46
   39      Mark        MRK    138   61   38    0,90   99
   39   Solecismic     SOL    138   94  101    0,94   195
   39       UCS        UCS    138   51   64    0,95   115
   39      Wolfe       WOL    138   29   17    0,94   46
   47     Ashburn      ASH    139   15   16    0,97   31
   47    BoCaDuck      BCD    139   74   47    0,90   121
   47Bowl Champ Series BCS    139   48   36    0,95   84
   47 Boyer-DeSimone    BD    139   60   81    0,95   141
   47    Claassen      CLA    139   45   61    0,96   106
   47      Reese       RSE    139   39    9    0,93   48
   53      ARGH        ARG    140   50   56    0,95   106
   53    E-Rating       E     140   25   86    0,96   111
   53      Maas        MAA    140   25   86    0,96   111
   53     Marsee       MAR    140   77   14    0,94   91
   53     Pigskin      PIG    140   59   24    0,95   83
   53    Whitlock      WLK    140   36    7    0,96   43
   59    Armstrong     ARM    141   49   58    0,95   107
   59      Moore       MOR    141   90   93    0,93   183
   59   PerformanZ     PRZ    141   37   52    0,97   89
   59    Rudacille     RUD    141   12    5    0,97   17
   59      Self        SEL    141    5   23    0,98   28
   64       CSL        CSL    142   76   30    0,91   106
   64      Welch       WEL    142   64   99    0,93   163
   64      Wobus       WOB    142   38   32    0,94   70
   67    Anderson      AND    143   44    8    0,95   52
   67     Bassett      BAS    143   34   49    0,96   83
   67     Daniel       DAN    143   57   98    0,94   155
   67       Eck        ECK    143   71   40    0,91   111
   67    Hermrats      HER    143   42   62    0,96   104
   67       MJS        MJS    143   80   60    0,91   140
   67 Stephens-Sabey    SS    143   86   89    0,92   175
   74      Elrod       ERD    144   82   88    0,92   170
   74     Holland      HOL    144   84   97    0,91   181
   74     Hubner       HUB    144   66   37    0,93   103
   74      Mease       MEA    144   31   11    0,94   42
   74 Random Monkeys    RM    144   17   39    0,95   56
   74    Tellshow      TSW    144   79   27    0,94   106
   80  Dolphin Pred     DP    145   87   70    0,94   157
   80      Rager       RAG    145   63   31    0,94   94
   80     Sauceda      SAU    145   21   35    0,97   56
   83     Maurer       MAU    146   67   46    0,95   113
   83    P-Rating      P10    146   98   20    0,86   118
   85     Sagarin      SAG    147   13    3    0,97   16
   87      Born        BRN    148   73   33    0,93   106
   87    Congrove      CGV    148   93   12    0,90   105
   87     Howell       HOW    148   65   25    0,94   90
   87     Krueger      KGR    148   83   79    0,94   162
   87    Pankratz      PFZ    148   91   59    0,93   150
   93      Hatch       HAT    149  102   96    0,90   198
   95     Colton       CTN    150   62   22    0,94   84
   95      Gupta       GUP    150  100  103    0,90   203
   95    Matschke      MKE    150   85  100    0,94   185
   98     Markov       MKV    151   78   91    0,95   169
   99     Kambour      KAM    152   95   34    0,93   129
  100       Laz        LAZ    153   47   67    0,96   114
  101     Dokter       DOK    156   88   90    0,94   178
  102      Reid        REI    163  101   43    0,89   144
  103    YourLinx       YL    177  103   94    0,87   197