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?

29 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 and POTEMKIN'S CONSENSUS

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   9   39    1,00     48
  2      McCormick     MCK   106   5    5    0,97     10
  3       Dolphin      DOL   120  23    1    0,95     24
  4      CPA Retro     CPR   123  11   66    0,96     77
  5   New York Times   NYT   124  53   102   0,93     155
  6     Sagarin-Elo     SE   125   7    3    0,95     10
  6        Ranma       RAN   125  71   47    0,93     118
  8      DeSimone      DES   126  74   19    0,89     93
  9         BMC        BMC   127  92   79    0,91     171
 10       Fleming      FMG   128  36   30    0,96     66
 10       Wilson       WIL   128   3   80    0,96     83
 12     Greenfield     GRN   129  10    4    0,96     14
 12      Dwiggins      DWI   129  82   62    0,92     144
 12       Dunkel       DUN   129  85   83    0,95     168
 15       McMurry      MMY   130   8   16    0,96     24
 15        Wolfe       WOL   130  32   23    0,94     55
 15     Massey BCS      MB   130   4   55    0,96     59
 15      Matthews      MAT   130  16   44    0,97     60
 15        Maas        MAA   130  26   84    0,95     110
 15      E-Rating       E    130  22   94    0,95     116
 15       Gindin       GRS   130  57   69    0,94     126
 15      Armstrong     ARM   130  45   92    0,96     137
 23  Potemkin's CONSENSUS    131  65   97    0,96     152
 23       Rothman      RTH   131   1    6    0,97      7
 23  The Sports Report TSR   131   2    9    0,97     11
 23       WAJL10       WAJ   131  43   24    0,95     67
 23        Bihl        BIH   131  13   56    0,96     69
 23         CPA        CPA   131  38   88    0,94     126
 23        Craig       CRD   131  38   88    0,94     126
 23        Imes        IMS   131  65   75    0,93     140
 23       Hubner       HUB   131  66   86    0,92     152
 31     Montgomery     MGY   132  17   21    0,96     38
 31       Coffey       COF   132  37   70    0,95     107
 31       Flyman       FLY   132  72   97    0,91     169
 34        Self        SEL   133   6   22    0,97     28
 34         UCS        UCS   133  50   18    0,95     68
 34        Suni        SUN   133  41   41    0,95     82
 34      E-Rating       ER   133  25   67    0,96     92
 34      Sorensen      SOR   133  21   77    0,97     98
 39       Massey       MAS   134  20   13    0,96     33
 39  Bowl Champ Series BCS   134  28   20    0,95     48
 39     Billingsley    BIL   134  55   32    0,92     87
 39    Dolphin Pred     DP   134  52   38    0,96     90
 39   Random Monkeys    RM   134  27   63    0,96     90
 39       Bobcat       BOB   134  18   73    0,97     91
 39          ?         TRX   134  49   59    0,94     108
 39   Boyer-DeSimone    BD   134  51   78    0,94     129
 39        Palm        PSR   134  70   99    0,92     169
 48      SportsDoc      SD   135  24    2    0,96     26
 48        Reese       RSE   135  34   11    0,93     45
 48      BoCaDuck      BCD   135  67   49    0,90     116
 48       Colley       COL   135  54   72    0,94     126
 48        Moore       MOR   135  89   65    0,92     154
 48        Kiser       KIS   135  59   98    0,95     157
 54       Pigskin      PIG   136  63   35    0,94     98
 54        Jones       JON   136  79   42    0,90     121
 56        ARGH        ARG   137  44   26    0,95     70
 56      Whitlock      WLK   137  40   40    0,96     80
 56     PerformanZ     PRZ   137  42   53    0,96     95
 56      Claassen      CLA   137  48   51    0,95     99
 56     Solecismic     SOL   137  90   101   0,93     191
 61      Rudacille     RUD   138  14   12    0,97     26
 61     Massey's CONSENSUS   138  35   45    0,96     80
 61        Mease       MEA   138  30   58    0,94     88
 61        Wobus       WOB   138  29   64    0,94     93
 61      P-Rating      P10   138  96   33    0,85     129
 61         MJS        MJS   138  77   76    0,91     153
 61        Welch       WEL   138  62   95    0,93     157
 61         CSL        CSL   138  76   100   0,91     176
 69       Ashburn      ASH   139  12   15    0,97     27
 69      Anderson      AND   139  31    7    0,95     38
 69       Bassett      BAS   139  46   52    0,96     98
 69        Born        BRN   139  73   28    0,93     101
 69       Daniel       DAN   139  56   93    0,93     149
 69   Stephens-Sabey    SS   139  88   82    0,91     170
 75      Tellshow      TSW   140  83   25    0,93     108
 75        Rager       RAG   140  64   48    0,94     112
 75        Mark        MRK   140  61   90    0,91     151
 75       Holland      HOL   140  84   91    0,91     175
 79       Sagarin      SAG   141  15   17    0,97     32
 79      Hermrats      HER   141  33   81    0,96     114
 79       Colton       CTN   141  58   74    0,94     132
 79         Eck        ECK   141  69   68    0,91     137
 79        Elrod       ERD   141  81   71    0,91     152
 84       Sauceda      SAU   142  19   34    0,97     53
 85       Howell       HOW   143  60   36    0,93     96
 85      Congrove      CGV   143  93   14    0,89     107
 87       Maurer       MAU   144  68   29    0,95     97
 87      Pankratz      PFZ   144  91   46    0,92     137
 89       Marsee       MAR   145  75   27    0,94     102
 89          ?         SCP   145  95   37    0,88     132
 89        Hatch       HAT   145  98   87    0,91     185
 92       Kambour      KAM   146  94   31    0,93     125
 92       Dokter       DOK   146  87   43    0,94     130
 92      Matschke      MKE   146  86   96    0,95     182
 92        Gupta       GUP   146  97   103   0,90     200
 96         Laz        LAZ   148  47   60    0,96     107
 96       Krueger      KGR   148  80   50    0,94     130
 98       Markov       MKV   149  78   61    0,94     139
 99        Reid        REI   159  99   57    0,88     156
 100     YourLinx       YL   173  100  85    0,87     185