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 only one of possible elementary arithmetic expressions and no more that.

To look as influence various  estimation models of the RANK, I used some more expressions

2. RANK ESTIMATION = N / RANK - gives more "attention" to the top rank

3. RANK ESTIMATION = (N - RANK) ^ 2

4. RANK ESTIMATION = RANK / (N - RANK) - gives more "attention" to the top rank

                                         N-R     (N-R)^2 N/R     (N-R)/R
Rnk M Link              ABR   M9  M8 M9-MVal Rnk Val Rnk Val Rnk Val Rnk
  1   Slots             SLT   49         178  16 228  28  9   97  12  97
  2   Massey BCS         MB   70  73  -3 155  1  185  1   7   31  9   35
  3   Sports            TSR   77  68  9  155  2  185  2   3   1   4   1
  4   Wilson            WIL   78  68  10 162  4  203  5   7   10  9   10
  5   New York Times    NYT   79  65  14 190  32 240  41  8   63  10  64
  6   CPA Retro         CPR   79  57  22 181  20 221  20  6   8   8   8
  7   Bowl Champ Series BCS   80         181  19 223  21  7   18  9   19
  7   Massey COMP       CONS  80  83  -3 185  28 224  24  7   20  9   21
  7   Sagarin-Elo        SE   80  76  4  168  9  212  10  7   23  9   26
  10  Wolfe             WOL   81  58  23 177  15 216  14  7   12  9   12
  10  Kiser             KIS   81  76  5  207  55 250  50  7   21  9   20
  10  Self              SEL   81  70  11 166  6  208  9   7   28  9   29
  13  McCormick         MCK   82         164  5  205  6   6   6   8   6
  13  Bobcat            BOB   82  70  12 192  35 243  45  8   65  10  65
  15  Bihl              BIH   83  84  -1 167  8  202  4   6   7   8   7
  15  Craig             CRD   83  73  10 195  38 242  43  7   53  10  53
  17  Wobus             WOB   84  76  8  197  44 234  35  7   13  9   13
  17  Eck               ECK   84  71  13 211  60 251  52  7   22  9   23
  17  Rothman           RTH   84  73  11 159  3  197  3   7   27  9   27
  17  Random Monkeys     RM   84         184  24 233  33  7   37  9   38
  17  CPA               CPA   84  65  19 186  29 224  23  7   47  10  46
  17  BoCaDuck          BCD   84  78  6  212  61 263  72  7   52  10  51
  17  Matthews          MAT   84  76  8  192  36 242  44  8   69  10  70
  24  Claassen          CLA   85  81  4  197  42 237  37  7   15  9   14
  24  Imes              IMS   85  81  4  214  65 258  61  7   26  9   25
  24  Billingsley       BIL   85  66  19 183  23 219  17  7   36  9   39
  24  Colley            COL   85  76  9  210  58 254  56  7   40  9   41
  24  Maas              MAA   85  77  8  196  40 253  54  8   73  10  74
  29  Ashburn           ASH   86  76  10 176  13 219  16  7   25  9   24
  29  Boyer-DeSimone     BD   86  75  11 202  50 252  53  7   35  9   34
  29  Sorensen          SOR   86  76  10 197  43 254  57  8   57  10  58
  29  Gindin            GRS   86  74  12 214  67 266  75  8   85  11  84
  33  Palm              PSR   87  69  18 214  66 260  64  7   50  10  50
  33  Dwiggins          DWI   87  82  5  197  45 238  38  8   59  10  59
  33  E-Rating           ER   87  75  12 214  68 267  77  8   64  10  63
  33  Suni              SUN   87  74  13 174  12 214  12  8   68  10  71
  33  Flyman            FLY   87  77  10 226  84 277  87  8   70  10  68
  38  Daniel            DAN   88  77  11 184  25 232  32  6   5   8   5
  38  Welch             WEL   88  83  5  210  57 255  59  7   41  9   42
  38  DeSimone          DES   88  86  2  205  53 233  34  7   45  10  45
  38  WAJL10            WAJ   88  84  4  201  47 245  47  8   62  10  62
  42  Mease             MEA   89  76  13 191  34 226  25  6   9   8   9
  42  Mark              MRK   89  77  12 180  18 207  8   7   14  9   15
  42  Colton            CTN   89  83  6  201  49 239  40  7   16  9   17
  42  Coffey            COF   89  81  8  184  26 217  15  7   33  9   33
  42  Holland           HOL   89  78  11 227  86 277  86  7   44  9   43
  42  Armstrong         ARM   89  81  8  210  59 260  65  7   48  10  48
  42  Rager             RAG   89  80  9  215  69 262  69  8   87  11  88
  42  Montgomery        MGY   89  75  14 181  21 226  26  9   93  11  95
  42  Anderson          AND   89  64  25 214  64 273  81  17 102  23 102
  51  Greenfield        GRN   90  74  16 170  10 212  11  7   30  9   32
  51  MJS               MJS   90  77  13 216  71 258  62  7   34  9   31
  51  McMurry           MMY   90  76  14 166  7  207  7   7   51  10  52
  51  Massey            MAS   90  83  7  178  17 221  18  7   54  10  55
  55  Reese             RSE   91  76  15 191  33 230  30  7   11  9   11
  55  Dolphin           DOL   91  79  12 190  31 229  29  7   29  9   28
  55  Hermrats          HER   91  81  10 201  48 237  36  7   42  9   44
  55  Rudacille         RUD   91  62  29 174  11 214  13  7   46  10  47
  55  SportsDoc          SD   91  78  13 183  22 223  22  8   58  10  60
  55  CSL               CSL   91  82  9  224  81 274  83  8   67  10  67
  55  Dunkel            DUN   91  71  20 217  72 265  74  8   74  10  73
  62  Sagarin           SAG   92  84  8  176  14 221  19  7   38  9   40
  62  Elrod             ERD   92  84  8  213  62 248  48  8   56  10  56
  62  Fleming           FMG   92  79  13 203  51 255  58  8   72  10  72
  62  Howell            HOW   92  80  12 206  54 253  55  8   76  10  76
  62  Gupta             GUP   92  63  29 221  75 273  80  9   98  12  98
  67  P-Rating Hard     P05   93  87  6  246  96 292  93  6   4   7   4
  67  Bassett           BAS   93  82  11 195  39 239  39  7   32  9   30
  67  Sauceda           SAU   93  81  12 184  27 230  31  8   61  10  61
  70  UCS               UCS   94  78  16 222  78 263  70  7   43  9   37
  70  BMC               BMC   94  84  10 221  76 260  63  9   94  11  94
  72  ARGH              ARG   95  87  8  190  30 226  27  7   55  10  54
  72  Stephens-Sabey     SS   95  87  8  241  93 298  95  8   71  10  69
  72  P-Rating Hard PowP05S   95         230  89 281  89  8   80  11  78
  72  Krueger           KGR   95  91  4  194  37 241  42  8   84  11  85
  72  Ranma             RAN   95  84  11 226  85 260  66  11 101  14 101
  77  Matschke          MKE   97  83  14 200  46 250  49  7   24  9   22
  77  Congrove          CGV   97  90  7  232  90 274  82  7   39  9   36
  77  Tellshow          TSW   97  87  10 223  79 271  79  8   66  10  66
  77  Hatch             HAT   97  83  14 225  82 286  90  8   81  11  81
  81  P-Rating Real     P10   99  90  9  250  99 296  94  5   2   6   2
  81  PerformanZ        PRZ   99  85  14 204  52 251  51  7   17  9   16
  81  Whitlock          WLK   99  82  17 196  41 245  46  7   49  10  49
  84  Solecismic        SOL  100  81  19 218  74 265  73  7   19  9   18
  84  Å-Rating Soft    E1000 100  73  27 209  56 262  68  8   82  11  82
  84  Laz               LAZ  100  94  6  223  80 275  84  8   83  11  83
  87  P-Rating Soft     P20  101  93  8  258 102 302  96  5   3   7   3
  87  E-Rating Hard     E20  101  76  25 217  73 263  71  8   75  10  75
  87  Dokter            DOK  101 100  1  225  83 270  78  8   77  10  77
  87  E-Rating Real     E31  101  75  26 213  63 262  67  8   78  11  79
  91  Moore             MOR  102  95  7  251 100 317 100  9   89  11  89
  92  Marsee            MAR  103  91  12 215  70 256  60  8   79  11  80
  92  Pigskin           PIG  103  93  10 229  88 289  92  9   95  11  93
  94  Born              BRN  104  92  12 234  91 287  91  8   88  11  87
  94  Markov            MKV  104  94  10 228  87 275  85  19 103  25 103
  96  Maurer            MAU  105  70  35 222  77 267  76  9   96  12  96
  97  P-Rating Real PowP10S  106         255 101 302  97  8   86  11  86
  98  Kambour           KAM  108  99  9  248  98 307  98  8   60  10  57
  98  Pankratz          PFZ  108  92  16 241  92 280  88  9   92  11  92
 100  P-Rating Soft PowP20S  109         274 103 323 103  19 104  25 104
 101  YourLinx           YL  113  87  26 304 104 373 104  10 100  13 100
 102  E-Rating Soft PowE1000S116         244  95 318 101  9   91  11  91
 102  E-Rating Hard PowE20S  116         248  97 320 102  10  99  13  99
 104  E-Rating Real PowE31S  120         244  94 316  99  9   90  11  90