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Rank of rating systems.

Eugene Potemkin in Atlanta 1996 :) and as WSJ has wrought :)  
Moscow - Volga - Onega :)

Possible You do not know that e-rating help Bill Gates to be 6-th in Forbes Rank List. I think that he do not know about it too. So let him know :))

Pleese, help Bill Gates :))

BCS Problem - from Absolute to Relative theory

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

For the elementary estimation of the RANK of participants was used

RANK ESTIMATION = N - RANK

However it is not only one of possible elementary arithmetic expressions.

  • Err - number of errors
  • RnkE - rank by errors
  • WE - weighted errors
  • RnkW - rank by weighted errors

Err gives us teams points of view. (The less number of errors - the better)

WE presents fans points of view. (Errors in top of ranking list has lager weight)

Saturday, December 5, 2004 (105 Rankings)

                                 Teams PW    Fans PW     Trade PW     TOTALS
 Rnk Links               ABR      Err   Rnk    WE   Rnk   Adv   Rnk   SumRnk
  2  The Sports Report   TSR       98    17   193    4     88    1      22
  3  Massey BCS          MB        98    17   198    5     94    2      24
  5  Wilson              WIL       98    17   203    8     95    3      28
 22  Wobus               WOB      101    31   227    35    98    4      70
  3  Rothman             RTH       98    17   191    2     99    5      24
  1  CPA Retro           CPR       81    4    206    11   100    6      21
  8  Ashburn             ASH      101    31   199    6    102    7      44
 12  Sagarin-Elo         SE       101    31   209    14   104    8      53
 14  Sagarin             SAG      101    31   215    21   105    9      61
  7  Slots               SLT       74    2    218    26   105    10     38
 51  Daniel              DAN      111    79   240    55   108    11    145
 11  BC Moore            BCM       98    17   216    23   108    12     52
 14  Matthews            MAT      102    38   205    10   108    13     61
 24  Bihl                BIH      103    43   213    18   108    14     75
 19  CollemanMV          CMV       54    1    237    50   109    15     66
 25  Boyer-DeSimone      BD       104    50   208    13   109    16     79
 17  Random Monkeys      RM        98    17   221    30   110    17     64
  9  Dolphin             DOL       89    5    215    22   112    18     45
 10  E-Rating (BSJ)      ER(BCS)   97    10   213    17   113    19     46
 41  Claassen            CLA      106    62   237    49   113    20    131
 29  Mease               MEA      102    38   230    41   114    21    100
  6  Self                SEL       96    8    193    3    115    22     33
 45  Wolfe               WOL      104    50   243    60   116    23    133
 17  Rudacille           RUD      101    31   204    9    117    24     64
 38  Bobcat              D1A      105    58   232    42   117    25    125
 21  Massey              MAS       99    24   214    19   117    26     69
 32  Minton              MTN      107    65   215    20   117    27    112
 14  CPA                 CPA       98    17   212    16   118    28     61
 32  Massey COMP         Consens  104    50   223    33   118    29    112
 19  Greenfield          GRN       99    24   207    12   118    30     66
 55  Laz Index           LAZ      107    65   243    59   118    31    155
 41  Junky's             JNK       99    24   251    75   118    32    131
 31  Colley              COL       96    8    246    67   119    33    108
 23  Anderson            AND       97    10   218    27   119    34     71
 58  Howell              HOW      104    50   256    79   119    35    164
 35  Sauceda             SAU      107    65   211    15   120    36    116
 46  Reese               RSE      103    43   239    54   120    37    134
 41  Overtake & Feedback OAF      120    92   170    1    121    38    131
 40  McMurry             MMY      107    65   217    25   121    39    129
 39  Rager               RAG       97    10   253    77   122    40    127
 44  Curtiss             CUR      102    38   239    53   123    41    132
 26  Bobcat              BOB       92    6    228    39   125    42     87
 61  Real Time RPI       RTR      108    73   240    56   125    43    172
 37  Craig D             CRD      101    31   236    47   126    44    122
 30  Maas                MAA       99    24   222    32   126    45    101
 48  Schmidt             SCH      107    65   221    31   127    46    142
 48  Whitlock            WLK      105    58   227    37   127    47    142
 48  Palm                PSR       99    24   249    70   127    48    142
 13  McCormick           MCK       79    3    201    7    129    49     59
 54  Coffey              COF      105    58   234    43   129    50    151
 28  Bowl Champ Series   BCS       97    10   227    38   130    51     99
 47  Welch               WEL       99    24   245    65   131    52    141
 68  ARGH                ARG      110    77   244    63   131    53    193
 65  Colton              CTN      108    73   244    62   131    54    189
 27  Sorensen            SOR       97    10   216    23   131    55     88
 76  Mark                MRK      116    85   251    73   133    56    214
 73  MAU                 MAU      114    82   247    68   133    57    207
 69  Billingsley         BIL      106    62   251    74   134    58    194
 79  GB Eldredge         GBE      107    65   280    94   134    59    218
 72  BoCaDuck            BCD      107    65   258    81   135    60    206
 65  Eck                 ECK      103    43   260    85   138    61    189
 53  Suni                SUN      104    50   227    36   138    62    148
 64  MJS Standings       MJS      102    38   261    87   139    63    188
 57  Armstrong           ARM      104    50   235    45   139    64    159
 88  Elrod               ERD      115    84   293    96   142    65    245
 63  Graham              GRM      103    43   252    76   142    66    185
 80  CSL                 CSL      106    62   274    92   143    67    221
 75  DeSimone            DES      104    50   275    93   143    68    211
 89  Tellshow            TSW      118    88   290    95   145    69    252
 71  Gupta               GUP      104    50   260    84   145    70    204
 62  Hermrats            HER      103    43   243    61   148    71    175
 52  AccuRatings         ACU       97    10   244    64   150    72    146
 58  Trexler             TRX      103    43   236    48   150    73    164
 34  Fleming             FMG       95    7    224    34   152    74    115
 70  Solecismic          SOL      102    38   272    90   155    75    203
 74  GRS                 GRS      114    82   239    51   155    76    209
 60  Imes                IMS       99    24   245    66   157    77    167
 36  Dokter              DOK       97    10   220    29   159    78    117
 95  Pankratz            PFZ      122    95   308   100   165    79    274
 67  Kiser               KIS      103    43   247    69   168    80    192
 86  Marsee              MAR      110    77   259    82   168    81    240
 92  P-Rating            P+       108    73   333   102   180    82    257
 56  Bassett             BAS      101    31   235    44   195    83    158
 81  Dwiggins            DWI      105    58   259    83   195    84    225
 94  Moore               MOR      123    97   263    89   201    85    271
 84  Reid                REI      118    88   241    58   201    86    232
 86  UCS                 UCS      107    65   261    88   203    87    240
 81  Keeper              KEE      113    80   240    57   206    88    225
 90  Lawler              LAW      121    93   249    71   209    89    253
 91  Kislanko            KLK      121    93   250    72   210    90    255
 99  DKC                 DKC      125    99   313   101   217    91    291
 93  Congrove            CGV      113    80   306    98   219    92    270
 98  D1ACF               DCF      123    97   308    99   220    93    289
 85  Dolphin Pred        DP       119    90   239    52   220    94    236
 76  Real Time RPI       RPI      108    73   236    46   224    95    214
 95  Markov              MKV(E-R) 126   100   255    78   233    96    274
 100 Kambour             KAM      139   104   273    91   233    97    292
 103 Gridmarks           GM       126   100   342   103   243    98    301
 95  Pigskin             PIG      122    95   257    80   243    99    274
 81  Yearsley            YEA      116    85   229    40   263   100    225
 78  Nutshell            NUT      117    87   219    28   276   101    216
 104 MAY                 MAY      126   100   344   104   310   102    306
 105 SCP                 SCP      147   105   365   105   312   103    313
 102 Born                BRN      128   103   260    86   321   104    293
 100 SportsDoc           SD       119    90   294    97   380   105    292