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College Football Ranking of Rankings Systems

November,  22, 2008 (108 Rankings)

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)

      Teams PW Fans PW TOTALS
Rnk Links to methods ABR Err Rnk WE Rnk SumRnk
1  Coleman's MinV   CMV 54 1 191 5 6
2  CPA Retro   CPR 94 6 175 1 7
3  McCormick   MCK 86 5 202 9 14
4  Sagarin-Elo   SE 104 12 185 3 15
5  PGH  PGH 104 12 201 8 20
6  E+ Å+ 105 14 201 7 21
7  TUB  TUB 103 8 213 15 23
7  Ashburn BCSC   ABC 106 17 196 6 23
9  ISR   ISR 103 8 214 16 24
10  Krach   KRA 105 14 205 11 25
11  Bowl Champ Series   BCS 103 8 214 18 26
12  Dolphin   DOL 103 8 217 19 27
13  Sorensen   SOR 99 7 218 23 30
14  Massey BCS   MB 109 28 186 4 32
15  Wobus  WOB 106 17 214 17 34
16  GTF  GTF 61 3 235 39 42
17  E-Rating   ER 107 22 217 21 43
18  TOL  TOL 106 17 223 30 47
18  Random Walker   RW 107 22 219 25 47
20  GFM  GFM 68 4 237 44 48
20  Anderson   AND 105 14 226 34 48
22  Random Walker FL   RFL 107 22 219 27 49
23  Fitzgerald   FIT 110 32 217 22 54
24  Greenfield   GRN 113 43 210 13 56
25  Maurer   MAU 107 22 227 35 57
25  Ashburn  ASH 113 43 212 14 57
27  Maas   MAA 110 32 219 26 58
27  Rothman   RTH 114 48 202 10 58
29  Bihl  BIH 110 32 223 31 63
29  Dokter   DOK 112 39 219 24 63
31  Rewards   REW 109 28 228 36 64
32  BSS  BSS 109 28 232 37 65
33  Wolfe   WOL 111 35 224 32 67
34  RTR  RTR 106 17 246 54 71
34  Waits  E-Cons 115 51 217 20 71
36  Mease   MEA 113 43 223 29 72
37  Kellner   KEL 109 28 237 46 74
38  Self   SEL 117 63 205 12 75
39  Colley   COL 111 35