Rank Rank 0707
• Äîìàøíÿÿ • Ââåðõ • Rank Rank 0707 • Rank Rank 0706 • RankRat • Rank Rank 05 • Rank Rank • RankRat • 11 October • 11 October • 1 November • 8 Novenber • 15 November • 22 Novenber • 25 october • 6 December •

 

• WWRR •
• ÁÀÑÊÅÒÁÎË •
• ÕÎÊÊÅÉ •
• ÒÅÍÍÈÑ •
• ÔÎÐÌÓËÀ 1 •
• CF •
• ÁÅÍÄÈ •
• ÝÊÎÍÎÌÈÊÀ •


Ãîñòåâàÿ

 

Ðåéòèíã@Mail.ru

Rambler's Top100 Service

271314@mail.ru

ÔÓÒÁÎË

ØÀÕÌÀÒÛ

Ó.Å.ÍÎÒÀ

ÕÎÊÊÅÉ

ÒÅÍÍÈÑ

ÝÊÎÍÎÌÈÊÀ

ÎËÈÌÏÈÀÄÛ

 

College Football Ranking of Rankings Systems

October,  14, 2007 (112 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 Trexler TSR 72 5 181 1 6
2 CPR CPR 72 5 184 2 7
3 Slots SLT 68 2 191 6 8
4 BMC BMC 68 2 194 7 9
5 Wilson WIL 75 7 195 9 16
6 WTS WTS 75 7 196 10 17
7 Rothman RTH 78 15 186 3 18
8 E-Rating = Å= 75 7 200 13 20
9 Self SEL 77 13 199 11 24
10 Greenfield GRN 79 22 187 4 26
11 UCS UCS 71 4 207 23 27
12 K-Rank KRA 76 11 204 18 29
13 Sagarin-Elo SE 79 22 195 8 30
14 Massey BCS MB 78 15 205 21 36
15 SLN SLN 76 11 209 29 40
16 WIS WIS 79 22 205 20 42
16 E-Rating + Å+ 78 15 209 27 42
18 Ashburn BCSC ABC 80 32 202 16 48
18 Massey COMP Cons 79 22 209 26 48
20 Ashburn  ASH 81 37 199 12 49
21 Rudacille RUD 81 37 201 15 52
22 Bobcat BOB 78 15 212 38 53
23 Sorensen SOR 78 15 212 39 54
24 CLA CLA 79 22 211 33 55
25 Sagarin SAG 81 37 204 19 56
26 WOB WOB 79 22 211 35 57
27 Bihl BIH 79 22 212 37 59
28 Massey MAS 80 32 209 31 63
28 MLR MLR 78 15 215 48 63
30 FIT FIT 80 32 210 32 64
31 BSR BSR 78 15 216 50 65
31 EL EL 81 37 209 28 65
33 Imes IMS 75 7 219 59 66
34 SAU SAU 84 55 201 14 69
35 BCS BCS 81 37 212 36 73
36 MCK MCK 77 13 220 62 75
37 Mease MEA 81 37 212 40 77
38 Maas MAA 81 37 215 46 83
39 HAN HAN 86 62 206 22 84
40 DeSimone DES 79 22 221 64 86
40 Junky's JNK 81 37 216 49 86
42 E-Rating Year ER 80