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College Football Ranking of Rankings Systems

December,  02, 2006 (105 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)

The simplest algorithm of e-rating WIN!!

Rating = Sum (Rating defeated) / number Los