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The Purpose: Success not Perception

For obvious reasons, gamblers design rankings based on the perceived quality of the teams.  Many pundits in the world of college football also adhere to this principle.  However, FBS LOGICAL Football Rankings is adamantly opposed to this approach and believes that its influence is detrimental to the sport.  Rankings should reflect what has already happened on the field and should allow the result of each successive game to refine the previous rankings.  The unapologetic function of FBS LOGICAL Football Rankings is objective evaluation of accomplishment rather than prognostication of results.

The Foundation: Earned Wins

In the world of major college football, how much is a win worth?  The obvious but general answer to this question is that it depends on what team the win was against.  If a team beats an opponent with zero wins, the victory is not worth much; however, if a team beats an opponent with eleven wins, the victory is substantial since it was something eleven other teams failed to do.

My attempt to answer the question of precisely how much a win is worth led to the invention of a statistic I call Earned Wins.  The basic premise of the statistic is that not every actual win of a given team  is necessarily earned in comparison with the wins of other teams.  In other words, one team may earn all of its actual wins by playing a difficult schedule, while another team will only earn part of its actual wins if its schedule is weak relative to the first team.

The following hypothetical example will serve to illustrate the rationale behind the statistic, Earned Wins, and the derivation of its rudimentary formula.

In an ideal league with a 12-game schedule, there would be 13 teams and every team would play each other exactly once. There would be no upsets, so the best team would win all of its games, the second best team would finish 11-1, the third-place team would go 10-2, and this pattern would continue and finally stop with the worst team ending at 0-12.  If a team gets 11 win points for beating an 11-win team and 10 win points for beating a 10-win team and so forth; and if a team gets 11 loss points for losing to an 11-loss team, 10 loss points for losing to a 10-loss team and so forth, then the table below summarizes the results.
#1 12 0 66 0 66
#2 11 1 55 0 55
#3 10 2 45 1 44
#4 9 3 36 3 33
#5 8 4 28 6 22
#6 7 5 21 10 11
#7 6 6 15 15 0
#8 5 7 10 21 -11
#9 4 8 6 28 -22
#10 3 9 3 36 -33
#11 2 10 1 45 -44
#12 1 11 0 55 -55
#13 0 12 0 66 -66
For every team in the table above, Actual Wins = Difference/11 + 6.  
This is the basic formula for Earned Wins for a 12-game season.  

For a detailed explanation of the calculation of the adjusted form of Earned Wins, see the Glossary.

The Structure:  Logical Rankings

Every year it is impossible to produce rankings free of contradictory results.  This is due to upsets that create "circles" of teams.  A classic example of this occurred in the 2008 Big XII South.  Texas beat Oklahoma, then Texas Tech beat Texas, and then Oklahoma beat Texas Tech.  Each team finished the regular season with no other losses.  The challenge was to put the most deserving team at the top of the circle and the least deserving team at the bottom of the circle.  Most agreed that Texas Tech belonged at the bottom of the circle due to having played the easiest schedule, getting blown out by Oklahoma, and narrowly winning at home versus Texas.  The decision by the BCS to place Oklahoma at the top of the circle was extremely controversial and ultimately cost Texas a chance at a national championship.  

In 2014, another much-publicized controversy in the Big XII was due to a circle.  Baylor defeated TCU, then West Virginia defeated Baylor, and then TCU defeated West Virginia.  It was obvious that West Virginia belonged at the bottom of this circle, so much of the debate centered around the outcome of the Baylor-TCU game.  Objectively, the fairest way to settle such a dispute is to use SOS, but subjectively, most fans tend to favor the winner of the game between the top two teams.

Ultimately, it is the responsibility of the ranker to avoid clearly illogical rankings and to arrange teams within a circle using objective and equitable criteria.  As I write this, the first College Football Playoff rankings of 2015 are barely a day old.  By placing Alabama at #4, the selection committee created avoidable contradictions within its rankings.  Alabama lost to Ole Miss who lost only to unbeaten Memphis and 1-loss Florida.  Florida's only loss was to undefeated LSU.  The lack of a circle including both Ole Miss and Alabama implies that Ole Miss, Florida, and Memphis all should have been ranked ahead of Alabama.

The Details: Balancing SOS and Winning Percentage     

If Earned Wins are the only metric used to rank the FBS college football teams, the results are relatively reasonable, similar to the Colley Matrix and other mathematical ratings that employ an iterative process.  Nevertheless, no single number exists that accounts for SOS, winning percentage, and logical consistency.  

After sixteen years of intense and thorough analysis of ranking systems, I am confident that Earned Wins is unsurpassed in its ability to quantify the accumulated success of each team.  However, rankings should reflect the relative success of each team as well and should be internally congruous.  

FBS LOGICAL Rankings assigns a RATING to each team by modifying each team's Earned Wins according to the following formula: RATING = MIN(CEILING(EW,0.5),MAX(LEVEL,0.5 x INT(2 x EW)+P/M)). The teams are then ranked according to RATING with Earned Wins as the tiebreaker.  

The final stage involves rearranging teams such that the rankings are as non-contradictory as possible.  If a team has a negative  P/M, then upset losses are examined.  If a team has a positive P/M, then upset wins are examined.  Teams are re-ranked only if the sum of the absolute values of the resulting P/M of both teams is less than the sum of the absolute values of the initial P/M of the teams.                       

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