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.
|TEAM||WINS||LOSSES||WIN POINTS||LOSS POINTS||DIFFERENCE|
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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