Tuesday, November 24, 2009

RBA and the BCS Log-Jam

RBA currently identifies the top five teams as having statistically indistinguishable records:  Texas, Boise State, Florida, TCU, and Pittsburgh.  What is particularly interesting about these five teams is that we cannot create an ordering based on expected head-to-head matchups.  The reasoning behind this is intuitive; teams simply match up better against certain other teams.  Given this information, who wins the national championship in a round robin home-and-home battle royale?  Full details after the jump.

The following table demonstrates how the top seven teams would perform in a round robin home-and-home series.  The rows of the tables represent the home team.  The columns represent the away teams.  The score for each game is shown in the table with the color code representing the victor for each game.  (My algorithm does not currently handle neutral site games, but you can approximate it by averaging home and away scores.) Gray squares represent predicted ties.  We have added Cincinnati and Alabama for reference because they are considered by the public to be among the top teams.

click to enlarge image

We observe some interesting trends from this figure.  First, home field advantage provides Texas, Boise State, Florida, and Pittsburgh a serious leg up on the competition.  All four of these teams are undefeated at home.  TCU is undefeated at home but plays a tie against Texas.  The major differences between the teams are their performances against Cincinnati and Alabama.  Cincinnati has the offensive firepower to keep up with Texas and TCU, forcing 24-24 ties with each, and outscore Alabama at home 24-17.  Alabama has the top-ranked defense but simply lacks the offense to keep up with the top five teams, who have good, although not necessarily exceptional defenses.

Among the top seven teams, we would expect the following records for the home-and-home round robin play:
  1. Texas:  7-3-2
  2. Boise State:  8-4-0
  3. Florida:  8-4-0
  4. TCU:  6-4-2
  5. Pittsburgh:  8-4-0
  6. Cincinnati:  1-9-2
  7. Alabama:  1-11-0
Alabama still has one more game before the SEC Championship to demonstrate that they can score enough to keep up with other elite teams.  (Hint:  Throw Julio Jones the freaking ball.)  Likewise, if Cincinnati can learn how to play defense against Illinois or Pittsburgh, they may change their fortunes.  RBA is just a prediction algorithm, but Alabama and Cincinnati simply don't look like they're in the same class as Texas, Boise State, Florida, TCU, and Pittsburgh.

The most important thing to note from this analysis is that, contrary to what conference partisans may suggest, the top five teams are evenly matched.  Any combination of them would make an excellent championship game.  We all have our own opinions about the BCS, and somebody's bound to get screwed by the system.  However, don't assume that any game between any of the top five teams constitutes a fraud.