August 13, 2011

Why BCS Lovers Should Rethink Their Stance

     
     A lot of arguments against the BCS consist of intangible things like fairness, greed, and playing games on the field rather than on paper.  This is not one of those arguments.
     As a sports fan, I love the BCS.  It forces teams to schedule tough (aka exciting) games, it makes for amazing discussion between college football watchers, it gives teams an incentive to try in every regular season game, and it adds a level of excitement to mid-season games that normally wouldn't be there.  There's one problem with the BCS though.  It does a horrible job with the one thing any postseason is meant to do:  find the best team.
     I know what you're thinking.  How is an undefeated team not the best team?  Look at it this way:  If a team has an 80% chance of winning each game, there's a 5.5% chance that they win 13 in a row.  A team that wins 90% of its games has a 25% chance of winning 13 in a row.  We get undefeated teams by a combination of skill and luck, not because a certain team is unbeatable.  So while it's more common for a better team to go undefeated than a merely good one, the better teams still have a low chance of achieving a perfect season.
     This idea led me on one of my random mathematical experiments back in January.  What if we knew exactly how good each team was before the season started?  How often would the BCS crown the actual best team as the champion?  Would a 4, 8, or 16 team playoff really be better?
    
     Note:  The red brackets signify text under the Unnecessary Math Talk Alert.  Skip ahead if you wish.
   
     [I started by creating a hypothetical NCAA, giving each of the 120 teams a True Winning Percentage (my term for how often a team would win in an infinite number of games against an average team).  The top team was given a TW% of 90%.  Using those percentages, I simulated 50 seasons consisting of 12 games against average teams.  (There was an average of 2.22 undefeated teams per year.)  Ties were broken in a random fashion.  The final step was simulating a 2, 4, 8, and 16 team playoff for each season, using Bill James' Log5 formula in combination with the TW%'s.]
     Here's how it went:

BCS

In Numbers:
Average Actual Rank of Champion:  9.40
Standard Deviation of ARC:  11.32
Percentage of Correct Champions:  4%
Median of ARC:  5
Worst ARC:  59
Champion is in the Actual Top 2:  18%
Champion is in the Actual Top 5:  52%
Champion is in the Actual Top 10:  76%

In Words:
     The hypothetical BCS crowned the best team as champion only 4 percent of the time, by far the worst among the postseasons tested.  It was the worst in every category measured.  The real best team made the BCS title game 12% of the time, which is less than the frequency with which it won the championship in every other situation.  The BCS even gave a title to a truly average, 59th best team.

4-Team Playoff

In Numbers:
Average Actual Rank of Champion:  6.68
Standard Deviation of ARC:  7.92
Percentage of Correct Champions:  14%
Median of ARC:  4
Worst ARC:  39
Champion is in the Actual Top 2:  30%
Champion is in the Actual Top 5:  66%
Champion is in the Actual Top 10:  86%

In Words:
     The 4-team playoff settled in nicely as the 2nd worst option.  It named top-2 and top-5 teams as champions more frequently than the 8-team playoff but was still prone to some really bad seasons.

8-Team Playoff

In Numbers:
Average Actual Rank of Champion:  5.56
Standard Deviation of ARC:  4.48
Percentage of Correct Champions:  18%
Median of ARC:  5
Worst ARC:  20
Champion is in the Actual Top 2:  28%
Champion is in the Actual Top 5:  58%
Champion is in the Actual Top 10:  88%

In Words:
     The 8-team playoff was the "game manager" of postseasons.  It didn't crown great teams as often as its 4-team and 16-team counterparts did, but it didn't produce any ridiculously bad results.  Auburn started last season ranked #22 and won the title.  That's the equivalent of the worst season the 8-team playoff put up in this simulation.

16-Team Playoff

In Numbers:
Average Actual Rank of Champion:  5.60
Standard Deviation of ARC:  6.25
Percentage of Correct Champions:  18%
Median of ARC:  4
Worst ARC:  32
Champion is in the Actual Top 2:  34%
Champion is in the Actual Top 5:  70%
Champion is in the Actual Top 10:  90%

In Words:
     If the 8-team playoff was the "game manager" of the simulation, then the 16-team playoff was its Brett Favre.  It was the best at making great teams the champion, but it did produce some crazy seasons as well.  In one, the 32nd best team won as a 9-seed.  In another, the 29th best team won as a 16-seed.  I may write that off as a flaw, but I'm sure somebody out there loves the possibility of a Cinderella/David that this system allows.

The Conclusion:  I started this project hoping to get numerical "proof" that the BCS was the way to go, and I was completely proven wrong.  The BCS doesn't work because of the sheer number of teams competing for the title.  There are so many decent teams that one of them is probably going to end up winning 13 games in a row.  By adding a playoff, those teams are forced to win 14, 15, or 16 games in a row, which is really tough when you're not that good to begin with.
     I want to throw my support toward the 8-team playoff because it's still sort of close to the BCS I love, but looking at the numbers objectively, I have to say that the best plan is a 16-team playoff, using the AP rankings, with no conference tie-ins.  You win, condescending media jerks.

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