## Statistical Proof that the Head-To-Head Tiebreaker Cannot ID the Better Team

Co-Champions of a round-robin tournament have always been exactly that without regard for who won the head-to-head meeting. But when only one team can advance to a post-season, there is a need to choose from among co-champions. In basketball and baseball, there is, to this day, a one-game playoff to decide which team advances; with no regard for the record of games between them during the season. Even if the Yankees swept the Red Sox in the season series, if they have the same record at the end of the regular season, they are tied for the division and an extra game is played to decide who advances to the post-season as the division champion representative.

The extra game is impractical in football, and so other tiebreakers were needed. In college football, when it was simply deciding who would represent the conference at the showcase bowl game, the invitation sometimes went to the team that had gone longer without representing. It made sense to simply choose to share the wealth because to choose based on the results of one game while disregarding the results of all others is statistically illogical. But when conferences must choose among division co-champs to see who goes to the conference championship game, the label has much more meaning. Enter the head-to-head tiebreaker.

The winner of the head-to-head game is the superior team, right? I mean, they proved it on the field, right? Never mind that the winner must have necessarily lost to a lesser conference team, thereby creating the duplicate record. Never mind that the head-to-head tiebreaker produces an unsolvable conflict in the event of a three-way tie. The head-to-head tiebreaker is a god among tiebreakers.

Except when it's wrong.

The bottom line is that the head-to-head tiebreaker is entirely incapable of identifying the superior team. All other sports are well-aware of the illusion of the head-to-head tiebreaker. Only football allows themselves to be deceived. I have developed a proof that demonstrates what all other sports have known all along: the teams are tied and a better method is needed to identify the superior team. Here is a PDF of that proof.

I've long been an advocate of eliminating divisions within the conferences and allowing them to match the two best teams in the conference championship game. It makes little sense to choose one of a conference's two best teams to meet a team that is third or worse in the conference simply because of arbitrarily drawn divisions. This silliness is exacerbated when the two best teams are tied and the conference uses the deceptively misleading head-to-head tiebreaker to choose among them.

Penn St. and Ohio St. were Big Ten Eastern Division Co-Champions. But who was the better team? Most said that Penn St. was better, because they proved it on the field. This is the illusion of the head-to-head tiebreaker. The problem with the head-to-head tiebreaker is that it ignores that the winner must necessarily have lost to a lesser conference team -- a very important quality indicator. (By "lesser" I mean "more losses than the co-champs.")

Like all FBS conferences, the Big Ten buys into this illusion. Their preset tiebreaker decreed that Penn St. represent the Eastern Division in the Big Ten Championship Game. Clearly, the playoff selection committee is well-aware of the illusion. They believed Ohio St. was the better team, as indicated by Ohio St's selection to the four-team playoff. And we are left with the non sequitor of a conference runner-up being selected to the playoff while that conference's champion is left out -- entirely antithetical to the spirit of competition. And my accusatory finger is pointed, not at the selection committee, but squarely at the Big Ten Conference.

Finally, I leave you with this point: if the Big Ten were without divisions, then the teams with the two best records (Penn State and Ohio State) would have met in the Big Ten Championship Game and the winner would have been an undisputed selection to the four-team playoff; and the loser would have been an undisputed omission.