An Illusion of Fairness: March Madness is Mad for a Reason

At its core, college basketball is an egalitarian sport. There are 345 Division One basketball teams who theoretically contend for the national championship each year, yet only 120 FBS football teams are eligible for their championship game. Who could imagine a team from the Horizon League beating a Big Ten team in football, or a Colonial Athletic Association squad upsetting Connecticut on the gridiron? Both events, and numerous others just as improbable based on name brand, have taken place in the NCAA Tournament this decade, inevitably leading to predictable stories about teams proving they belong.

But teams don't really prove they belong in the NCAA Tournament. In basketball, a sport where one athlete can make a team and roster sizes are small, upsets happen frequently. And in a single-elimination tournament, where one team can have the worst shooting night of their entire season, upsets can be devastating to an otherwise excellent year.

Virginia Commonwealth's victory over Kansas doesn't prove they are better than Kansas-- there's actually quite a bit of evidence to indicate they are not-- and it doesn't prove that we habitually underrate mid-major teams come Selection Sunday. Single-elimination tournaments in a sport as upset-conducive as basketball will always have statistical anomalies and surprising outcomes;  and while the specific upsets are surprising, it shouldn't shock anyone that they exist.

A 2002 study published by Éric Marchand in the Journal of the Royal Statistical Society, entitled On the Comparison between Standard and Random Knockout Tournaments, examined the end-result differences between standard single-elimination tournaments, e.g. the NCAA Tournament, and random single-elimination tournaments, i.e. tournaments that do not match teams up by perceived strength.

In theory, the standard tournaments should end up with more higher seeds advancing deeper into their bracket than the random tournaments. For top seeds, the theory plays outs. But for everyone else, it doesn't.

It is interesting that, for other players ranked highly but not first, such as players ranked third of 16 and eighth of 64, the probabilities cross, indicating that the random draw becomes more advantageous for sufficiently large values of θ despite the fact that they are ranked highly and obtain a favorable first-round match with the standard draw.

Essentially, unless you are a No.1 seed, Marchand's analysis indicates that you would have a better chance of advancing deeper into the NCAA Tournament if your opponents were randomized instead of matched up according to perceived ability. This study corroborates the historical data we have for the NCAA Tournament. No. 4 seeds don't have any advantage over No. 5 or No.6 seeds in reaching the Final Four, and No. 2 seeds only have the tiniest of advantages over No. 3 and No. 4 seeds in reaching the championship game.

The majority of upsets that draw viewers, the enchanting No. 12 seed over No. 5 seed type, occur in single-game bursts; a lower-seeded team upsets a higher-seeded team only to immediately lose to another higher-seeded team a game later. It's exceedingly rare for lower-seeded teams to go on deep runs into the tournament, VCU and Butler notwithstanding.

From No. 2 to No. 8 seeds-- eight being the lowest seed to ever win an championship-- the NCAA Tournament amounts to a statistical crapshoot because of its single-elimination nature. Any team can shoot poorly one night, no matter how good they were during the season, and lose because they got cold at the wrong time.

And here's where the flaw of the tournament really reveals itself. Although No.1 seeds have an overarching advantage in advancing deeper, it does not translate to individual contests. Against teams with No. 2 to No. 4 seed rankings, the No.1 seed has only won 59% of its games; when the field is expanded to No. 2 to No. 6 seeds, the winning percentage grows to 66%; only when you include No. 2 to No. 10 seeds do top seeds win an overwhelming majority of games.

Ultimately, the only thing VCU's success has proven is the importance of timeliness in college basketball. It's more important to be lucky and playing well during a six game stretch in March than it is to be consistently excellent throughout a 34 game regular season.

When there are so many peripheral factors at play in the NCAA Tournament, so much noise affecting individual results, a single-elimination format ceases to function in its chief role: determining the best college basketball team in the country. Really, the NCAA Tournament is not any more efficient at determining a champion than the BCS system used in college football. It just provides an illusion of fairness through a single-elimination playoff system.

So, why has the NCAA Tournament been universally embraced and the BCS almost universally criticized? Is it because the term playoff connotes fairness to a sports fan? Are we so hard-wired to think that even a fatally flawed playoff system, one prone to statistical anomalies and extreme cases of luck, is any better than no playoff at all?

My initial answer, and I'm very interested in hearing other theories, is that the recurring drumbeat of "settling it on the field" has taken hold in most fans' minds, and it's so strong that it pushes aside the obvious fact that the regular season is played on the field, as well. People see playoffs as a time of ultimate performance, when the elites separate themselves from the pretenders and the weak succumb to the extreme pressure.

There's another line of thinking, of course, that the NCAA Tournament doesn't need to truly find the best team-- it just needs to be fun. But if we accept inadequacies in the NCAA Tournament, why do we demand perfection in college football when evaluating the BCS?