Last year, I was watching commentary on the NCAA Basketball Tournament (March Madness to the layperson), and looking at the seeds in this year's Sweet Sixteen, I can't help but think about this argument.
Essentially, the commentator claimed that the seeding is generally wrong every year (ex post). His argument was that if the decision makers had seeded properly, there would be no upsets, as the teams would be seeded in such a way that the team who wins was the better team, and thus had earned the higher relative ranking. At first, I scoffed at this notion, and I still do now. The speaker's lack of understanding of the conception of the time/space continuum still bothers me to this day. Seeding clearly has to be done before the tournament. However, this is before the realization of random events that change the outcome of games. The arguer wants to see all the results, seed, then start the tournament.
Perhaps more troublingly is this sportscaster's (I wish I could recall his name) is implication that there is no stochastic element to the play of any given team, and thus presumably individuals that comprise the team. People get hurt, sick, have bad days, and conversely, sometimes, people play well beyond their normal levels. Even if everyone plays at the same level, there are in game factors that change matchups, negate advantages, and clearly alter the nature of the tilt (foul trouble, style of play, game plans, etc.). Since the sportscaster is acknowledging that there are upsets, it doesn't seem like an unfair assumption to assume that style of play entering into matchups is somewhat stochastic (in the sense that no one can predict with certainty what any given matchup will be as the tournament progresses).
The last point is that we've seen time and time again that transitivity is violated in sports. A beats B, B beats C, and then C beats A. That's a simple example with three teams, and an adaptation needs to be made for a tournament setting since it is single elimination. However, the point still holds. If the 1st seed matches up well against the 2nd, but not the 3rd, and the 2nd matches up well against the 3rd, you've got this scenario. To take this even further, there is no commutativity in sports. That's of course why there are season splits in any sport where teams play an opponent multiple times in one season. It would be absurd to say that a 1st seed would beat a 2nd seed every single time they played (often due to the stochastic events noted above).
Given this, I offer not only my rejection of the commentator's claim, but a stronger statement. I would argue that if there were no upsets, THEN the seeding was wrong. The reason that there would be no upsets would seem to imply one of two things: 1. There were no random events, and 2. If there was randomness, it never went in the way of the underdog (at least not to a great enough degree). Clearly, there are stochastic elements to sports, so one is out. As for the second, the teams are often so closely matched talentwise that in many cases, any amount of randomness is a "great enough degree" to alter the outcome. There are often many games played between said closely matched teams that it seems extremely improbable that the randomness would always aid the overdog.
On a final note, if the commentator had been less fundamentally flawed (and even correct by some minor miracle), betting would be a slam dunk (pardon the pun).
-FSG
