Sunday, March 22, 2009

Are champions the best?

I think not necessarily. 
I think that a champion is the winner of a systematic competition. A champion is not necessarily the best.

Conflicting opinion: The champion is the best until beaten. They are the best until proven otherwise.

All events have a random or unexplained element in them. If I flip a coin and it lands heads, do I assume that heads is the more probable outcome? If I cannot repeat the experiment I have nothing else to base it on. I submit that there is not evidence to support any hypothesis.
One competition can tell you absolutely who won that specific competition. The winner of a championship competition is by definition the champion. To find out who the best team is, there needs to be a larger sample size to approach the truth. I see the characteristic of being better or worse than someone as a mean and variance, not a single draw. A single draw from a distribution does not provide evidence to prove or disprove anything about mean or variance of the distribution. Likewise a single elimination championship game does nothing to prove or disprove which person or team is better.

Here are some practical examples. If I play ping pong with two friends. I can nearly always beat Dan, but Dan can almost always beat Landin. Alas, Landin can almost always beat me. So who is the best? I think it is very hard to tell. Is Landin better than me because he can beat me most of the time? The champion depends almost entirely on the systematic set up of the competition, primary which two play first (in single elimination.) 

So the winning team of the NCAA men's basketball tournament is clearly the champion, but are they the best? They might be, but I do not know. There is insufficient evidence to support that claim. Since there is definitely randomness in basketball games, the results will form a distribution if the experiment is repeated. With only one game it is hard to tell. Therefore, the more games that are in each round, the more likely the better team will prevail. The same way that more coin flips will tend to bring the flipper closer to the true distribution of outcomes.

To me this explains why there are less upsets in NBA playoffs compared with NCAA. Honestly, I really like March College hoops and think the randomness adds to the fun. I do not care if the tournament determines the best team or not. I think it is fun to watch and because there are high stakes, there is a high excitement level as well. Champion is good enough for me.

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