Post
by slofstra » Mon Mar 22, 2010 12:33 pm
Mark,
Your point about choosing the favourite bracket. It's true that this has the greatest odds of yielding the best bracket. That is, of all bracket possibilities that one has the greatest possibility of being correct. However, even in a straight scoring contest, say, most picks correct, that bracket might not be your best choice.
Here is why. There are actually 2 exp 63 bracket possibilities or 9223372036854775808 bracket combinations possible (over 9 quintillion or 9 billion billion). So you can see that while the odds that the favourites bracket will be correct is greater than other brackets, these odds are still infinitesimally small. Depending on the number of entries in the pool, a large number of possible outcomes will allow your entry to win, and the probabilities of the outcomes that give you the most picks correct have to be summed to determine your probability of winning. So, for example, if you have picked an outlier (say Cornell) to be champion, and you are the only one to have picked Cornell, then your probability of winning increases because many possible outcomes (there are 9 quintillion / 64 of them) will allow you to win. Similarly, if you had picked Kansas and a million other people also picked Kansas to win, then other game picks start to factor down the number of outcomes that will yield success for your bracket. And if you picked favourites throughout, then with other entries also picking favourites the possibilities start to narrow. In short, the probability of your bracket winning depends also on the other brackets entered in the pool. In reality, in a very very large pool like the ESPN pool with millions of brackets, a bracket choosing Cornell as champion might have much greater probability of winning than a bracket choosing Kansas. In our contest, with 89 entries, you would have a relatively low probability of success compared to choosing a more successful team. At the same time, your probability of winning might still be much higher with Syracuse or a '2' seed than with Kansas.
Here's another illustration. You're in a contest with 5 people. You, along with other contestants, have to predict the number of heads that will turn up in 100 coin tosses. Whoever is closest wins the contest. You know that a guess of '50' has the highest probability of success. Now if you know (or guess) that the other guesses will be numbers like 48, 46, 50 and 55, without knowing the exact choices, you might be better to pick an outlier like 60 or 40 than to pick 52 or 49 since more outcomes will make you the winner. (It's a great advantage in this kind of contest, like guessing someone's age or weight, or the total score of a game, to be the last to guess).
Last edited by
slofstra on Mon Mar 22, 2010 12:43 pm, edited 2 times in total.
In our contest, 23 out of 89 picked Cornell to win that game. Some of the experts called it. Actually, any opening game won by a 9 to 12 seed is not really that unusual. Because of the nature of team selection, the actual quality in the 5 to 12 seed range is all over the place. Interestingly, 10 out of 89 have picked Cornell for tomorrow's game. And one bracket has them going all the way. If they get to Sweet 16 I might root with you. Everyone loves an underdog.
So much for my bracket. 
