Given what you know about college basketball, the NCAA Tournament, and probability, are you surprised there are two that are correct? Or would you have expected there to be more that were correct? Or less?
If you answer, make sure you justify your answer.
Now I'm not totally sure if my way of calculating these probabilities are legitimate, especially because I didn't really know how to take the probability of a team losing and incorporate it into my calculations. Basically I calculated the probability of such a bracket twice.
ReplyDeleteThe first time, I assumed that each team automatically had a one in two chance of winning, no matter the seed. This would mean that Kentucky, Butler, and UConn all had a one in sixteen chance of making it to the final four because they all played four games to get there ( (1/2)^2 )=1/16. VCU, however, had to win an extra game that none of the other final four teams did since they were tied for eleventh seed, so their probability of making it to the final four was (1/2)^5 or 1/32. At this point, one would multiply the four probabilities together to calculate the odds of all four of these teams making it to the final four: (1/16)(1/16)(1/16)(1/32)=1/131072. This means that these four teams would get to the final four once in every 131072 random trials of March Madness. This is obviously a poor calculation since over five million people submitted a bracket to ESPN and only two successfully predicted the final four perfectly. Of course it is worth mentioning that probability and someone filling out a bracket are two very different things. When the typical person fills out a bracket, he picks teams that are seeded well, or perhaps the college he attended, or maybe predicts a year of total upsets. This is important to recognize because I’m willing to bet that very few people filled out brackets at random, however probability is very useful in looking at the odds of certain events playing out the way they do, and not so much the brackets that were predicted because I’m also willing to bet that there were hundreds of brackets that people submitted with even larger upsets than the ones that happened. In fact, many people use a coin and toss it for every game, assigning heads to one team and tails to another to pick wins for the entire tournament. The above calculation, then, is one that reflects the odds of Abraham Lincoln, AKA your average penny picking the Final Four perfectly.
Clearly, though, seeds play a huge role in the average person’s bracket. So instead of allowing each team a .5 chance of winning any given game, I gave seeds 1-4 a ½ chance of a win, seeds 5-8 a 1/3 chance of a win, seeds 9-12 a ¼ chance of a win and seeds 13-16 a 1/5 chance of winning. Kentucky and UConn, then, have a .5 chance to win a game, Butler has a 1 in 3 chance, and VCU has only 1 in 4. Using the same method of calculation as my previous one, the chance of Kentucky, UConn, Butler and VCU making the Final Four are 1/16, 1/16, 1/81, and 1/512 respectively. Then, multiplying these four probabilities together the result is 1/10,616,832. That’s more like it. With the seeds now considered, it shows a much more realistic projection of the final four being the way it is. If 5.9 million people submitted a random bracket, then hypothetically one predicting the Final Four is highly improbable. However, it is important to reiterate that brackets are rarely predicted at random. Perhaps the lucky author of one of the two ESPN brackets attended VCU and is a big fan. Maybe he flipped a coin. Maybe he got lucky. Everyone has to agree with the latter. March Madness is a perfect example of probability. Maybe VCU’s coach can give a more inspiring halftime speech than any other in the league. Maybe Butler’s coach does. Probability is only a way of looking at events or in this case a series of events and predicting the chances of results without considering flukes or luck. I’d say that predicting the Final Four on a year such as this one is extremely difficult and a tremendously (lucky) accomplishment. In fact, I won in my own March Madness bracket simply because I put Butler through to the final four when no one else did. These two very improbable and lucky brackets are definitely freakish, in my opinion.
correction- in my first calculation it should be (1/2)^4 not (1/2)^2
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