Mike and I heard a trivia contest on the radio. The question was:
In the March Madness games, what are the odds of predicting the entire bracket correctly?
1 in 35,000
1 in 35,000,000 or
1 in 35,000,000,000
Mike and I (nerds that we are) sat and figured out that there are 63 games being played (32 the first round, then 16, then 8, then 4, then 2, then 1). Each game has 2 possible outcomes. So, 2 to the 63rd power should get you close to one of the answers. (We didn't have a calculator on us, so we didn't know exactly which one to pick, but we agreed up to that point.)
However, then Mike said that not all teams are evenly matched, so each game can't be a 50/50 shot. I said that there are still 2 possible outcomes and only 1 will be correct, so you still have a one out of 2 shot for guessing the game correctly. But Mike argues that especially in the first round of games, he thinks the better teams have more than a 1/2 chance of winning.
So, math friends, help us out. Is there a one in two chance of getting the correct outcome for each game, or are some games weighted due to the team's skill?
8 comments:
P.S. I am also now wondering if we needed to get a different probability at each level. The first 16 games you had a 1/2 chance of picking each correctly, but the next level of games you only had a 1/4 chance, the next level only a 1/8 chance, etc. So now I think we we wrong with the whole 2 to the 63rd power anyway. Oh, well. We're really not huge sports fans anyway, just big math nerds! :)
Teams ARE seeded according to rank, yes (ie, 1 plays 16, 2 plays 15, 3 plays 14,etc.). That means you get rewarded for being good by getting to play an easier team.
HOWEVER, I think that means the PROBABILITY of the higher-ranked team winning is higher than that of the lower-ranked one. But, the ODDS will never change; they will ALWAYS be 50/50, like you said. Either team A wins or team B wins. There's NO other possibility.
So it depends on if we're talking about probability or odds (or chance, I guess; is that synonymous with one of the others?). The question "What is the probability of a team winning the national championship?" is much different from "What are the odds of you PICKING the correct bracket?" Picking is much more limited than are winning probabilities; again, it's either a or b.
PS - yes, your comment above is also correct. Because the 2nd round depends on the first, your odds change if you get something wrong. Ex. if you choose BYU to win the first AND second rounds, and they lose in the first, then your second round pick is obviously already wrong. That's why when people pick a team to win the national championship (or even go to the Final Four or the Elite Eight), but the team gets knocked out in the first round, those people lose a TON of potential bracket points, because future rounds' picks are wrong before the round is even played, because the team picked is gone.
PPS - Also, as a point of note, there are actually 65 teams invited to the tournament; teams 64 and 65 play the very first game to see who gets to have a spot in the first round of the actual bracket that we're used to seeing. So that would be 1 more game you'd need to include in your calculations.
PPPS - Point of interest: As of Friday before the USU/Texas A&M game, there were only 3 perfect brackets left (among the 14.5 million that were registered on ESPN.com). Then USU lost, so there aren't any perfect ones left.
PPPPS - Did you ever find out the answer, anyway?
I agree with Spencer's second paragraph. But the rest of it, I just don't really care much about. I just get bugged that my other shows (NCIS and Grey's Anatomy) are reruns the first couple weeks of March Madness. Bleck.
The radio said it was a 1 in 35 BILLION chance of predicting the correct bracket. Mike used that to further his point. He said that if it was a straight 50/50 shot, then only one bracket would be correct every 5 or so years, assuming that every single of the 6 billion or so humans participated. Since there are more winners than that, he says that the ranking changed the probability. But I like what you said, SJ, about the probability of a team winning might be higher, but the ODDS of picking the correct outcome of any game are still one in two.
I agree with Lisa about not really caring about the actual sport. However, I do NOT care about the March Madness mustaches that guys in my ward are doing. Gross! (And most of them think that it is gross as well.) How do mustaches coorelate to March madness? Are the bball players sporting mustaches? Do people in your neck of the woods sport mustaches for this March madness?
um, no. that sounds kind of white trashy. ;)
So the "right" answer is (1/2)^64 which is way more than the 35 billion they said on the radio.
I think I qualify as a math nerd too. I read all of Spencer's comment. Not only did I read it, but I understood it AND I thought it was incredibly entertaining and interesting! :)
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