courtesy USA TODAY Sports Images
I seem to get less response here on Older Eyes – Bud’s Blog to posts on sports and on science than any other topic. So, the odds are, I’ll get even less response to this one, which touches on both. Given that it’s posted on Saturday, which, in my experience and that of several websites that track blog traffic, is the least busy day of the week, I am probably writing to myself. Which is OK. I find this topic interesting. Today … halfway through the first round of the NCAA Men’s Basketball Tournament … there are no perfect brackets left in the Quicken Loans Billion Dollar Challenge. Or in the ESPN Bracket Challenge. According to Yahoo, One perfect bracket – “Brad’s Breathtaking Bracket” – remained after the 25th game in Yahoo Sports Tourney Pick ‘em, but that bracket was not entered in the billion-dollar challenge. As an engineer with a heavy background in statistics, I’m certainly not surprised. Whether the odds of winning are 9,223,372,036,854,775,808 to 1 as most sources report or approximately one in 128 billion as Jeffrey Bergen, a math professor at DePaul University, calculated, it translates to chances of slimski and noneski. And as reported online, slimski seems to be out of town. Yes, I’d be willing to make a substantial bet that Brad’s Breathtaking Bracket won’t survive Saturday.
As is frequently the case on Yahoo Sports, the comments on articles are more interesting than the articles themselves. Is it possible the popular homepage is named after the people who comment on their articles? Some comments were funny: Jim A said, Hell, I was eliminated yesterday. I took my lobster back to the grocers and exchanged it for Ramen noodles. The grocer
understood totally as he had to return his Ferrari. Some are clueless. Lambaster claims, The key to picking is four stats: (I’ve missed five, because I ignored theses stats on those games) first: rebounds, second: assists, third: (tie breaker) field goal percentage, and if your pic rates higher in assists then they must rate better than the other team in free throw percentage. Almost infallible. No, Lambaster, it’s the odds. There are usually conspiracy theorists: Bruce B: This Guy that has a perfect bracket , is probably a hacker that can manipulate the system. No one could predict all the upsets that have happened. Yes, Bruce B, someone could. The odds will tell the likelihood. Some resort to social commentary. BidNow73: Depending on who you ask, the odds of picking a perfect bracket sit somewhere between 1 in 128 billion and 1 in 9.2 quintillion, give or take a few decimal points. So much for the mathematics curriculum in the public school systems in the United States. Aren’t you curious what BidNow73‘s education is, spending Friday night as he does, trying to sound smart on a Yahoo Sports page?
So, OK, why the discrepancy between the quoted odds of 1 in 128 billion and 1 in 9.2 quintillion. It has to do with the nature of probabilities. If you want to compute the odds of winning a lottery, you calculate the number of combinations of numbers possible. For instance, there are 258,890,850 combinations in the Megamillions lottery. Since any number is equally likely in a random draw (unless you are a conspiracy theorist), then the odds are 1 in 258,890,850. However, in March Madness, two things are different. All outcomes aren’t equally likely. A 16 seed has never beaten a 1 seed, for example. This changes the likelihood of winning combinations in the first round. The probabilities of games in the later rounds depend upon who won in the first round. For instance, the odds of a particular second round game are very different if both teams were favored in the first round than if one underdog slips by. In statistics, we say that the 9.2 quintillion combinations are not only not equally likely, the are not independent. This makes the exact calculations of the odds virtually impossible. That’s why Jeffery Bergen said approximately 1:128 billion. He likely based his calculations on historical averages or did many trials using a computer simulation. And, at the end of the day, these are college kids, capable of rising above or falling below historical (or Las Vegas) odds.
A final note to BidNow73: Does that sound like the sort of thing you learned in the public school system? And: If you want to sound smart, get yourself a blog.
