# Doing the math on the NCAA tourney

Posted: March 17, 2014

I am reading about graph theory and the pairwise relationships between objects. Very soon, there will be many pairwise relationships scheduled between basketball teams, and it is very important to understand these.

Reading about graph theory is not fun - at least not for me - but it will be necessary to understand when it is time to decide if there is a graph that can properly predict whether the fourth representative from the Atlantic Coast Conference is superior in time, space, and three-point percentage to the automatic qualifier from the Sun Belt Conference.

The bracket for the NCAA men's basketball tournament will be announced Sunday night, so there isn't much time to study. If someone can correctly predict the outcome of every game of the tournament, including the April 7 championship, the Quicken Loans company has promised a prize of \$1 billion, or a quarter-percent break on refinancing your next mortgage, whichever you prefer.

The contest is backed by Quicken boss Jay Farner and insured by Warren Buffett, who is not known to make bad investments. It would be nice to win this contest, even though the prize isn't paid out in a Scrooge McDuck pile of cash big enough to fill the living room. The winner, if there is one, would get an annuity of \$25 million for the next 40 years, or if that sounds like a bad bet, a lump payment of a mere \$500 million.

It might also be tempting to turn down the prize in exchange for Farner's promise to stop doing those television commercials, but, in all likelihood, if someone wins, he or she will take the money.

"While there is no simple path to success, it sure doesn't get much easier than filling out a bracket online," said Buffett.

The mathematics people do not necessarily agree with Mr. Buffett about the ease of traveling the straightest line from laptop to success by way of this contest. They are working on it and publishing papers and putting forward their theories, but they still think it's pretty hard.

That is why graph theory has its place, but I am learning about transitivity, too. This is also vital as a means of ranking the value of two competing forces. I am working through the Massey Method, as invented by a mathematician named Ken Massey and is considered so important and smart that it was incorporated into the calculations that screw up football's BCS rankings every year.

Transitivity means that one outcome from the past can tell you a lot about a potential outcome in the future. It goes like this: Villanova beat Kansas by four points. Seton Hall beat Villanova by one point. Therefore, Seton Hall would beat Kansas by five points.

This, of course, is not what transitivity really is, but that is the sportswriter explanation. The mathematicians will quickly add that the two forces being ranked must also be weighted in other ways. It would have to be factored in that Villanova beat Kansas in November in the Bahamas, which is not the same as the Big East tournament in Madison Square Garden in March. It would also have to be factored in that Kansas is a very good team and Seton Hall, not to be unkind, is somewhat less.

What the math guys do, and this is what makes them math guys, is figure out numbers that correspond to all those factors. And yet, there is no equation to account for a driving layup that is deflected by a fingertip, bounces off the rim, is batted against the backboard, caroms into the hands of a trailing offensive player, who is then fouled while dunking the ball, and the play - which could have been worth zero or two points - is worth three points instead and a game that was about to be decided in one direction goes the other way.

I have looked at the graph theory and I just don't see that in there.

The way the contest is set up, with so many permutations possible in the bracket, there are 9,223,372,036,854,775,808 ways to fill out an entry form. That's 9.22 quintillion possibilities, a quintillion being a number followed by 18 zero places. Quicken, thinking just the way you do, has limited entries to one per household and to a total number of 15 million entries.

If you do the math - go ahead, you do it - subtracting the 15 million entries from the 9.22 quintillion possible outcomes, there is quite a gap there, even though the theory of infinity holds that if you gave an unlimited number of monkeys unlimited access to computers there will eventually either be a winner or the invention of Twitter.

In times of severe doubt, I go to the source of all wisdom regarding the NCAA tournament. This, naturally, is Joe Lunardi, who is an expert on the bracket and all things tournament related, which is a great surprise to those of us who have known Joe for 30 years. Nevertheless.

Lunardi says that someone would have "a better chance of landing a plane on the sun" than submitting a perfect tournament bracket. But how much better a chance? One would need to know the exact composition of the plane, the skill of the pilots, the surface temperature of the sun, and whether Joel Embiid will recover from his back issues in time to play later rounds of the tournament.

I trust Joe on the basketball bracket, and I trust that Mr. Buffett gets good advice on financial matters. But you know what else I trust? I trust the string theory of physics, which explains the relative relation of big objects in the universe, like galaxies and stars and power forwards.

The hour grows late. There is much reading still to be done on the string theory and it is almost time for Greg Gumbel to unveil the East Region. A billion dollars hangs in the balance like a free throw that quivers on the rim as the ball makes up its mind.

Here's something. Maybe the string theory is related to the twine theory. I understand the twine theory. Twine is very good. Twine wins games. But predicting the twine? Yes, I see it now. That's the catch.

bford@phillynews.com

@bobfordsports

inquirer.com/postpatterns