The Collision of Game Theory & NCAA Brackets, part 1

When not toiling away with Vlookup Functions and the infamous Index(Match()) combo, Vlookup Vince actually has other interests in life in addition to sports.  Nerdily enough, Game Theory is near the top of that list.  Game Theory tries to capture people’s behaviors using math, and is most often applied to the arena of economics.  Your boy John Nash, of Beautiful Mind fame, is rumored to be the legitimate father of this world.   I had no intention of jumping head first into a ‘how to fill our you bracket’ discussion, especially from a game theory perspective, but the events of the weekend, and a fascinating scenario in my person pool has left me no option.  Vlookup is compelled to engage in a fascinating conversation regarding game theory and brackets.  Academics and the boring stuff aside, we all rock some Game Theory when we fill out our brackets, whether we know it or not.

Each of us fill out our brackets with with the same goal: winning mad cash money by accumulating more points than anyone else.  However, everyone else in our pools has the exact same goal, which is precisely where Game Theory comes in.  One of the fundamental tenants of Game Theory is basing our decisions on how we think others will act.  You are trying to put together the bracket that gives you the best chance to win against the other members of your pool, while they are doing precisely the same thing.

Will everyone have Louisville wining it all?  Of the one seeds, which is the one most people will have losing early?  Where can I squeeze out a few extra points out versus everyone else?  Subconsciously, many of us ask ourselves these questions as we pick our teams – clearly basing our decisions on our expectations of how others will act.  This leads Vlookup Vince to using one of two strategies:

Pick one of the two favorites, along with more upsets, especially early upsets:

Seems most years there are two favorites.  This year, Louisville and UNC seem to be the two squads of choice for the majority.  Across ESPN’s 5 million brackets, the two aforementioned squads are the champion in well over 50% of the entries.  In any given year, it is entirely likely that one of these two teams will in fact win it all, yielding many of these entrants with the right champion, and nothing to show for it – and what is more frustrating than that?  The right champion, a strong final four, but even heading into the last weekend, you know you can’t win because you are in 10th place – among people with UNC as the champion. The problem:  you followed the consensus for the most part, had a weak first few rounds, and were too far behind to win any money, even with the strong finish.  The solution:  If you are going to go with one of the favorites, make sure to pick more upsets than normal in the first few rounds, so that if the favorite pans out you have a chance of being near the top heading into the last weekend.  Of course, the bigger your pool, the more upsets you need.  By implementing some simple game theory, and considering how the other pool members are going to pick can help ensure you don’t end up in 6th place, or 15th place, but rather have a better chance of ending up in 1st or 2nd.  Of course there is an entirely other option, using the same fundamentals of game theory.

Pick one of the second tier champions (teams 3-5), with few upsets early on.

Again using ESPN’s millions of entries, Pitt, UNC, and Memphis averaged about 30% of the entries – averaging 10% each, rather than the 25%+ from each team in the first scenario.  If you are in a pool of 40 or 50 people, you are in the top 4 or 5, simply by having one of these teams as your champion (and, of course, if they win).  If your pool pays the top 5, you are already in the money, or at least knock knock knocking on heaven’s door.  To ensure a top 3 finish, at this point, you don’t need outlandish picks, you simply need to play the role of the turtle – slow and steady wins the race – and go with favorites otherwise.  Your champion is your (relatively) ‘outlandish’ pick, which differentiates your bracket; no need to pick upsets in the early rounds to get your extra points.

Filling out your bracket is more about what you expect others in your pool to do in developing your strategy/champion than what you actually think of the squads.  And thus filling out a bracket is as much an expedition into Game Theory as it is an analysis of Missouri’s 40 minutes of hell, and the strength of the Big East.  As alluded to at the top, however, this year’s tournament has led to a bit of a peculiar scenario, which shall be discussed in part 2, later this week, and the opportunity to bring some more Game Theory to into the mix.