In part I of The Collision of Game Theory & NCAA Brackets, Vlookup Vince tossed out some ideas about how Game Theory can be leveraged to gain an advantage in filling out one’s annual NCAA bracket. Part II digs into the peculiarities of the 2009 tourney, and how Vlookup Vince again faces the opportunity to use Game Theory prior to this weekend’s Final Four for a win-win-win scenario. Rather than rehash my overview of Game Theory, this clip from The Princess Bride summarizes Game Theory quite aptly.
As we eagerly anticipate Saturday’s Final Four games, we find ourselves in a situation where 2 of the 4 teams fit into one of the aforementioned strategies, while the other two are lower seeds that very few had in the Final Four. The 5 million plus ESPN brackets had Villanova in the Final Four just 3.1% of the time, and similarly, Michigan St. in about 6% of the Final Fours. That was solely in the Final Four, let alone winning any more games, and thus earning people more points.
Why does any of this matter? In normal years it is likely for both of the favorites to make the Final Four (this year Louisville & UNC), along with one or two of the second tier teams (Pitt, UConn, & Memphis this year – see part I for more on this), and possibly a deeper team. Normally, many pool entries have 3 or 4 Final Four teams, and there are half a dozen people that can still win, and 10 or 15 that can be in the top 5.
However, this year, we have one tier 1 team, one tier 2 team, and two teams that almost no one has winning another game, and thus unlikely to earn any more points. The outcome? In most pools, only two people can win: the highest placed entry with UNC, and the highest placed entry with UCONN. In order to be the highest placed entry at this point you had to get at least two of the final 4 teams (likely UCONN & UNC), and thus no one is going to leapfrog the leaders because so few people have Villanova or Mich. St winning another game. It is because of this 2 winner scenario that the opportunity to come to a mutually beneficial agreement is available. Normally, there are half a dozen people still in the mix, and coming to an agreement is almost impossible. This year things are different.
Vlookup Vince looks at his pool and knows that he wins if UCONN wins it all. His colleague, we’ll call him Jorts McGee, wins if any of the other three teams win (due to a 3 point lead at this juncture…damn you Florida St.) – its make or break for both – first place or nothing. And this is where the game theory comes into play again. What is the right amount for Vlookup to offer Jorts to broker a deal that works for both of them? What is an offer that Jorts will take?
Jorts is clearly in the better position, but how much better? All Vlookup needs to worry about is the likelihood of UCONN winning. That can happen if they beat Michigan State, then the UNC vs. Villanova winner in the final. We’ll estimate the likelihood of beating MSU is 75%, and the likelihood of UNC beating Villanova is 65%. We’ll say the UNC vs. UCONN game favors UNC 65%/35%, but a UCONN vs. Villanova final favors UCONN 75%/25%. Lots of assumptions, but running those numbers gives UCONN a 37% chance of winning it all, which seems pretty fair. That, roughly, puts Jorts in a 2:1 favorable position. If the pool winner pulls $300 and this scenario played out 100x times, then Jorts would expect to pull $200 each time, while Vlookup snags $100.
However, it is only played out once. Obviously, both can roll the dice and take their chances – and that gets into a whole other conversation of risk aversion/risk tolerance. Alternatively, is the opportunity for those two to broker a deal. Does Jorts see the tournament playing out as Vlookup does (as laid out above)? Does Jorts favor his position more than he should? Is a $100 payout (if UCONN were to win) even meaningful to Jorts, or does he want the full $300 or nothing? These are the types of questions Vlookup is asking himself as he thinks about a possible deal. Jorts may or may not be asking himself these same questions, but the opportunity to apply some game theory in making an offer are clear – and thats only the case because of how this year’s tournament played out – with only two people likely to be able to win most pools at this point.
I’m so confused about how Princess Bride explains game theory there. Was it the poison? Is that game theory? It’s easier to win the game if you poison your opponent? If so, I say poison Jorts McGee, change his will and testament to reflect you as his sole beneficiary, and cash out no matter what, plus whatever he took in during his measly lifetime. Of course, this would depend on your relative aversion to risk. It’s pretty risky to kill someone and forge his or her will, especially if it’s just an NCAA Tournament pool.
It’s 4:30 at work and I’m getting punchy.
[...] former more focused on strategies to use while filling out a bracket, while the latter was about peculiarities of this year’s tournament and the bizarre situation I found myself in. For those losing sleep on how my bracket played, I [...]