Sunday, September 30, 2007

Sunday Afternoon Game Theory

By the time you read this, it will almost certainly be moot, but I am intrigued by the possibility of a three-team tie after today's games in the National League Wildcard Race. (This may have something to do with the fact that meaningful September baseball is being played in Colorado for the first time in more than a decade.)

Baseball's methodology for resolving a three-team tie is called the ABC method. Team A hosts Team B, with the winner hosting Team C the next day. The winner of this mini-tournament reaches the National League Division Series (NLDS).

The team involved in the three-way tie that has the best head-to-head record against the other two at the end of the regular season gets to select whether to be Team A or Team C (there is no rational reason to choose to be Team B).The advantage of choosing to be Team C is a day off and the fact that you need only win one game to proceed to the NLDS. The advantage of choosing to be Team A is home-field advantage.

So, the question is: If you have your choice, do you choose to be Team A or Team C.

The simplest way to decide this question is to calculate your odds of reaching the NLDS under each scenario. So, if you have won 60% of your home games and 40% of your road games this year, your odds of winning two home games are 36% (60% x60%) while your odds of winning a single road game are slightly higher (40%) and you should choose to be team C. In fact, you should choose to be Team C under this methodology if your home winning percentage squared is greater than your road winning percentage.

Of course, this is only a first approximation. Other factors are involved. One is that if you choose the day off, you may be able to juggle your starting rotation in order to have your best pitcher available for the deciding game. This might improve your chances of winning the road game, particularly against a team that had to play the day before.

The X factor, of course, is money. If you choose to be Team A, you can expect either one or two additional home games (on average, 1.6 home games, assuming the winning percentages above) whereas if you choose to be Team C, you will only have a home game if you win the one-game playoff. Thus, an owner or general manager might decide that if everything else is a wash, the possibility of more home dates tips the scales in favor of becoming Team A.

What does any of this have to do with MoneyLaw? Well, I guess it goes back to a post I put up when I started here. The only way to know whether you're winning or not is to have your goals established beforehand. Thus, a rational decision-maker with an eye on the bottom line might decide to sacrifice a 4% greater chance of reaching the NLDS for the financial reward of 1.6 home games.


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