MLB Playoff Series Wagering Analysis

Let’s take a break from Lending Club and discuss another type of investing, wagering on sports. Specifically wagering on the MLB playoffs. There are two decisions to make. Who to bet on? How much to bet? Following is a step by step mathematical approach to answering these two questions. We’ll be using the Cleveland and New York series as an example.

The first question is who. Recognize that there is no certain winner. Each of the teams has a certain probabilty of winning. Determining that probability is the key. Once you have that number, the rest is simple spread sheet analysis. For this exercise I am going to use the probability estimate from the website fivethirtyeight.com. They have Cleveland with a 67% chance. Hence New York’s chance is 33%. If someone offered you an even money bet, it’s easy, take Cleveland.

But the bookmakers won’t offer an even money bet. They will specify a money line for each team. Currently Cleveland is -185. That means you would have to bet $185 on Cleveland to win $100. New York’s money line is +170. If you bet $100 on New York and they won, you’d win $170. Not so simple.

The next step in the process is to convert the money line (ML) to European style odds. Following is the Excel formula; =IF(ML>0,(ML+100)/100,(ML-100)/ML). In this case the resulting odds are Cleveland 1.54 and New York 2.60. This means that for every dollar you bet on Cleveland you get back $1.54, and for New York $2.60. If we multiple these odds by each team’s probability we would get the expected return for either wager. The result is Cleveland $1.032 and New York $0.891. Since you would expect a positive return on Cleveland, that’s who you pick.

Now, how much to wager. For this we'll use the Kelly Criteria. This formula tells you what percentage of your bank roll to wager given the above data. The Excel formula is; (Odds*Prob-1)/(Odds-1). This suggests a wager of 6.0% on Cleveland and -8.9% on New York. So, we’ll wager that amount on Cleveland. Below is the spread sheet for the two games starting today.

	538 Prob	ML	Eur	Exp Ret	Kelly
Indians	67%	-185	1.541	$1.032	6.0%
Yankees	33%	170	2.700	$0.891	-6.4%
Red Sox	40%	155	2.550	$1.020	1.3%
Astros	60%	-167	1.599	$0.959	-6.8%

I’ll post the National League series tomorrow.