## Wednesday, February 25, 2015

### A Lesson in Probability Theory (and calculating fair moneylines)

Sports betting is math. You may be a dinosaur and refuse to believe that sports are about numbers (although numbers are quite literally how it’s determined which team wins), but there’s not much of an argument to be made that betting isn’t about math. A bet is worth making when the expected value is positive, meaning that the payout outweighs the risk. When a moneyline is +150, that implies a 40% chance of winning. If you were to make 10 bets at a +150 price and win 4 of them, you would be exactly even (4 wins x 1.5 = 6, 6 losses x 1 = -6, hence a net profit of 0). A bet at +150 is worth making if you have a greater than 40% chance of winning it.

A bet against a point spread is no different, but the moneyline odds are usually -110 rather than +150. A price of -110 implies a 52.4% chance of winning, so in order to have positive expected value on a point spread bet you need to have greater than a 52.4% chance of winning.

(Here is a simple tool to convert moneylines into their implied percentage counterparts)

I generally use a larger threshold than 52.4% (typically 55% or higher) to give myself some margin for error, but the point here is that you shouldn’t bet something just because you think you will win. You need to have a positive expected value. This is why you can’t simply bet favorites on the moneyline in all the games and expect to turn a profit. The underdogs win the games a certain percentage of the time due to randomness. Randomness is why a good foul shooter can’t make every single free throw, and why even the best hitters sometimes strike out.

The philosophy that the best sports gamblers employ is this: make as many wagers with positive expected value as you possibly can. The more times you expose yourself to positive expected value, the more likely you are to have long term success. This is due to something called the “law of large numbers” which dictates that the more times a fair coin is flipped, the more likely you are to see the breakdown of heads/tails approach a 50/50 split. This can be applied to sports in general, e.g. the more times a .300 hitter comes to the plate, the more likely you are to see him bat close to .300. In one day or week or even season, anything can happen. But over the course of an entire career, a .300 hitter is very likely to bat close to .300. In betting, this means that the more positive expectation bets we make, the more likely we are to see positive results overall. This methodology isn’t necessarily just for people who bet a lot. Even if you’re a casual gambler you still want to give yourself the best chance to win, right?