The Math of Sports Betting

» Posted on 05/06/2010
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The Math of Sports Betting

On the surface, betting on sports seems pretty simple. You find a team that’s going to win, and you bet on them – or you find a team that will cover the spread, and pick them. When you pick right, you make money, and when you pick wrong, you lose.

But of course, winning at sports betting is a little more complicated than that. It’s not enough just to count up your wins and losses and hope you win more than you lose. The odds offered by sportsbooks vary tremendously, and that has a huge effect on how often you’re going to need to win to come out ahead. Many bettors underestimate just how critical understanding the odds is in sports betting, and how much a seemingly small change in a money line can affect whether or not a bet is worth taking.

For instance, let’s talk about money lines. Say Team A is favored over Team B in a certain game, but you think Team B has a fighting chance. You see that Team B is being offered at +170 to win the same. Should you take this bet?

The correct answer is: you don’t have enough information to say either way yet! We can’t just speak in general terms; we need to come up with an estimate as to what we think Team B’s chances are before we can know if we have an edge here or not. Let’s say we think Team B has a 35% chance of winning. What do those odds tell us now?

To figure out if this bet is good for us, we need to do a little math. If we’re right about Team B’s chances, then 35% of the time, we’ll win 170 units, and 65% of the time, we’ll lose 100. We can figure out our expectation with a formula that looks like this:

(.35 * 170) – (.65 * 100)

59.5 – 65 = -.5.5

So in this case, we can expect to lose 5.5 units on average on a 100 unit bet. In fact, we’d need just over a 37% chance to win to make this bet breakeven at +170. However, if that line moved to just +190, we’d now have a small edge on this bet! Small changes in money lines can have a tremendous impact on how good a bet looks to us.

This is also true when it comes to betting the spread. Usually when you bet the spread, you’ll get odds of -110. To break even, you’ll have to win about 52.4% of the time. If you get a very good -105 line (often available on a promotion), that drops to 51.2%, cutting the house edge in half. What about if the line goes to -120, as often happens when you buy half a point? You then have to win about 54.5% of the time to break even. It’s rare that getting a half-point will make you win 2% more often, which is why this bet is usually not a smart play.

This math really isn’t that hard to do, so anyone serious about winning at sports betting should learn how to do it, or at least learn the basics about how percentages match up with the odds given by bookmakers. The hard part should be figuring out exacting how likely teams are to win bets, not whether or not the math works out in your favor.

William Hill

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