# The Logic Of Sports Betting by Ed Miller, Matthew Davidow – Summary

So the break-even percentage for +120 is  BE% = 100 / (100 + 120) = 45.5%

The break-even percentage for +390 is  BE% = 100 / (100 + 390) = 20.4%

If it’s a minus number, you take the listed number and divide it by 100 plus the listed number. So the break-even percentage for -110 is BE% = 110 / (100 + 110) = 52.4%.

The break-even percentage for -260 is  BE% = 260 / (100 + 260) = 72.2%

Break-even percentage = Risk / (Risk + Win

If the break-even number is exactly 50%, the bet will pay even money. For every \$100 you bet, you stand to win \$100. Those odds can be listed as -100, +100, EV, or maybe something else some sportsbook thinks is cute.

I really can’t overemphasize how important it is to get in the habit as soon as possible of converting all these numbers in your head directly to break-even percentages. Do not use the American odds numbers directly in your thought process. Convert everything to break-even percentages and work with those.

Here’s why. The goal of all this is to make bets that win more often than the break-even percentage. Given that, which is the better bet? A -110 bet if the fair price is -130? Or a -340 bet if the fair price is -380?

The break-even percentage of -110 is 52.4% like I calculated above. The break-even for -130 is 130 / 230 = 56.5%. So you’re making a bet that breaks even if it wins 52.4% of the time, but it will actually win 56.5% of the time. Pretty good.

The break-even percentage of -340 is 340 / 440 = 77.3%. The break-even percentage of -380 is 79.2%. Still a good bet, but 56.5% vs 52.4% is much better than 79.2% vs 77.3%

A nice feature of decimal odds is that to fi nd the break-even percentage you just take the reciprocal. The break-even percentage of 1.91 is 1 / 1.91 = 52.4%. The break-even percentage of 3.3 is 1 / 3.3 = 30%. And so on. You don’t have to mess with different formulas for plus and minus numbers.

Never bet parlays. They’re for suckers.” Honestly, I couldn’t tell you how often I’ve heard that advice.

Because while it’s certainly true that “suckers” (just people who bet sports recreationally) love to bet parlays, it doesn’t at all follow logically that it somehow makes them bad bets.

A lot of people think parlays are bad because they hold a lot for sportsbooks. And that’s sort of true—the average three-leg \$10 parlay might hold \$1.25 on average for the book, or 12.5%.
But the reason the parlay “holds 12.5%” isn’t because parlaying bets together somehow takes good bets and turns them into terrible bets. All a parlay does is blow up the betting volume.

Therefore, your average betting volume for the \$10 parlay isn’t really \$10. It’s  Volume = 0.5 × \$10 + 0.25 × 29.09 + 0.25 × 65.53 = \$5 + \$7.27 + \$16.38 = \$28.65

the course of the eight bets, you haven’t bet just \$80.
You’ve actually bet \$229.24. And of that \$229.24 total bet, you lose \$10. Which works out to a 4.4% hold.

Which is roughly the same old hold we’re always looking at on straight bets.
Parlays don’t hold more. They make you bet more money.

But the basic idea is there. You take information about the strength of the teams (pregame closing lines), information about the game state (the score, the inning and/or how much time is remaining, and any other relevant information like who has the ball, position on the fi eld, and so on), and combine them intelligently to come up with a line.

There are two major problems with this, and you may already have thought of them both.
The first problem is that there is an enormous amount of information available once the game starts that wasn’t reflected in the pregame lines.

Maybe a player or two got injured during the game.
Maybe the teams are playing different strategies than the market expected before the game started.
Maybe the teams are playing faster or slower.
Maybe they’re fouling more or less.
Maybe the weather took an unexpected turn.
Maybe one key player is playing at a much higher (or lower) level than their usual standard. Much of this is information that is readily available to anyone with a web browser and a TV. It’s also information that is—as you might imagine once I described how the lines get made—extremely diff i cult (in some cases) or nearly impossible (in others) to account for correctly, in real time, second-by-second, in an in-play line feed.

Of the zillions of lines that sportsbooks offer every day, some of those lines are made through a very robust process where a market maker books millions of dollars of action on both sides. And some are pulled directly out of someone’s ass.
You want the ass bets.

Take this to its logical extreme. They’ve trained AIs now to beat humans in darn near every game we’ve ever invented. How hard do you think it would be to train an AI to beat any human bettor in the “I have the entire company’s betting history and your entire betting history and I get to accept or reject any bet as I please and—oh yeah—I have a 5% hold on every market too” game.

The only reason you can win at all is because the current software sucks and humans run the show.

Sportsbooks have a lot of advantages over the bettor, but the bettor has a few potential advantages also.