When you hear pros or semi-pro bettors talk about sports betting, you’ll hear expected value (EV) come up a lot. It’s for good reason, because pros use expected value in almost every single betting decision they make. But what exactly is EV, and how does it compare to other ways we make value decisions? Expected value, prospect theory, and utility theory all relate to sports betting in slightly different ways.
Expected Value
EV is a way to measure how much of an edge you have on any given bet. It's a concrete, mathematical, logical way to determine value. If you want to be a successful bettor, you'll need to understand expected value. EV tells us the average outcome to expect if we repeat an action over and over. In sports betting, calculating the expected value is a way to estimate whether a bet will, over time, be profitable. This definition of value is completely numbers based. You calculate it using probabilities and dollar amounts. The equation looks like this:
E(x) = x1p1 + x2p2 + ... + xnpn
If I translate that equation to English, it means "The expected value of something equals the value of outcome 1 times the probability of outcome 1, plus the value of outcome 2 times the probability of outcome 2, and so on for all the possible outcomes". If I'm rolling a 6-sided die the equation looks like this:
E(x) = 1*(1/6) + 2*(1/6) + 3*(1/6) + 4*(1/6) + 5*(1/6) + 6*(1/6)
Which ends up being 3.5.
When you're calculating EV for betting outcomes, generally when the expected value is positive, you bet. If it’s negative, you don’t bet. It’s designed to be very black and white so we don’t let biases creep in and affect our decisions, but in reality it's usually trickier than that.
EV isn't the only determinant of value. Psychologists have studied several ways people make value decisions. There are two popular theories to help explain this kind of decision making, called prospect theory and utility theory. These are more subjective, and take personal preferences and personality traits into account.
Prospect Theory
Prospect theory was developed by two psychologists, Daniel Kahneman and Amos Tversky. It includes the idea that losses have more of an emotional impact on someone than wins do, which is called loss aversion. So prospect theory is different from expected value because it accounts for loss aversion. People tend to like bets where the losses don't hurt as badly.
You might see this come into play in different ways, depending how you think about it. If you're betting on favorites, you might need to bet a lot to win a little. You might see the favorite as having a low chance of losing, so that doesn't trigger your loss aversion. Or, you might look at it as only winning a little, so the win isn't going to feel that good anyway but the loss will definitely hurt.
Parlays are another example. Multiple teams have to win for your parlay to win, and you get paid out a lot for betting a small amount. Many bettors view the bet as hard to lose because it involves all favorites. These end up usually being one of the worst bets you can make, but there are strategies where they are useful, which I talk about in my courses.
Utility Theory
Utility theory focuses on how happy spending money makes us, meaning what "utility" or "usefulness" we get out of spending money. In betting, utility theory says we make decisions based on the happiness or excitement we get from an outcome, beyond the amount of money you win. So this all depends on personal preferences, how much money you’re starting with, and how much you like risk. This can explain why some bettors might choose a bet that has a negative expected value but offers a chance to win a lot of money. People get a huge amount of personal satisfaction from betting on longshot parlays and occasionally winning one. They ignore the fact that huge parlays are usually one of the worst bets you can make because they get a thrill out of it and they can brag after a rare win. So they get a lot of personal use, or personal utility from those bets.
Again, these are three common, general ways we can explain value-based decision-making. When most people think about betting, their actions can be explained pretty well by utility or prospect theory, or a combination of the two. I do think it’s important to consider how betting emotionally impacts you, and you shouldn’t trade your mental health for your money. But, if your goal is to make the most money possible, you should be using expected value. That’s the bottom line. If you want to maximize profits, your emotions should be completely taken out of the equation. That might not be possible for everyone, or maybe for anyone, but that’s ultimately the goal.
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If you're serious about becoming a successful bettor, check out Bettor Ed's free psychology course to explore more ways to think about sports betting, and our other courses for more on other strategies.
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