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To date, we’ve covered the concept of value betting, what value even is, how to get the odds market’s view of a match, and why it’s important to build a prediction independently of the market. It’s finally time to put it all together. In the final installment of our intro to betting series (don’t worry, there will be an intermediate series coming), we’re going to cover how to directly compare your predicted probabilities to the market, and what that comparison means.

Probability as a story

We’ve defined a bet as worth taking if it has positive expected value. Calculating EV is pretty straightforward. All you need is a view of the probability of winning the bet and the payout for winning. However, this doesn’t give a particularly intuitive sense of why that bet was worth taking. For example, “I think this team has a 70% chance to win and the market is paying out -150, so it’s worth betting,” may all be correct but it doesn’t tell much of a story.

What that statement actually boils down to is your view of that team’s chances of winning versus the market’s view of that team’s chances of winning. If we take that payout of -150 and get the probability implied by that payout, we get 60%. Now, the story becomes, “I think this team has a 70% chance to win, and the market is paying out as if they only have a 60% chance to win, so it’s worth betting.”

The lower a team’s chances to win, the higher the payout. So, the market will pay out more if they believe a team to have a 60% chance to win rather than if they agreed with you that this is a 70% matchup. In this instance, your breakeven is at 60%. This means that if you can win that bet 60% of the time you’ll break even in the long run. Since you expect to win more often than that, you’ll come out ahead.

Value by a different name

The above claim is: if your predicted probability of an event is greater than the probability implied by market odds, then the bet is worth taking, and vice versa. To rephrase that in terms we’re used to:

The EV of a bet is positive exactly when our predicted probability for an event is greater than the market-implied probability.

Let’s prove it:

Given our predicted probability w and market probability m:

payout p = 1 / m

EV = w * (p – 1) + (1 – w) * (-1)

EV = w * (1 / m – 1) + (1 – w) * (-1)

EV = w / m – w -1 + w

EV = w / m – 1

For EV to be positive:

EV > 0

w / m – 1 > 0

w / m > 1

w > m

EV being positive is equivalent to our probability of w being greater than the market-implied probability m.

Normalization

There’s one hiccup in our story. We’re comparing our probability to the probability implied by the market payout, not what the market actually believes. The vig creates a disparity between the odds that an oddsmaker offers and their true belief of the outcome of an event. For our purposes, however, we don’t really care what they actually believe; we just care about what they’re paying out. That’s where our profit and, thus, our EV comes from, after all. In an extreme example, the vig could be so high that their view is irrelevant. If an oddsmaker says, “I think this matchup is 50/50 but I’m going to just pay out $101 on a $100 bet; have fun with your one dollar of profit,” you’re not taking that bet even if you think your team of choice has a 90% chance to win.

Here’s a more realistic scenario. An oddsmaker is paying out +183 / -241 on a match between Team A and Team B. You think that Team A has a 35% chance to win.

If you convert the market’s odds, you get 35.33% and 70.67%. Normalizing that yields 33.33% and 66.67% as the market’s true view of this match.

We think that Team A is more likely to win than the market does. However, while the market may believe that Team A has a 33.33% chance to win, they’re paying out as if they actually have a 35.33% shot. This is above our prediction and, thus, pushes us below our breakeven.

In fact, the market’s implied probabilities are higher than ours on both sides (35.33% vs. 35% and 70.67% vs. 65%), so we shouldn’t bet on either side. In a fair market, any disagreement would mean that we should have one side worth betting on. In a real market, our predictions are often fairly close to the odds, and the vig washes out any edge we have.

In short: Compare your prediction to the odds-implied probability, not to the market’s true view. Fortunately, this actually simplifies the process for us, as we can skip the extra normalization step in determining whether to bet or not.

Binary bets

So far, all we’ve done is answer a very simple question: “should I bet?” If you’ve kept up with our bet suggestions, however, you’ve probably noticed that there’s a bit more to it than that. We recommend bets of different amounts on different matches. There are a few basic heuristics here which line up with intuition:

The higher the EV of a bet, the more you want to wager.

The more likely a bet is to pay out, the more you want to wager.

The exact formulation of these concepts is something we’ll leave for a future article. For now, simply choosing whether or not to bet, and not worrying about the exact amount, will get you pretty far. Scaling your wagers appropriately will help you squeeze out that last bit of value in the long run, so it’s worth keeping in mind.

Betting for value

And that’s it! Congratulations, you now understand how to bet for value. There’s a fair amount of math involved (we are trying to be systematic, after all) but it really boils down to a single point:

To find betting value, you have to disagree with the odds market, and you have to be right.

Choose your bets wisely. Don’t just bet on everything for the sake of betting. Think about why you’re betting. Trust your process and don’t try to overcorrect. If you’re consistently seeing strange predictions, that’s a wake-up call to rethink your fundamentals. But don’t give in to emotional bias; odds markets are specifically designed to prey on that.

Vanya is the founder of alacrity.gg, where he leverages seven years of quantitative finance experience to build esports prediction models. He'll happily debate you on anything from math to video games to the impending subjugation of the human race by artificial intelligence.
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