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Understanding the Math Behind Edge (Expected Value)

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August 11, 2023

When examining a Rithmm bet recommendation, your attention is drawn to a trio of key figures: win probability, odds, and edge (aka expected value or EV).

The win probability showcases the likelihood of the recommended pick winning, per your model's assessment. The odds originate from the sportsbook designated as your default in your account settings, while the edge embodies your expected value – the disparity between market odds and your model's insights.

Given the dynamic nature of odds influenced by market fluctuations, the edge percentage mirrors this variability. For an in-depth exploration of the edge calculation, we're about to delve into the mechanics behind it.

Let's zoom in on a bet. Essentially, you're examining two potential outcomes – a win or a loss – and assessing the associated probabilities and payouts.

The edge calculation entails multiplying the probability of winning by the corresponding payout for a win, and the probability of losing by the payout for a loss. This product is then divided by the original bet.

Allow us to illustrate with an example. Consider the Rithmm bet recommendation for the UMass @ New Mexico State match.

Here's the breakdown: the Rithmm model predicts an 82.4% win probability that New Mexico State wins. The sportsbook odds stand at -315, yielding an 8.5% edge. These odds imply that a $315 bet is needed to secure a $100 win, translating to a $415 payout. 

Now, let's unravel the edge calculation.

Multiply the estimated win rate (82.4%) by the win payout ($415) to obtain the EV of a Win ($341.96). Multiplying the estimated loss rate (17.6%) by the loss payout ($0) yields a result of $0.

Sum the EV of a Win and the EV of a Loss, then divide by the initial bet ($315). The outcome – an expected value of 1.085.

Shift the decimal two places and you've got your edge percentage (8.5%).

Different users adopt varying approaches – some scrutinize all figures, others fixate on the edge, while some lean towards win probability. No matter your perspective, our aim is to facilitate your comprehension of these insights by shedding light on the calculations underpinning them.

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