What is Implied Probability and How to Calculate It

Level: Advanced
Updated: Aug 22, 2025
2 min read

Key Takeaways

As outlined in What is Expected Value the most important thing needed to determine if a bet is +EV or not is determining the probability of winning. For some casino games, this is easily determined. In American Roulette, for example, we know that the probability of winning if we wager on a specific number is 1 in 38 or 2.63%. We also know the payout is 35:1. This allows us to determine the expected value of betting $100 on one number in roulette.

\[ \begin{aligned} \text{EV} &= (\text{Win \%} \times \text{Win Profit}) - (\text{Loss \%} \times \text{Loss Amount}) \\ \text{EV} &= (2.63\% \times \$3{,}500) - (97.3\% \times \$100) \\ \text{EV} &= \$92.05 - \$97.30 \\ \text{EV} &= -\$5.25 \end{aligned} \]

In sports betting, determining the probability of winning can be much more difficult. There are an almost unlimited number of factors that can come into play.

Injuries and player availability
Weather
Which team has been playing better
Which team has better coaching/preparedness
Home field advantage
Travel and schedule
Officiating

What is Implied Probability?

Implied probability is the likelihood of a particular outcome happening derived from a sportsbook's odds. A sportsbook's odds include the built-in margin, or vig. Understanding implied probability is essential because it allows bettors to identify when odds represent a positive or negative expected value.

Sports Betting Odds and Implied Probability

Before proceeding into more detail about +EV betting, it is essential to understand how sports betting odds relate to implied probability. Sports betting odds can be converted into probabilities. Converting sports betting odds to implied probabilities lets you see the sportsbook's estimate of an event's likelihood. This conversion is essential for spotting discrepancies between different sportsbooks and finding +EV bets.

Calculating Implied Probability From Sportsbooks' Odds

American Odds: Positive Odds

Example with odds of +200

\[ \begin{aligned} \text{Implied Probability} &= \dfrac{\strut 100}{\strut (\text{Odds} + 100)} \\ \text{Implied Probability} &= \dfrac{\strut 100}{\strut (200 + 100)} \\ \text{Implied Probability} &= \dfrac{\strut 100}{\strut 300} \\ \text{Implied Probability} &= 0.3333 \ \text{or} \ 33.33\% \end{aligned} \]

American Odds: Negative Odds

Example with odds of -200

\[ \begin{aligned} \text{Implied Probability} &= \frac{\strut |\text{Odds}|}{\strut |\text{Odds}| + 100} \\ \text{Implied Probability} &= \frac{\strut |-200|}{\strut |-200| + 100} \\ \text{Implied Probability} &= \frac{\strut 200}{\strut 200 + 100} \\ \text{Implied Probability} &= \frac{\strut 200}{\strut 300} \\ \text{Implied Probability} &= 0.6666 \ \text{or} \ 66.66\% \end{aligned} \]

Decimal Odds

Example with odds of 3.6

\[ \begin{aligned} \text{Implied Probability} &= \frac{\strut 1}{\strut \text{Decimal Odds}} \\ \text{Implied Probability} &= \frac{\strut 1}{\strut 3.6} \\ \text{Implied Probability} &= 0.2778 \ \text{or} \ 27.78\% \end{aligned} \]

Fractional Odds

Example with odds of 3/2

\[ \begin{aligned} \text{Implied Probability} &= \frac{\strut \text{Denominator}}{\strut \text{Numerator} + \text{Denominator}} \\ \text{Implied Probability} &= \frac{\strut 2}{\strut 3 + 2} \\ \text{Implied Probability} &= \frac{\strut 2}{\strut 5} \\ \text{Implied Probability} &= 0.40 \ \text{or} \ 40\% \end{aligned} \]

Now that we know how to convert sportsbook odds into implied probabilities, the next lesson looks at how to determine the true probability, which differs from the implied probability.

What is Expected Value?

Determining Fair Odds

Related Topics

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Sports Betting Basics

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