At some point throughout your journey into the Wide World of Sports Betting most of you have likely heard someone mention the term Implied Probability. Or depending on how well your long-term memory serves, you may recall Mr. Harwood in 10^{th} Grade Statistics harping down this exact concept.

What is Implied Probability in Sports Betting?

Implied Probability is a percentage that is derived by converting the given betting odds that represent the likelihood of that outcome occurring. This percentage factors in the bookmaker’s profit margin as well.

How to Use Implied Probability in Betting

One way to use implied probability with betting odds is to compare the implied probability of a betting market against the actual “fair” probability of that market – without the juice or vig baked in. If we find that the offered implied probability is lower than the fair probability (based on the no-vig line), then we’ve officially located the all-elusive bet we want to take – a bet with Positive Expected Value!

As we all know, the odds change leading up to the game as more & more bets are placed. This means that the implied probability is also changing regularly. Knowing this information, we now also know that the displayed odds by a bookmaker aren’t always correct.

Obviously, we all want to bet on ‘winners’ but much more importantly we ONLY want to bet on teams where the implied odds are either lower or accurately represent the chance of that team winning. The key to locating valuable betting opportunities is finding an actual winning probability that is greater than or equal to the implied winning probability estimated by the sportsbook based on the fair odds or the odds without the vig baked in.

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How to Calculate Implied Probability of Betting Odds

Nothing in this world seems to be universal these days, betting odds included. The three formats that you’ll run into most are American, Decimal & Fractional. If you encounter some betting odds that look like total nonsense to you – don’t fret, you are a basic formula away from converting these odds back into your preferred format.

All three odds forms can also be converted to show as an implied probability percentage.

OddsJam has an “Odds Converter Calculator” that provides you with all three major odds formats, including the implied probability of those odds, all within an instant.

However, if you are anything like the nerd I am, you would prefer to convert these odds by hand. Here are the formulas to convert these odds into their implied probability. Let’s use the 2022 Super Bowl as an example, where the closing lines at Pinnacle (widely known as the sharpest sportsbook available) in American Odds were as follows:

Cincinnati Bengals +188 and Los Angeles Rams -213.

How to Calculate Implied Probability from American Odds

Converting American odds can be more confusing than the rest (Americans just love doing things differently, don’t we?) as it requires two formulas, one for both the Positive Odds & Negative Odds.

So, using our real-life example :

The Bengals implied odds to win: +188

The Rams implied odds to win: -213

How to Calculate Implied Probability from Decimal Odds

Decimal Odds are the standard format in most countries around the world and commonly are referred to as European Odds. They are the most straightforward odds and can tell you exactly what your potential winnings would be with just a glance.

The decimal represents the amount of money won for every dollar wagered. If the odds are 4.50 and you bet $10, the payout upon a win will be $45. The formula to convert American Odds into Decimal Odds is as follows :

Step 1: Determine if odds are positive or negative.

Step 2:

So, given our previous example, a very simple calculation determines that the Bengal’s decimal odds were 2.88 and the Ram’s decimal odds were 1.47. Now, we need to convert these decimal odds into implied probability.

That formula is as follows :

How to Calculate Implied Probability from Fractional Odds

Lastly, we need to discuss Fractional Odds. They are sometimes referred to as British Odds or Traditional Odds. You typically find these odds across the UK and throughout Ireland as well. These odds portray the potential profit should the bet win, quoted as a fraction or sometimes a ratio of the stake (risk amount). Converting fractional odds into either decimal or American odds is quite simple. First, you must solve the fraction. If the solution is > 1, multiply it by 100, and if the solution is < 1, take -100/answer to find the corresponding American Odds. Just add 1 to the solution to find the corresponding decimal odds.

The 2022 Super Bowl closing line in fractional odds on Pinnacle Sportsbook were as follows :

Cincinnati Bengals: 47/25

Los Angeles Rams: 47/100

Let’s now determine how to calculate the implied probability from these fractional odds:

How Does the Juice or Vig Impact Probability

While reading this article, if you’ve been wondering why the implied odds we calculated didn’t add up to 100%, good job. You’re onto something very critical. Due to this excess, we can show exactly why the house always wins.

Our Super Bowl example had a house edge baked into the odds considering that the total implied probability totaled 102.77%. If a sportsbook ever offered the fair “no-vig” odds, the implied probability would add up to 100% exactly. As long as the sportsbook accepts bets at the proper proportions, they have guaranteed themselves to make a profit, this is called the Vig or Juice.

From our example, Pinnacle’s perspective is for every $102.77 in bets they accept, they only have to dish out $100. Given this information, calculating a sportsbook’s expected profit margin is simple. All you do is divide this excessive implied probability (also known as “round-over”) by the total amount of implied probability. Therefore, (2.77/102.77) = 2.69% profit margin. Now, if that seems minuscule to you, consider multiplying it by the total betting handle (millions and millions of dollars).

On that type of scale, making a near 3% risk-free profit is downright astonishing. Sportsbooks will always remain profitable no matter what because they utilize implied probability to their favor. Our best move is to use this awareness to our advantage and spot bets where the actual fair probability of an event surpasses the house’s implied probability of the same event, also known as +EV Bets. Stay focused, have fun & best of luck!