Understanding Implied Probability In Sports Betting

In the realm of gambling, terms like ‘odds’ and ‘probability’ often find themselves in various contexts, each carrying its own unique meaning and significance. We encounter concepts like payout odds, true odds, odds as chances or likelihoods, implied odds, mathematical probability, and implied probability, all of which share a common mathematical foundation. Despite their similarities, these terms are distinct and should not be used interchangeably in the world of gambling, as doing so can lead to misunderstandings, depending on the context.

In this informative article, we will explore the concept of implied probability in sports betting. We will delve into how to accurately calculate it and, most importantly, how to interpret this valuable concept to make informed and strategic betting decisions.

What is Implied Probability

Implied probability, despite its name, diverges from the realm of mathematical probability commonly associated with rigorous statistical analysis. Unlike mathematical probability, which relies on a structured mathematical framework where events are treated as equally possible elementary events, implied probability takes a different path.

In the world of sports betting, implied probability serves as a tool for expressing payout odds in the form of a percentage. This percentage is an attempt to convey the likelihood of an event occurring, albeit driven by human intuition rather than empirical evidence. To truly grasp the essence of implied probability, we’ll explore how it is calculated and, more importantly, how to interpret its implications.

Whether you view ‘odds’ as a representation of probability or payout, there exists a fundamental formula that facilitates the conversion of odds into a percentage. In the parlance of gambling, this conversion is often referred to as “odds to probability,” and the formula is elegantly simple:

probability = odds / (1 + odds)

This formula holds true when odds are expressed as a subunitary fraction, allowing us to bridge the gap between the numerical odds and the perceived probability they signify.


To convert odds of 3 to 2 (3 : 2) into a percentage, begin by representing the odds as a fraction: 2/3 (two out of three). Now, apply this fraction to the formula mentioned above:

Probability = (2/3) / (1 + 2/3) = (2/3) / (5/3) = (2/3) x (3/5) = 2/5.

The final step is to transform the result into a percentage:

Divide the numerator by the denominator: 2 : 5 = 0.40

Multiply the outcome by 100 and append the % symbol: 0.40 x 100% = 40%.

So, 3 : 2 odds can be converted into a percentage, which equals 40%. If we interpret 3 : 2 as odds representing probability, then this probability stands at 40%, akin to a mathematical probability. However, if 3 : 2 signifies a payout rate (such as in blackjack), its percentage form is termed implied probability, although it doesn’t adhere to the strict mathematical probability definition.

The formula mentioned above serves as the mathematical foundation for implied probability, elucidating its essence as a method for expressing the payout odds or rate of a wager, applicable in various games of chance.

Specifically, in sports betting, the calculation of implied probability employs a distinct algorithm tailored to the specific format in which the payout odds are presented.

Calculating implied probability for the various formats of odds

There are three primary formats for payout odds in sports betting: fractional (British), decimal (European), and moneyline (American). Let’s delve into each of them to understand in detail how they translate into implied probability.

Converting Fractional Odds Fractional odds are represented as a fraction, specifically, the ratio of the potential profit earned (P) to the initial stake (S):

O (f) = P / S

For example, if you encounter odds of 5/2, it implies that you could earn $5 in profit for every $2 wagered, resulting in a total return of $2 + $5 = $7.

To convert fractional odds into implied probability, follow these steps:

  1. Add the numerator and the denominator of the initial fraction: P + S. In our example, 2 + 5 = 7.
  2. Create a new fraction with the numerator as the denominator of the initial fraction and the denominator as the result obtained in step 1: S / (S + P). In our example, 2/7.
  3. Divide the numerator by the denominator of the fraction from step 2 and express the result as a decimal rounded to four decimal places: S / (S + P) = /0.xyzt. In our example: 2 / 7 = 0.2857.
  4. Multiply the result from step 3 by 100 to obtain the implied probability as a percentage: /0.xyzt x 100% = / xy.zt%. In our example, 0.2857 x 100% = 28.57%.

Converting the decimal odds

Decimal odds, also known as European odds, represent the gross payout rate of a bet. In other words, it’s the number by which your stake is multiplied to calculate your total payout if your bet is successful. To put it simply, it’s the payback of a won bet with a stake of 1. Decimal odds are expressed as a decimal number greater than 1 and typically include two decimal places:

O (d) = 1.xy

For example, if you encounter odds of 1.85, this means that you will receive a payout of 1.85 times your stake if you win the bet. So, if you wagered $1, your total return would be $1.85, resulting in a profit of $0.85.

To convert decimal odds into implied probability, follow these straightforward steps:

  1. Multiply the decimal odds by 100: / 1.xy x 100 = / 1xy. For example, 1.85 x 100 = 185.
  2. Divide 100 by the result from step 1 and express it as a decimal rounded to four decimal places: 100 : / 1xy = /0.ztvw. In our example, 100 : 185 = 0.5405.
  3. Multiply the outcome from step 2 by 100 and add the percentage symbol to find the implied probability: /0.ztvw x 100% = / zt.vw%. For instance, 0.5405 x 100% = 54.05%.

Converting the moneyline

Moneyline odds do not indicate rates or multipliers; instead, they represent either the stake or profit of a potential winning bet. These odds apply to bets on events with two possible outcomes: a win or a loss for the team or competitor you’ve wagered on.

For favorites, the odds are expressed as negative integers (prefixed with a minus sign) and indicate the amount you must bet to make a profit of $100:

O (mf) = -n

For underdogs, the odds are expressed as positive integers (prefixed with a plus sign) and indicate the profit you’d make on a $100 bet:

O (mo) = +m

For example, consider a match between Team A and Team B with the following moneyline odds:

  • Team A: –130
  • Team B: +110

To convert these odds into implied probabilities for each competitor, follow these steps:

Team A (the odds with minus):

  1. Remove the minus sign from the odds (–n) to get a positive number (n) and add 100 to it: n + 100. In our example, 130 + 100 = 230.
  2. Divide the positive odds (n) by the number obtained in step 1 and express the result as a decimal rounded to four decimal places: n : (n + 100) = /0.xyzt. In our example, 130 : 230 = 0.5652.
  3. Multiply the result from step 2 by 100 and append the percentage symbol to find the implied probability: /0.xyzt x 100% = / xy.zt%. In our example, 0.5652 x 100% = 56.52%.

Team B (the odds with plus):

  1. Add 100 to the odds: m + 100. In our example, 110 + 100 = 210.
  2. Divide 100 by the number obtained in step 1 and express the result as a decimal rounded to four decimal places: m : (m + 100) = /0.vwqr. In our example, 100 : 210 = 0.4761.
  3. Multiply the result from step 2 by 100 and append the percentage symbol to find the implied probability: /0.vwqr x 100% = / xw.qr%. In our example, 0.4761 x 100% = 47.61%.

Now you know how to convert any payout odds into implied probabilities. But how can this format be useful, and how should we interpret it?

Using implied probability

Implied probability may seem like just a different way of presenting payout odds, something we’re already familiar with when browsing through sportsbook listings. However, when expressed as a percentage, these payout odds take on a new role – they reflect the likelihood or the degree of belief in the event’s occurrence. This is precisely why it’s referred to as “probability.” This degree of belief is relative to 100%, which represents absolute certainty in the event happening.

As a measure of likelihood, implied probability becomes a valuable tool for assessing your chances of winning a bet based on the odds offered by the bookmaker. It also takes into account the beliefs of other bettors, as payout odds can shift continuously based on incoming bets for that event.

Implied probability offers a more intuitive way to grasp this likelihood compared to the odds format, particularly for fractional and moneyline odds.

When used to gauge likelihood, implied probability not only helps you assess your bets individually but also aids in structuring your betting strategy within a specific competition and market. By converting odds into implied probabilities and tracking results over a set period, you can better categorize competitors as heavy favorites, clear favorites, slight favorites, potential toss-ups, or underdogs. It’s a tool that enhances your ability to spot valuable opportunities in sports betting odds.

Beyond its practical use as an analytical instrument, understanding implied probability can deepen your comprehension of sportsbook odds and offer you a broader perspective on the strategic aspects of betting.

Interpreting implied probability

Many gamblers often mistake implied probability for the mathematical probability of the events they’re betting on. However, it’s crucial to clarify that implied probability is not a mathematical probability. The key distinction arises because sports events don’t fit the necessary mathematical structure for assigning probabilities. For instance, when rolling a die and assigning a probability of 1/6 to a specific outcome, we can do so because a mathematical structure exists where each outcome is equally likely due to randomness. Sports events, on the other hand, are influenced by numerous factors that can’t be quantified mathematically to assign probabilities. Their nature leans more towards determinism than stochastic randomness.

Consider a previous example when converting moneyline odds to implied probability. The implied probability for Team A to win was 56.52%, and for Team B, it was 47.61%. If these were mathematical probabilities, their sum would be 1. However, this isn’t the case: 56.52% + 47.61% = 104.13%. The surplus beyond 100% actually represents the bookmaker’s vigorish or house edge. Similar to casino games, the difference between payout odds and true odds serves as the bookie’s profit margin. If implied probability equated to true odds, the bookie would make no profit from the bet. This introduces another way to interpret implied probability: If a mathematical probability were applicable to a sports event, the implied probability would be the value at which a bet on that event would have zero expected value, often referred to as a fair bet.

Nevertheless, sports events’ potential outcomes are evaluated by bettors and experts, and implied probability serves as a tool for assessment. It gauges the collective tendencies of bettors since it reflects payout odds as expressions of bettors’ intentions. Under this perspective, implied probability takes on the role of a subjective probability – a theoretical probability defined as a degree of belief in terms of betting intentions. When bookmakers initially set payout odds for an event, they consider past statistics of the competitors and their historical performances. Subsequently, the initial payout odds evolve with incoming bets, but they fundamentally reflect the initial statistical analysis. In this sense, implied probability also aligns with frequentist probability, defined as the relative frequency of an event’s occurrence.

Regardless of the interpretation, it’s essential to remember that implied probability is merely a way to present the payout odds of a bet. It represents the “probability” the bookmaker offers for a winning bet, which you can accept or reject as an assessment tool. In essence, sports betting revolves around evaluating assessments and leveraging information from sources beyond the sportsbook to inform your own judgments.


Implied probability is a method of representing payout odds in percentage form, resembling a probability. This format offers a clearer view of your chances of winning a bet, particularly when the payout odds are presented in fractional or moneyline formats. It also aids in better structuring your betting activities. It’s important to note that implied probability shouldn’t be taken as an absolute indicator of the event’s likelihood that you’re betting on. Instead, it primarily mirrors the predictions made by bookmakers and bettors regarding that specific event.

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