Implied Probability In Sports Betting: Calculation And Interpretation

In the realm of gambling, the terms ‘odds’ and ‘probability’ hold diverse meanings and are employed in various contexts. Payout odds, true odds, odds as measures of chance or likelihood, implied odds, mathematical probability, and implied probability are all terms encompassing distinct concepts, albeit sharing a common mathematical foundation. Frequently, these terms are used interchangeably in gambling discourse, potentially leading to confusion depending on the context. In this article, we will explore the concept of implied probability in sports betting, elucidating its calculation and providing a clear understanding to inform our betting decisions.

What is Implied Probability

Implied Probability decimal odds

When delving into the concept of implied probability, it’s essential to clarify that, despite its name, it differs from mathematical probability. Mathematical probability quantifies the likelihood of an event occurring within a well-defined mathematical framework, where certain events, known as elementary events, are considered equally possible.

In the realm of sports betting, implied probability doesn’t conform to this mathematical measure. Instead, it serves as a means of expressing payout odds as a percentage, ostensibly reflecting the likelihood of an event (similar to mathematical probability) but founded on human judgment rather than empirical data. We’ll delve deeper into the nature of implied probability as we explore how to calculate and interpret it.

Whether we’re discussing odds as a measure of probability or as payout figures, there exists a general formula for converting odds into percentages—a common practice in the parlance of gambling often referred to as “odds to probability”:

probability = odds / (1 + odds), where odds are expressed as a fractional value.

For instance, let’s take the conversion of 3 to 2 (3 : 2) odds into a percentage. First, we represent these odds as the fraction 2/3 (two out of three) and then apply the formula as follows:

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

The final step involves converting this result into a percentage:

By simplifying the fraction 2 : 5, we get 0.40.

To express this as a percentage, we multiply by 100 and append the ‘%’ symbol: 0.40 x 100% = 40%.

Converting 3 : 2 odds into a percentage yields a value of 40%. If we interpret 3 : 2 as odds representing probability, then this probability aligns with the mathematical probability of 40%. However, if 3 : 2 signifies a payout rate, such as in blackjack, its percentage representation is referred to as implied probability, distinct from mathematical probability.

The formula presented above serves as the mathematical underpinning for calculating implied probability. In essence, implied probability serves as a means to articulate the payout odds or rate of a bet within the context of any game of chance.

Specifically in the realm of sports betting, the calculation of implied probability employs algorithms tailored to the particular format in which payout odds are expressed.

Calculating implied probability for the various formats of odds

In the realm of sports betting, payout odds come in three distinct formats: fractional (British), decimal (European), and moneyline (American). In the following sections, we will delve into each format, providing a comprehensive understanding of how they translate into implied probability.

Converting the fractional odds

Fractional odds are presented as a fraction, representing the potential profit (P) in relation to the stake (S):

O (f) = P / S

To illustrate, consider 5/2 odds, indicating a $5 profit for a $2 stake, resulting in a total return of $7.

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

  1. Add the numerator and denominator of the initial fraction: P + S. In our example, 2 + 5 = 7.
  2. Rewrite the fraction with the numerator as the denominator of the initial fraction and the denominator as the result from step 1: S / (S + P). In our example, 2/7.
  3. Divide the numerator by the denominator from step 2 and express the result as a decimal rounded to four 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 serve as a straightforward representation of the payout rate for a bet – essentially, it’s the multiplier applied to your stake in case of a winning bet. In other words, it signifies the return on a successful bet with a stake of 1. These odds are expressed as a decimal number greater than 1, typically with two decimal places:

O (d) = 1.xy

For example, if you encounter odds of 1.85, it means that for every $1 you wager, you’ll receive $1.85 in return, 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. In our example, 1.85 x 100 = 185.
  2. Divide 100 by the value obtained in step 1 and express the result as a decimal, rounded to four decimal places: 100 : / 1xy = / 0.ztvw. In our example, 100 : 185 = 0.5405.
  3. Multiply the result from step 2 by 100 and represent it as a percentage to determine the implied probability: / 0.ztvw x 100% = / zt.vw%. In our example, 0.5405 x 100% = 54.05%.

Converting the moneyline

Moneyline odds operate uniquely, as they don’t represent multipliers or rates but rather specific amounts related to either the stake or potential profit of a winning bet. These odds come into play when wagering on matches with potential outcomes of either a win or a loss for the selected competitor.

For favorites, the odds are presented as a negative integer (accompanied by the minus sign), indicating the amount needed to stake to yield a profit of $100:

O (mf) = -n

For underdogs, the odds are displayed as a positive integer (accompanied by the plus sign), signifying the profit earned for a $100 stake:

O (mo) = +m

Let’s 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 team, follow these steps:

Team A (negative odds):

  1. Remove the minus sign from the odds (–n) to obtain 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 represent it as a percentage to determine the implied probability: /0.xyzt x 100% = / xy.zt%. In our example, 0.5652 x 100% = 56.52%.

Team B (positive odds):

  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 represent it as a percentage to determine the implied probability: /0.vwqr x 100% = / xw.qr%. In our example, 0.4761 x 100% = 47.61%.

You’ve learned how to convert payout odds into implied probability. But why is this information useful, and how should we interpret it?

Using implied probability

We’ve established that implied probability is essentially the payout odds expressed as a percentage. While this information is already presented when you view a bet on the sportsbook’s list, its percentage form conveys something more than just numbers. It reflects a degree of belief in the event’s possibility, akin to a probability.

This degree of belief is relative to 100%, which signifies absolute certainty in the occurrence of an event. In this context, the implied probability is a valuable tool for assessing your chances of winning the bet, considering both the odds offered by the bookie and the beliefs of other bettors. Payout odds are constantly adjusted based on incoming bets, making this likelihood crucial for making informed decisions.

Implied probability offers a clearer perspective, particularly for fractional and moneyline formats, as it visually represents your belief in the event’s outcome. By converting odds to implied probability and tracking results over time, you can categorize competitors as heavy favorites, clear favorites, slight favorites, potential toss-ups, or underdogs. This categorization sharpens your ability to identify value opportunities in sports betting odds.

Beyond its practical use as an analytical tool, understanding implied probability enhances your comprehension of sportsbook odds and broadens your perspective on the strategic aspect of betting.

Interpreting implied probability

Many gamblers often mistake implied probability for the mathematical probability of the events they bet on. However, it’s crucial to clarify that implied probability isn’t a mathematical probability due to the unique nature of sports events. Unlike rolling a die, where each outcome has an equal mathematical probability, sports events are influenced by numerous complex factors that cannot be neatly quantified mathematically. They lean more towards determinism than randomness.

Consider the example of converting moneyline odds to implied probability. Team A had an implied probability of 56.52%, and Team B had 47.61%. If these were mathematical probabilities, their sum should be 1. However, the actual sum is 104.13%, reflecting the bookie’s vigorish – the house’s advantage. Similar to casino games, the difference between payout odds and true odds represents the bookie’s profit margin. If implied probability were equivalent to true odds, the bookie would not make any profit from the bet. This provides another perspective on implied probability: If a mathematical probability were applicable to sports events, implied probability would be the value at which a bet on that event would have an expected value of zero, making it a fair bet.

Nevertheless, sports events are evaluated by bettors and experts, and implied probability serves as a valuable assessment tool. It essentially gauges the collective sentiment of bettors, as it expresses payout odds in terms of their intentions. In this sense, implied probability acts as a form of subjective probability, representing the degree of belief based on betting intentions. When bookies initially set payout odds for an event, they consider past statistics of the competitors and their matches. These initial odds are then adjusted with incoming bets, but their foundation remains rooted in that initial statistical analysis. Consequently, implied probability also functions as a form of frequentist probability, reflecting the relative frequency of event occurrence.

Regardless of interpretation, it’s essential to remember that implied probability is merely a way of presenting the payout odds of a bet. It’s the “probability” the bookie offers for winning the bet, and you can either accept or use it as an assessment tool. Ultimately, successful sports betting involves leveraging assessments and incorporating external information into your analysis.


Implied probability serves as a valuable tool for transforming payout odds into a percentage format that resembles a probability. This presentation style offers a clearer perspective on the likelihood of winning a bet, particularly when dealing with fractional or moneyline odds. Additionally, it aids in organizing your betting endeavors. It’s important to note that implied probability is not an absolute indicator of the event’s likelihood; rather, it reflects the predictions made by both bookmakers and bettors regarding the outcome.

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