What Are Implied Odds? Implied Probability In Betting Explained


Introduction To Implied Odds

Implied probability, sometimes called implied odds, actual probability, and value bets are tools bettors can use to assess whether the odds given by a bookmaker are a good deal. The odds given to an event should generally reflect the level of risk involved, and represent a bookmaker’s assessment of how likely an event is to occur. As a bettor, you can use implied probability and actual probability to determine if the bookmaker is being fair in their assessment, or if they’re charging too much for the vigorish. In other words, do the odds accurately reflect the likelihood of winning and the risk involved? Or has the sportsbook weighed the odds in their favour?

This article deals with implied probability and how to determine if a bet has valuable odds, and includes the following:

What Are Implied Odds?

Implied probability, or implied odds, is the likelihood of an event happening as implied by the odds set by the sportsbook. It represents the bookmaker’s assessment of the probability of an outcome and is expressed as a percentage. Successful sports betting requires a deep understanding of both implied and actual probabilities, along with the ability to identify value bets. It’s important to remember that no bet is guaranteed to win, but responsible odds assessment can go a long way in making wise decisions

Probability itself is a mathematical concept that can be used to better interpret odds. As discussed in our previous article, bookmakers hire mathematicians to develop algorithms which produce odds. This allows the odds to accurately reflect something arbitrary like “how many injuries does this team have?” or “do they have a home team advantage?” as a real number. Through that algorithm, the bookmaker implies what they think the probability is of a win, hence, we get implied probability. 

We also use percentages to help us better interpret the odds, given that odds themselves are not actual probabilities, they simply reflect the price the sportsbook is requesting to bet on a certain event. While the odds, in theory, should always reflect the given risk level and likelihood of winning, which are just alternative ways to describe probability, this is not always the case. The reason is because the primary goal of the sportsbook is to attract bettors on both sides of the bet. To do this, they may need to make one bet slightly more valuable than it’s actually worth in order to attract bettors. In addition, sometimes the algorithm doesn’t work perfectly, or doesn’t account for all factors. 

For example, in the UFC, sportsbooks tend to set odds that favour the reigning champion. This is because the reigning champion is ranked #1 in their weight division, with their opponent ranked between #2 and #5. That alone can sway the algorithm to favour the champ. Often, UFC fighters will come from different fighting backgrounds and have different strengths. The reigning champion may fight better on the ground, while the challenger is a boxer and notoriously good at staying on his feet. In this situation, a savvy UFC fan would know the challenger, with his skill set, is likely to keep the upper hand and win his bout. All the same, the sportsbook is likely to give odds that favour the champion because their ranking in their weight division may be worth more in the odds calculation. It’s instances such as this where the odds are set a certain way simply because the sportsbook has an algorithm to follow – in turn creating a situation where the odds do not accurately reflect the likely outcome. It’s situations such as these that may allow bettors to “beat” the sportsbook.

Calculating Implied Probability From Odds

Converting odds to implied probability is an easy but important skill in sports betting, and the method for doing so varies depending on the odds format used. Here, we’ll explain how to convert odds to implied probability in the three formats: American odds, decimal odds, and fractional odds.

To convert American odds to implied probability, it depends whether the odds are negative or positive. 

For positive American odds, use the following formula: 

Implied Probability (%) = 100 / (Odds + 100)

For example, if the odds are +200 in American format:

Implied Probability (%) = 100 / (200 + 100)

Implied Probability (%) = 100 / 300

Implied Probability (%) = 0.3333 or 33.33%

For negative American odds (e.g., -150), use the following formula: 

Implied Probability (%) = Absolute Value of Odds / (Absolute Value of Odds + 100)

*Note: Absolute value simply means remove the – sign. So the absolute value of -150 is 150.

For example, if the odds are -150 in American format:

Implied Probability (%) = 150 / (150 + 100) 

Implied Probability (%) = 150 / 250 

Implied Probability (%) = 0.6 or 60%

To convert decimal odds to implied probability, use the following formula:

Implied Probability (as a %) = 1 / Odds

For example, if the odds are 2.50 in decimal format:

Implied Probability (%) = 1 / 2.50 

Implied Probability (%) = 0.40 or 40%

To convert fractional odds to implied probability, you need to add the numerator and denominator together and then divide the numerator by the total.

Implied Probability (%) = (Denominator / (Denominator + Numerator)) * 100

For example, if the odds are 5/2 in fractional format:

Implied Probability (%) = (2 / (2 + 5)) * 100 

Implied Probability (%) = 2 / 7 * 100 

Implied Probability (%) = 28.57%

What Is Actual Probability?

Actual probability, as the name suggests, is the true likelihood of an event happening based on factors such as statistics, team or player performance, injuries, or weather conditions. The term actual probability is, essentially, just another way to say the bettor’s estimate of the probability as opposed to the sportsbook’s estimate. Bettors can estimate the actual probability of an event and compare it to the implied probability set by the bookmaker through their own statistical model. If the bettor’s estimate suggests that the actual probability is greater than the implied probability, this could indicate a value bet. Bettors can also seek out betting experts who use their own statistical model, such as on The Puck Portfolio.

The true “actual” probability of success is nearly impossible to know. That said, we use these terms “implied” and “actual” as a way to estimate if the bookmaker sets odds that feel fair when we compare their estimate with our own expertise on a given sport. As we said before, this is particularly relevant if the sportsbook has changed the odds to benefit them more financially. 

What Is A Value Bet? How To Identify Value Bets

A value bet in sports betting is when the potential payout from a bet is higher than what you think is the real chance of the outcome happening. In other words, you believe a bet is more valuable than it has been priced, based on actual and implied probabilities. A value bet is typically a good deal because you have a better chance of winning than what the bookmaker’s odds suggest. 

To put this in terms of probability, the implied probability is what the bookmaker thinks the chances of an event happening are, based on the odds they offer. The actual probability is your estimate of how likely an event is to occur based on your research, knowledge, and analysis. If your actual probability estimate is higher than the implied probability, it should be considered a value bet. 

Suppose a bookmaker offers odds of 2.00 (+100, or 1/1 in fractional odds) on a soccer team winning a match. The implied probability is 50%. However, after analysing team form, player injuries, and their past winning streak, you believe the actual probability of the team winning is closer to 60%. In this scenario, you perceive value in the bet because your estimate of the actual probability (60%) is higher than the implied probability (50%). We would consider this a value bet.

Let’s look at a complete example using American odds. We have two teams given the following odds:

Team A: +150

Team B: -130

To determine if there’s a value bet, you need to convert these odds into implied probabilities and compare them to your estimate of the actual probability. Again, estimating the actual probability has no set method, unless you are a professional analyst with a statistical model. Instead it’s simply based on your own knowledge of the teams involved.

For Team A (+150):

Implied Probability (%) = 100 / (Odds + 100)

Implied Probability (%) = 100 / (150 + 100)

Implied Probability (%) = 100 / 250 

Implied Probability (%) = 0.4 or 40%

Let’s say after your analysis of the teams’ recent performances and other factors, you believe Team A has a 50% chance of winning this game (your estimated actual probability).

Now, because the bookmaker’s implied probability (40%) is lower than your estimated actual probability (50%), this suggests a potential value bet on Team A. In other words, you think they have a better chance of winning than what the bookmaker’s odds imply.

For Team B (-130):

Implied Probability (%) = Absolute Value of Odds / (Absolute Value of Odds + 100)

Implied Probability (%) = 130 / (130 + 100) 

Implied Probability (%) = 130 / 230 

Implied Probability (%) = 0.565 or 56.5%

In this case, the bookmaker’s implied probability of winning for Team B is approximately 56.5%.

Now, if your analysis suggests that Team B has a lower chance of winning, let’s say 50%, then you might see this as an opportunity to bet against Team B, as your estimate of the actual probability (50%) is lower than the bookmaker’s implied probability (56.5%).

So, a value bet in this scenario could be to bet on Team A (+150) if you believe they have a better chance of winning than what the odds imply or to bet against Team B (-130) if you think their chances are lower than the implied probability suggests.

In essence, a value bet is when you believe you have a better chance of winning than the bookmaker thinks, so you bet on it because you believe the odds are in your favour. It’s like getting a good deal in a store – you pay less but think the item is worth more. In sports betting, finding value bets can be a way to make a profit in the long run if your assessments are accurate.

What Is Expected Value In Sports Betting?

While it’s fairly simple to assess whether actual probability is higher than implied probability and identify a value bet, this calculation doesn’t tell us whether we can reasonably expect to win in the long-term. That’s where expected value comes in. Expected value (EV) in sports betting is a concept used to determine the potential profitability of a bet or series of bets on average. It helps bettors make informed decisions by assessing whether a particular series of bets is likely to result in a profit or loss based on the probabilities and potential payouts involved. In essence, it quantifies whether a bet is a good financial decision.

In mathematics, expected value is used to calculate a long-term average of many probabilities. In sports betting, professional bettors use EV to determine if a series of bets they want to make on average have positive EVs. This essentially tells them that, over the long-run of many bets, they will generate a profit overall even if some money is lost along the way. In essence, a positive EV bet could lose, but it still indicates you are more likely to generate profit in the long run than with a series of negative EV bets.

Here’s how expected value works in sports betting:

Expected Value  = (Probability of Winning * Potential Profit) – (Probability of Losing * Amount Bet)

You can use either implied probability or the actual probability you have calculated in this formula. Professional bettors more often use actual probability (i.e. their probability) as it relies on their own expertise in assessing odds, however implied probability can be used in a pinch. If the EV is positive, this suggests that you can expect to make a profit on your bet. Positive EV bets are considered valuable, and bettors should consider placing them. If the EV is negative, this indicates that on average you’re likely to lose money if you make this bet. 

Let’s say you’re betting on a basketball game. You estimate that Team A has a 60% chance of winning. The odds for Team A winning are +150, and you decide to bet $100.

Probability of Winning = 60% or 0.60

Potential Profit = $100 * 1.50 = $150

Probability of Losing = 1 – 0.60 = 0.40

Now, calculate the EV:

EV = (0.60 * $150) – (0.40 * $100) = $90 – $40 = $50

Now we know that you’re not actually going to win $50 if you bet $100, but the positive value indicates this bet could be worth taking.