Calculating Implied Odds in Sports Betting

Implied probability is an essential concept in betting that refers to the probability of an event occurring as reflected by the odds set by bookmakers. It represents the likelihood of a particular outcome based on the odds offered.

In betting, odds are typically presented in different formats, such as decimal, fractional, or moneyline. Implied probability is derived by converting these odds into a percentage.

To calculate the implied probability, you can use the following formulas based on the odds format:

Decimal Odds:

• Implied probability = 1 / Decimal odds

For example, if the decimal odds are 2.5, the implied probability would be 1 / 2.5 = 0.4, or 40%.

• Fractional Odds:

Implied probability = denominator / (denominator + numerator)

For example, if the fractional odds are 3/1, the implied probability would be 1 / (1 + 3) = 0.25 or 25%.

• Moneyline Odds:

Implied probability = 100 / (absolute value of the moneyline odds + 100)

For example, if the moneyline odds are -200, the implied probability would be 100 / (200 + 100) = 0.333 or 33.3%.

Implied probability is a valuable tool for bettors as it allows them to assess the value of a bet. If the implied probability is lower than your assessment of the likelihood of an event occurring, it may indicate a potentially profitable opportunity. Conversely, if the implied probability is higher than your assessment, it may suggest that the odds are not favourable.

However, it's important to note that bookmakers incorporate a margin, known as the "vig" or "overround," into their odds to ensure a profit. As a result, the sum of the implied probabilities for all possible outcomes will always be greater than 100%. This difference represents the bookmaker's profit margin.

Let's imagine there's a UEFA Champions League final match between Bayern Munich and Manchester United.

We'll create hypothetical betting odds for three possible results: Bayern Munich wins, Manchester United wins, and the match ends in a draw (which would force extra time and possibly penalties).

Let's say these are the decimal odds given by a bookmaker:

• Bayern Munich to win: 2.20
• Manchester United to win: 3.40
• Match to end in a draw: 3.20

We can calculate the implied probability for each outcome using the formula:

Implied probability = 1 / Decimal Odds

So the implied probabilities are:

• Bayern Munich to win: 1 / 2.20 = 0.455 or 45.5%
• Manchester United to win: 1 / 3.40 = 0.294 or 29.4%
• Match to end in a draw: 1 / 3.20 = 0.312 or 31.2%

If you add these probabilities, the total is 1.061, or 106.1%. The excess over 100% (6.1% in this case) is known as the overround or vigorish, representing the bookmaker's profit margin.

It's worth noting that these are theoretical probabilities based on the bookmaker's odds and don't necessarily represent the actual likelihood of each outcome. The real world is unpredictable, and the match's final result could be influenced by many factors not accounted for in these probabilities.

let's envision a hypothetical scenario with an Ice Hockey World Championship 2022 final match between Canada and Russia.

We will assign hypothetical odds for the three outcomes:

• Canada to win: 2.30
• Russia to win: 3.00
• Match to end in a draw (after regulation time): 4.50

These are decimal odds, and we can calculate the implied probability for each outcome using the formula:

Implied probability = 1 / Decimal Odds

Here's what we get:

• Canada to win: 1 / 2.30 = 0.435 or 43.5%
• Russia to win: 1 / 3.00 = 0.333 or 33.3%
• Match to end in a draw: 1 / 4.50 = 0.222 or 22.2%

Adding these probabilities together gives us 0.990, or 99.0%. In this hypothetical example, there isn't an overround (since the total is less than 100%), which is unrealistic in the real world. In a typical scenario, the total would exceed 100% due to the overround, the bookmaker's profit margin.

We'll create hypothetical decimal betting odds for the two possible outcomes: Player A wins or B wins.

There are no draw outcomes in tennis, so we don't need to consider that possibility. Note that because it's a final, the match will continue until there's a winner, even if it goes to a fifth-set tiebreaker or beyond.

Let's say these are the decimal odds given by a bookmaker:

• Player A to win: 1.75
• Player B to win: 2.25

We can calculate the implied probability for each outcome using the formula:

Implied probability = 1 / Decimal Odds

So the implied probabilities are:

• Player A to win: 1 / 1.75 = 0.571 or 57.1%
• Player B to win: 1 / 2.25 = 0.444 or 44.4%

Adding up these probabilities, the total is 1.015, or 101.5%. The excess over 100% (1.5% in this case) is the bookmaker's overround, also known as vigorish or juice, which is their built-in profit margin.