Betting Outcomes and Probability Computations
This page provides technical details for understanding and utilizing betting odds and probabilities that are foundational for developing sophisticated betting strategies.
- True Odds: The actual probabilities of outcomes without any bookmaker margin. True odds are rarely offered in sports betting as they do not provide any profit margin for the sportsbook.
- Implied Odds: These odds are derived from the betting odds offered by Cloudbet, indicating the implied chances of a particular outcome to be. Implied odds include the overround or vig, which is their built-in profit margin.
- Fair Odds: Also known as zero-vig or no-vig odds, these are calculated by removing Cloudbet’s overround from the implied odds. Fair odds show what the betting odds would be if Cloudbet did not apply a profit margin, providing a “fair” assessment of probability. Calculating fair odds is useful for bettors in assessing the value of the odds offered compared to the true likelihood of the event.
Conversion from US Odds to Probability
US odds represent the amount won on a 100 unit bet when positive, and the stake needed to win 100 units when negative. The probability implied by US odds is calculated as follows:
When odds are positive:
When odds are negative:
Conversion from Decimal Odds to Probability
Decimal odds represent the total payout (stake + win) for each unit bet. The probability implied by decimal odds is simpler to calculate:
Calculating Edge from Probability and Odds
The edge represents the expected value of a bet as a percentage of the bet amount. It indicates a player’s advantage (or disadvantage) against the odds offered by the bookmaker.
Using decimal odds:
Example: Calculating Edge from Probability and Odds
Let’s say you are considering a bet on a tennis player to win a match. The bookmaker offers decimal odds of 1.8 for this player to win. You estimate that the probability of the player winning is 60% (or 0.60). Plug in your values:
\( \text{Edge} = (0.60 \times 1.8) - 1 = 1.08 - 1 = 0.08 \)
This result, 0.08 or 8%, represents your edge. It indicates that you have an 8% advantage against the odds offered by the bookmaker. This is a positive edge, suggesting that the bet has a positive expected value, making it a potentially profitable bet if your probability estimation is accurate.
From Edge to Probability
Conversely, calculating the probability required to justify a bet at given odds can help bettors decide whether the bet has positive expected value.
Using decimal odds:
Example: Calculating Required Probability
Suppose a bookmaker offers odds of 2.5 for a particular team to win a game. You want to calculate the probability that justifies these odds, assuming you have determined an edge of 0.04 (or 4%). Plug in the values:
\( \text{Probability} = \frac{1.04}{2.5} \approx 0.416 \)
This result, 0.416 or 41.6%, is the minimum probability at which the expected value of the bet becomes neutral or positive, given the edge of 4%. It shows that if you estimate the true probability of the team winning is greater than 41.6%, the bet has a positive expected value, making it a potentially good bet.
Decision Making
If your analysis or model suggests that the actual probability of the team winning is higher than 41.6%, say 45%, then the bet is favorable because your estimated probability exceeds the break-even probability calculated. This suggests an expected value that is positive, making it a rational bet under these assumptions.
If your estimate is lower, say 40%, the bet does not justify the odds, indicating a negative expected value, and it would be advisable to avoid placing the bet.