Odds To Probability Formula
Calculate the probability of winning according to the odds formulas: 5/17 = 29.41%. Calculate the probability of losing according to the odds formulas: 12/17 = 70.59%. Check whether the result is correct with the betting odds calculator.
- The interpretation of an odds is more complicated than for a risk. The simplest way to ensure that the interpretation is correct is to first convert the odds into a risk. For example, when the odds are 1:10, or 0.1, one person will have the event for every 10 who do not, and, using the formula, the risk of the event is 0.1/(1+0.1) = 0.091.
- Implied probability is a conversion of betting odds into a percentage. It takes into account the bookmaker margin to express the expected probability of an outcome occurring. Knowing how to convert betting odds into implied probabilities is fundamental for betting as it helps you assess the potential value on a particular market.
When it comes to gambling, you won’t be able to find two more essential concepts than odds and probability. They are what makes the entire thing work. Odds are used to calculate both the payout a gambler can expect to receive from a winning wager and the implied odds of an outcome happening. Probability is just the likelihood that a given result will occur.
One essential concept to remember is that while probability and odds are both related and may seem very similar, they aren’t exactly the same thing. Probability represents the likelihood that something will happen.
It is calculated by dividing the number of wanted results by the total number of possible outcomes. Odds, on the other hand, present a ratio of wanted results to unwanted outcomes.
There are three primary ways of expressing odds. They are decimal, fractional, and moneyline (or American). No matter what odds format you use, these three types of odds all represent the same thing.
In fact, it is easy to convert one format to another, as you will see further down this guide.
Beyond governing how the entire world of sports betting works, odds play a vital role in helping a sports bettor decide if a bet is worth placing or not. All odds carry with them an implied probability, which we then compare to the real probability to determine whether a wager possesses positive value or not. A rule to live by in the gambling world is only to place bets with positive value.
For ExampleLet’s say we are gambling on the outcome of a single coin flip. Because there are only two sides of a coin, we know that each result has a 50% probability of occurring. For the sake of this example, we are betting tails. We can calculate this like so:
Our desired outcome is for the coin to land on tails, so there is one desired outcome.
We divide the amount of desired outcomes by the total amount of outcomes possible, then multiply the result by one hundred to get the probability. The formula looks like this:
1/2 = 0.5 X 100 = 50%
Now that we know the probability, let’s look at the odds being offered on this bet. For some reason, the odds for heads are set at -300, while tails are +260. This would be a very odd occurrence for such a bet but bear with me. Now we must calculate the implied probability of both lines being offered and determine which bet contains the most value.
First, we will solve the implied probability for heads. I find it easiest to convert the moneyline value to decimal odds before converting to a percentage:
Now we take our decimal odds and convert them to a percentage:
Odds To Probability Formula Cheat
This means the implied odds are a much higher percentage than the actual 50% probability that we already calculated. A bet on heads here would be a terrible decision with a negative value.
Now we will solve for tails:
In this instance, the probability of tails landing far outweighs the implied probability determined by the odds being offered. This is a high-value bet.
Calculating the real probability and comparing that number to the implied probability set by the odds is the primary strategy with which one should approach every bet.
Important:Understanding how to calculate betting odds and find value bets is essential to your long-term success in gambling.
In this guide, we will show you how to convert any format of odds to any other, as well as how to find the implied odds from any type of odds.
Types of Odds Formats
Decimal
Decimal odds are the favorite way to express betting lines in Europe. They are the most straightforward method of communicating odds. The decimal value is the amount that will be returned per each dollar bet. What makes this system particularly helpful is that both the amount staked and the winnings are included.
So let’s say we made a $10 bet at 3.5 odds. Our total return for winning that wager would be $35. $25 is the profit, with the other $10 being the return of our stake.
Fractional
Fractional odds are most commonly found at racetracks or for futures bets when there are entire pools of participants that can possibly win. This format expresses odds in the form of fractions such as 4/1, which would be pronounced “four-to-one.” Four-to-one odds means that you will earn $4 for every $1 that you stake.
Sometimes the fractions will be less straightforward. You may see numbers like 9/2, for example. To calculate the return on a 9/2 bet, let’s pretend that we bet $20 at 9/2 odds for a horse race.
Unlike decimals, fractional odds provide the total payout. They calculate the winnings only. To determine the total amount that you will receive for a winning bet, simply solve the equation above and add $20 to the total. So the formula looks like this:
Moneyline/American
The moneyline system of presenting odds utilizes negative and positive three-digit values to represent which bets are favored or underdogs. A positive number means that a play is considered the underdog. The quantity after the “+” is the amount that will be won for every $100 bet.
On the other end of the spectrum, favorites are displayed with a negative value such as -350. This means that you must bet $350 to win $100. Moneyline odds only calculate the amount potentially won on a bet, and not the total payout.
Calculating Odds
To learn how to calculate odds, let’s make things a bit more interesting with a switch from a coin toss to a roll of a six-sided die. The wager that we are making is that the die will land on 3. In this example, we are looking at one desired outcome. If there are six possible outcomes on a roll of the die, and only one outcome is desirable, that means there are five undesirable results.
Because we are calculating the odds, not the probability, we are expressing a ratio of desirable results to undesirable results. In this example, the ratio would look like this:
That means there’s one chance that we will win versus five that we will not. It is important to keep in mind that we are not calculating how likely we are to win, only the ratio of good results to bad.
Now we can calculate the odds against us winning, as well as the odds in favor of a win. To calculate the odds in favor, simply divide the one possible desired outcome by the total outcomes possible.
Conversely, the odds against our win can be solved the same way:
Converting Probability to Odds
You may want to calculate an odds ratio based on a particular probability. In order to solve this equation, we will need to express the probability as a fraction. Using the same six-sided die from before, the possibility of our number landing formatted as a fraction is 1/6.
Next, just subtract the numerator from the denominator:
The answer once again gives us the number of unwanted possible results. Now we just present the odds in ratio form, bringing us to 1:5 odds.
To solve for probability given an odds ratio, we merely reverse the equation. First, we put our odds ratio in fraction form:
Add the numerator and denominator together, which will give us the total number of potential results:
Last, just put the number of wanted outcomes over the total outcomes possible, and we’ve got our probability again!
Converting Odds
There are numerous odds calculators available online that are probably faster to use, but it’s still best that you understand the formulas for converting different odds types to other formats. Below are all of the equations required to transform any kind of odds to any other arrangement.
The odds always stay the same; they are just represented differently. At times, being able to convert formats can be extremely helpful, especially when switching to decimals when solving for implied probability.
Moneyline to Decimal
To convert positive moneyline odds, the equation is:
(Moneyline odds/100) + 1 = Decimal odds
To convert negative moneyline odds, the equation is:
(100/Moneyline odds) + 1 = Decimal odds
Moneyline to Fractional
To convert positive moneyline odds, the equation is:
(Moneyline odds/100) = Fractional Odds
To convert negative moneyline odds, the equation is:
-100/Moneyline odds = Fractional Odds
Fractional to Decimal
(Numerator/Denominator) + 1 = decimal odds
Fractional to Moneyline
(Numerator/Denominator)
If the result is greater than or equal to 1:
100 X (Answer) = Moneyline odds
If the result is less than 1:
-100/(Answer) = Moneyline odds
Decimal to Fractional
Decimal odds – 1 = X
Put X over 1
Example:
- 3.5 – 1 = 2.5
- 2.5/1 = 5/2
- 3.5 decimal odds = 5/2 fractional
Decimal to Moneyline
If decimal odds are greater than 2:
100 X (decimal odds – 1) = Moneyline odds
If decimal odds are less than 2:
-100/(decimal odds -1) = Moneyline odds
Calculating Implied Probability
To make use of our calculations solving for real probability, we must also determine the implied probability. Implied probability converts odds into a percentage.
Note:That percentage can then be compared to the actual likelihood of an event happening, which allows for intelligent decision making.
In the early coin toss example, we converted our odds from moneyline to decimal before solving for the implied probability. This is not necessary but is often the easiest way to complete the calculation.
From Decimal Odds
Finding implied probability from decimal odds is extremely easy. Let’s say the decimal odds are 2.5.
Formula To Convert Probability To Odds
- 1/2.5 = 0.4
- 0.4 X 100 = 40% Implied Probability
From Moneyline Odds
Calculating implied probability for a -150 favored moneyline bet:
- (- (-150)/((-(-150)) + 100 =
- 150/(150 + 100) = 150/250 = 0.6
- 0.6 X 100 = 60% Implied Probability
Calculating implied probability for an +250 underdog moneyline bet:
- 100/(250 + 100)
- 100/350 = 0.2857
- 0.2857 X 100 = 28.57% Implied Probability
From Fractional Odds
Denominator/(denominator + numerator) X 100
- Calculate the implied probability of 15/2 odds.
- 2/(2 + 15) X 100 = 2/17 X 100 =
- 0.12 X 100 = 12 % Implied Probability
In Conclusion
Understanding what odds and probabilities are, and being able to calculate both, are fundamental skills that anyone aspiring to find any success in sports gambling must possess. The two concepts are closely related and always intertwined, but they are not the same thing.
Odds are represented in ratios of wanted results to unwanted results, while probability is a calculation of wanted outcomes divided by all possible results. Whatever number that calculation produces is the percentage of likelihood that the outcome we want will occur.
Recommended Reading:To judge whether a bet is worth making or not, calculate both the real probability and the implied probability given by the odds being offered. If the actual likelihood is higher than what’s being suggested by the odds, that bet possesses value and should be wagered on. However, if the implied probability is higher, the gamble has a negative value and should be avoided.
Some of these concepts may seem confusing now, but the more you focus on value and calculating odds and probabilities, the easier betting becomes. No longer will you fall for suckers bets offering negative value, nor will you merely make picks based on who you think should win.
The sooner your betting habits become all about identifying valuable odds and betting accordingly, the sooner you’ll see your bankroll start increasing. And that entire process begins with calculating betting odds, so you’ve come to the right place.
Given here are the log odds and odds formulas to find the odds, log odds and expected proportion based on the values of any two. The expected proportion is the probability of success on each trial. The odds, also known as 'Odds for' reflect the likelihood that the event will take place, while the 'odds against' is the likelihood that the event will not take place. The log odds is the log of the odds ratio. The odds ratio is a measure of association between an event and the result.
Formula:
When Observed Proportion is Giveno = p / (1 - p)
l = log (p / (1 - p))
When Odds is Given
p = o / (1 + o)
l = log(o)
When Log Odds is Given
o = Exp (l)
p = o / (1 - o)
Where,
o = Odds
l = Log Odds
p = Observed Proportion
Related Calculator:
This log odds and odds formula help you solve your statistical queries related to events and their probabilities of their outcomes. Substitute your values in the formulae and verify your results by verifying it in the 'Log Odds and Odds Calculator' given under the related calculator section.