How To Convert Odds To Probability

• Converting Between Probability And Odds
• How To Convert Odds To Probability
• How To Convert Odds Ratio Into Probability
• How To Convert Odds Ratio To Probability
• How To Convert Betting Odds To Probability
• How To Convert Log Odds To Probability

In other words, odds of 1.65 means that for every 1.00 you place on a particular outcome, you will receive a profit of 0.65 should that outcome prevail. To convert these odds to their respective implied probabilities we make a simple calculation. 1 divided by the. Essentially, I'd like to see if I can provide insight into how much the probability is influenced by each feature. To do this, I used the following formula: 1 + 1 / exp (-logodd) and I would expect that after I convert all of the explanations for a specific prediction to probabilities, the sum should be zero.

If you can’t convert odds into the probabilities they imply, you are going to struggle in the long term to make money from your betting. How can you assess value if you don’t first know the probabilities the betting market is indicating?

It’s not a difficult thing to do and with a little practice you will be able to do it automatically every time you look at a betting market.

First we’ll look at conversion of fractional odds to probabilities as those are still the predominant type used in the UK.

Converting Fractional Odds

Fractional odds simply reflect the return you will get if your selection wins – bet £20 on a 4/1 shot and you’ll get £80 – 4 x £20 – back (plus your original stake of £20). However, they also reflect the bookmaker’s assessment of the chances of that selection winning . In addition, there’s an adjustment in there to cover the bookmaker’s profit margin (the overround) but for the purposes of this exercise we’ll ignore that.

So what percentage chance does the bookmaker think a selection has if he is offering 4/1? Here’s the calculation:

Divide the number on the right of the fraction by the total of both numbers in the fraction:

1 divided by (4+1) = 0.20

Then multiply that by 100 to give a percentage probability:

0.20 x 100 = 20%

So a 4/1 chance has an implied 20% chance of winning! Simples

Converting Decimal Odds

Again, like fractional, decimal odds are a reflection of the return you will receive if you win, including your stake. So if you have £20 on a winner with decimal odds of 7.0, you will receive £20 x 7 for a return, including stake, of £140 (£120 profit). To convert those odds into a probability, here’s the calculation:

Divide 1 by the decimal odds then multiply by 100 to give a percentage

1 divided by 7 = 0.143

0.143 x 100 = 14.3%

So a selection priced at 7.0 in decimal format has an implied 14.3% chance of winning!

These are very simple calculations and with experience you will be able to look at a betting market and instantly calculate the implied winning chance of all the runners based on the odds on offer.

Vice Versa

If you have reached the point where you are compiling your own tissue prices as part of a value finding exercise (and that should be your aim!), you will need to be able to convert percentage probabilities back to odds format for the purpose of comparison.

Converting Probabilities to Fractional Odds

Based on your own assessment methods, you have determined that a horse has a 10% chance of winning a race. To convert that into fractional odds format the calculation is

(100 divided by percentage probability) -1

(100/10) -1

10-1 = 9

So a selection with a 10% chance of winning should be priced at 9/1

Converting Probabilities to Decimal Odds

In this example you’ve found a horse that you think has a 60% chance of winning it’s race. To calculate it’s odds in a decimal format:

Divide 100 by the percentage probability

100/60 = 1.66

So a 60% chance is expressed as 1.66 in decimal odds format.

So there you have it. However, an even easier way to do it is to memorise the major odds and their respective implied probabilities using the table I have put together below!

Converting Between Probability And Odds

Here is a fairly simple question with an equally simple and straightforward answer. How does one convert the odds ratio to the probability of winning in sports handicapping. Crazy as it sounds, this question was right up my high school baseball coach’s alley, as he was also my teacher in probability and statistics (some fun school class I had back in the day). And yes, I did just put fun and school in the same sentence. And no, I wasn’t being sarcastic. He always made baseball fun, whether at practice, driving on a bus to an away game, or in the game itself. And his class was fun as well (at least for me). No idea if he handicapped sports, or if he ever ran equations in his head any time he flashed the bunt or steal sign. Anyway, without further ado…

Flipping a Coin – What are odds?

So, we all probably have no doubt that a coin flip would result in 50% chance of heads and 50% chance of tails. The coin only has two sides. So here, we simple divide our desired outcome (1) by the two possible outcomes (2) and multiply by 100 to give us our answer in a percentage.

1 / 2 x 100

.5 * 100 = 50%

A roll of a die (or singular form of dice)

Die or dice, whatever you want to call the singular form of dice. We have one. It has 6 sides, what is the probability that we get a 3 from rolling it? Well, to answer this, we take the 1 desired result (the 3) and divide it by 6 (the 6 possible outcomes). Then we multiply the answer by 100 to put our answer in percentage form.

1 / 6 * 100

.1667 * 100 = 16.67%

Here, we have a 16.67% chance of rolling our desired outcome.

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Types of Odds

The most common forms of odds used today are decimal odds, fractional odds and American odds (the moneyline). We will go through each below. First, however, why is this important? Well, by converting the betting odds into something often referred to as implied probability, we can better access the value of a particular market. Do they differ from what we believe the odds of winning should be? If the odds offered to us (the implied probability) are less than or greater than our personal assessment, then this would represent either an increase or decrease in betting value.

Decimal Odds – How to Convert Odds Ratio to Probability in Sports Handicapping

First on the above list, are the decimal odds. These odds are common in Europe. The decimal odds represent the amount that is won for every $1 wagered. Say for example the odds are represented as 2.5, this would imply that for every 1 you wager, you will gain a profit of 1.5 if the outcome was in your favor. Here, to convert odds ratio to probability in sports handicapping, we would have the following equation:

(1 / the decimal odds) * 100

or

(1 / 2.5) * 100

Quickly, doing the math in my head (kidding, I used a calculator), the answer is 40%

Fractional Odds – How to Convert Odds Ratio to Probability in Sports Handicapping

How To Convert Odds To Probability

When I think of the odds represented in a fractional format, I automatically think of horse racing. Let’s say the odds of Aggressive Neil to win are represented as 9 / 2, how do we translate? Well the equation is as follows:

Denominator / (Denominator + Numerator) * 100

Or with our 9 /2 example:

2 / (2 +9) *100

Using my overused calculator, I get an 18.18% chance of winning.

American Odds (The Moneyline) – How to Convert Odds Ratio to Probability in Sports Handicapping

Used much in North America for sports such as baseball, basketball, hockey and others, the moneyline is actually not as confusing as one would first think. Each game or match will have teams with either a plus moneyline or a minus moneyline. A +180 for example would imply that for every $100 wagered the winnings would be $180 gross or $80 net. So, the plus moneyline would represent the underdog for the game or match.

Conversely, a -180 line essentially means the team is the favorite to win, and to win $100, one would need to wager $180. So, here, how do we convert these odds into the probability of winning in sports handicapping?

Well, in the case of the moneyline, we have the following equation for the plus moneyline:

100 / (plus moneyline +100) * 100 (to put it as a percentage)

Or using the example above,

100 / (180 + 100) *100

Here my calculator gives me a 35.71% chance of winning.

And for the minus moneyline, I basically use the absolute value or (in my simple terms) remove the negative sign in the value. The calculation for chance of winning would then look something like this:

(absolute value of negative line odds) / (absolute value of negative line odds + 100)* 100 (to put it as a percentage)

Or using above example:

180 / (180 +100) *100

How To Convert Odds Ratio Into Probability

And, here, my calculator throws out a 64.29% chance of winning.

Places Online to Convert the Odds Ratio to Probability in Sports Handicapping

Ok, so maybe I should have blurted out the following websites right up front. But now, we at least understand the formulas used to convert the odds ratio to probability in sports handicapping. One webpage I found that calculates these odds into a percentage is from aceodds.com. Here is the link.

Another webpage, I found is from actionnetwork.com. Here is the link.

Moneyline (American Odds) to Percentage Conversion Chart

I personally like the online calculators mentioned above for our topic and mission here. However, you may want a spreadsheet version of the calculations instead. If this describes you, I’ll throw a quick moneyline to percentage conversion chart at the end of this article.

Why Do the Odds that Bookmakers Give You Not Add Up to 100%

So, why is it that the odds that bookmakers offer do not equate to 100% when combined? For example, in major league baseball, let’s say the Seattle Mariners are visiting the Oakland Athletics today. The odds may have the game at Seattle Mariners +120 and Oakland Athletics -130. Do the above equations and we come up with the Seattle Mariners percentage value of 45.45% and the Oakland Athletics percentage value of 56.52%. Add the two and we come up with a total percentage value of 101.97%. What is with this figure? Well, that 1.97% is the bookmakers edge incorporated into the odds, their expected return for setting up the bet.

Why Do the Odds Move Throughout the Day?

So, you probably have noticed the lines moving throughout the day. These lines are not static? In our Seattle Mariners vs. Oakland Athletics game above (which I did grab from a past game played), we again have the odds listed at Seattle Mariners +120 and Oakland Athletics -130. These were not, however, the odds the game opened at. The opening odds were actually Seattle Mariners +107 and Oakland Athletics -127. So, why did this particular sportsbook move the line from +107 to +120 and -127 to -130? Well, most likely the lines moved to entice more action to the Seattle Mariners. The sportsbook wants to “balance the books”, and they will move the lines one way or the other to entice more action to one side of the equation.

How To Convert Odds Ratio To Probability

In Summary

How To Convert Betting Odds To Probability

Hey, sportsbooks are around to make money for themselves. The lines may fluctuate throughout the course of the day in an attempt to match the bets as close to 50% one side and 50% the other. The left over percentage that we described above is how the books make money. Let’s say your assessed probability is of a greater percentage than that of the bookmaker’s implied probability. This creates an opportunity, a value betting opportunity.

And below is the a table of the moneyline to percentage conversion chart mentioned above.

How To Convert Log Odds To Probability