1. Odds And Probability Calculator
2. How To Convert Betting Odds Into Probability
3. How To Convert American Odds To Implied Probability

If odds are stated as an A to B chance of winning then the probability of winning is given as P W = A / (A + B) while the probability of losing is given as P L = B / (A + B). For example, you win a game if you pull an ace out of a full deck of 52 cards. Pulling any other card you lose. Convert Decimal Odds into Probability. If we use the decimal odds of 1.80 for this and use the following equation:. 1 / decimal odds x 100 = implied probability. So, 1 / 1.80 is 0.555 (rounded up to 0.56), giving the mathematical equation of 0.56 x 100 = 56%. This means that odds of 1.80 reflect a 56% chance of that particular outcome. Probability/Odds Conversion Converting probabilities into odds, we simply divide the probability by 1 less the probability, e.g., if the probability is 25% (0.25), the odds are 0.25/0.75, which can also be expressed as 1 to 3 or 1/3 or 0.333.

Logistic regression may give a headache initially. While the structure and idea is the same as “normal” regression, the interpretation of the b’s (ie., the regression coefficients) can be more challenging.

This post provides a convenience function for converting the output of the glm function to a probability. Or more generally, to convert logits (that’s what spit out by glm) to a probabilty.

Note1: The objective of this post is to explain the mechanics of logits. There are more convenient tools out there. (Thanks to Jack’s comment who made me adding this note.)

Note2: I have corrected an error pointed out by Jana’s comment, below (you can always check older versions on the Github repo).

So, let’s look at an example. First load some data (package need be installed!):

Compute a simple glm:

The coeffients are the interesting thing:

These coefficients are in a form called ‘logits’.

If coefficient (logit) is positive, the effect of this predictor (on survival rate) is positive and vice versa.

Here Pclass coefficient is negative indicating that the higherPclass the lower is the probability of survival.

To convert a logit (glm output) to probability, follow these 3 steps:

• Take glm output coefficient (logit)
• compute e-function on the logit using exp() “de-logarithimize” (you’ll get odds then)
• convert odds to probability using this formula prob = odds / (1 + odds). For example, say odds = 2/1, then probability is 2 / (1+2)= 2 / 3 (~.67)

This function converts logits to probability.

For convenience, you can source the function like this:

For our glm:

How to interpret:

• The survival probability is 0.8095038 if Pclass were zero (intercept).
• However, you cannot just add the probability of, say Pclass 1 to survival probability of PClass 0 to get the survival chance of 1st class passengers.

Instead, consider that the logistic regression can be interpreted as a normal regression as long as you use logits. So the general regression formula applies as always:

That is, in our example

where b_survival is given in logits (it’s just the b-coefficient of Pclass).

So, it’ simple to calculate by hand, eg., the survival logits for a 2nd class passenger:

Thus, the logits of survival are -0.25Now we can convert to probability:

Remember that (e^1 approx 2.71). That is, if your logit is 1, your odds will be approx. 2.7 to 1, so the the probability is 2.7 / 3.7, or about 3/4, 75%.

Similarly important, (e^0 = 1). Hence, your odds will be 1:1, ie., 50%.

Hence, whenever your logit is negative, the associated probability is below 50% and v.v. (positive logit <–> probability above 50%).

However, more convenient would be to use the predict function instance of glm; this post is aimed at explaining the idea. In practice, rather use:

In the 1st class, survival chance is ~65%, and for 2nd class about 44%.

Here’s a look up table for the conversion:

A handy function is datatable, does not work in this environment however it appears.

The package mfx provides a convenient functions to get odds out of a logistic regression (Thanks for Henry Cann’s comment for pointing that out!).

More convenient for an overview is a plot like this.

The relationship between logit and probability is not linear, but of s-curve type.

The coefficients in logit form can be be treated as in normal regression in terms of computing the y-value.

Odds And Probability Calculator

Transform the logit of your y-value to probability to get a sense of the probability of the modeled event.

Happy glming!

The Difference Between Odds and Probability

How To Convert Betting Odds Into Probability

Odds and Probability Conversion Calculator

Odds and probability are two different ways to describe the chance of an even occurring. Odds expresses chance as a ratio of success to failure, the number of desired outcomes to the number of undesired outcomes. Probability expresses chance as a ratio of the number of desired outcomes to the total number of possible outcomes.
As an example, consider a coin flip. The odds of getting heads is 1:1 because there is one way to get heads and one way to not get heads, i.e. getting tails. Odds are read 'x to y.' where x is the number of successes and y is the number of failures.
The probability of getting heads is 1/2 or 0.5. There is one desired event (heads) and two events total (heads and tails). Probability is read 'x out of z,' where x is the number of successes and z is the total number of possible outcomes.
Converting Odds to Probability:
To convert odds to probability, add the successes and failures to find the total. Then divide the number of successes by the total to calculate the probability.
Example: Suppose the odds of a casino game are 2:3. Since 2+3 = 5 we take 5 as the total. Thus the probability is 2/5 = 0.4 = 40%.
Converting Probability to Odds:
First express the probability as a fraction with the numerator equal to the number of successes and the denominator equal to the total. Subtract the numerator from the denominator to find the number of failures. Then you have the two numbers needed to express odds.
Example. Suppose the probability of winning a game is 1/5. Since 5-1 = 4, we take 4 as the number of unsuccessful events. Thus, the odds are 1:4.

How To Convert American Odds To Implied Probability

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