# Odds vs Likelihood

Odds is the chance of an event occurring against the event not occurring.

Likelihood is the probability of a set of parameters being supported by the data in hand.

In logistic regression, we use log odds to convert a probability-based model to a likelihood-based model.

In what way are odds & likelihood related? And can we call odds a type of conditional probability?

This is more of a semantic than a statistical question. But based on wikidiff we can say that talking about a coin flip:

The odds for each outcome are 50/50 whereas the likelihood of getting tails is 50%.

That is odds are the ratios of all outcomes and likelihood is the probability of a given outcome.

Your sentence: "In logistic regression, we use odds to convert a probability-based model to a likelihood-based model." does not make sense to me. Can you give a source and context for this statement?

• Source: geeksforgeeks.org/role-of-log-odds-in-logistic-regression The line being referred to: Log odds play an important role in logistic regression as it converts the LR model from probability based to a likelihood based model. Apr 14, 2022 at 9:50
• This is important, where aren't talking about "odds" here we are talking about log odds or the logit-function. This has nothing to do with the base term "odds". Apr 14, 2022 at 9:55

Here is a good detailed answer about the difference between probability and likelihood: https://www.youtube.com/watch?v=pYxNSUDSFH4 Since odds are a ratio of probabilities, it should give you some clarification, In a nutshell, given a probability distribution, you can view a probability as the area that between two abscissa corresponding to your event. On the other hand likelihood is measured on the vertical axis and varies with the distribution parameters, and gives a value of how likely the parameters of the distribution are given your sample.

• Hi. Thanks for the response. My doubt is the difference between Odds & Likelihood, not Probability & Likelihood. Apr 15, 2022 at 11:26