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How to calculate odds ratio and probability

Odds ratio are the ratio of the probability that an event will occur verses an event not occurring. For example, if you play 4 matches of football and win 3 games but lose 1, the odds of winning are calculated as:

(1/4) / (3/4) = 1.3, which is equal to 0.33.

The probability, or "risk" of losing, is different from the odds ratio. The risk of winning equals: (number of games won) / (number of games played), or 1/4 which is equal to 0.25.

 

How to Calculate Odds Ratio in a 2x2 Table

You can calculate your luck of one event occurring in a certain environment compared to another environment, for example, calculating the odds ratio of placing a bet on black or white, or calculating the odds ratio of fishing with and without bait. This is the simplest form to help you learn how to calculate odds ratio.

For this example we'll use the scenario of fishing with and without bait if you cast your rod 50 times:

Caught Fish (Number) Not Caught (Number)

With Bait: 25 25

Without bait: 2 48

 

The odds for catching fish with bait are 25/25, equal to 1.0

The odds of catching fish without bait are 2/48, equal to 0.02.

The odds ratio for catching fish with bait and without bait are therefore calculated as 1.0/0.02, which is equal to 50.

You can than calculate the probability of catching fish with bait and without bait from this by using the number of times you cast the rod, which was originally 50.

The probability of catching a fish with bait is 25/50, which equals 0.50 (or, a "fifty fifty chance"). The same calculation can be used to calculate the probability of catching a fish without bait.

By adapting this example, you can apply this method to most forms of betting, gambling or odds. Remember that the odds ratio is different from probability and can help you calculate the final risk.

 

Still not sure how to calculate odds ratio?

If you're still not sure how to calculate odds ratio, try using an online calculate that walks you through the basic steps and does the maths for you. One example is Hutchon.net, which is adapted to be used for a variety of reasons.

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