Odds ratio vs "normal" ratio?

Question

How to interpret 5 to 1 odds vs a 5:1 ratio i.e. both into a fraction

So like 5 to 1 odds of Horse A to Horse B winning a race implies Horse A is 5 times as likely to win. i.e. Probability horse A wins is 5/6 while horse B is 1/6.

But if I have a "normal" ratio 5:1 it would be converted, as a fraction, to 1/5 horse B wins vs 4/5 horse A wins. (see this simple video confirming this https://www.khanacademy.org/math/in-sixth-grade-math/ratio-and-proportion/inda-ratio-proportion/v/ratios-as-fractions-in-simplest-form )

Does this sound right or is there a better way of interpreting it?

Puzzling · Answer

A ratio is just expressing how two numbers are related.

If you have 5 to 1 odds in favor of horse A, that means that on average, horse A is expected to win 5 times for every 1 time that horse B would win.

Odds are expressed as the ratio of favorable outcomes (A wins) to unfavorable outcomes (B wins).

If you want to convert odds to probability, you instead switch that to a different ratio, namely the ratio of favorable outcomes (A wins = 5 times) to *total* possible outcomes (A or B wins = 6 times)

So the probability of A winning is 5/6 compared to the probability of B winning being 1/6.

Now I don't know what two values are being compared in your "normal" ratio 5:1. You have to explain how those numbers are related. 5 to 1 could be a ratio comparing most anything. It could be the ratio of wins for horse A (5) to those of horse B (1) and then you are just talking about the same thing as before.

I'm not sure where you are going with turning the ratio of 5:1 into 1/5. If you turn a ratio into a fraction, you don't flip anything around. The ratio 5:1 is the same as the fraction 5/1.

That means the probability of the first event happens 5 times as frequently as the second event.

So what do you mean by "normal ratio"?

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Odds ratio vs "normal" ratio?

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