Odds can be expressed as a ratio of two numbers [or] as a number, by
dividing the terms in the ratio [....] Odds range from 0 to infinity, while
probabilities range from 0 to 1 [...]”
Yes, that’s exactly what I said. There is no way to express a fraction greater than 100% using odds notation; Saying that odds are “1 million to 1” is 99.9999%, still under 1.
In the Wikipedia
article, take a
look at the table below the words “These are worked out for some simple odds”.
The odds that
TobyBartels is talking
about,
which one gets by dividing the
numbers in an “n to m” expression, and which go from zero to infinity, are
shown in the second and third columns of that table (o_f and
o_a). Probabilities, which go from 0 to 1 or 0% to 100%, are shown in the
fourth and fifth columns (p and q).
Did you actually read the article you linked? It says the exact same thing as I did, phrased differently. Their “Odds range from 0 to infinity” means that any number from 0 to infinity can be used in the odds ratio, but still always represent a probability between 0 and 1. Which is precisely what I said.
Um, representing a number between 0 and 1 is not the same as being a number between 0 and 1. The representation of p = 3⁄8 as odds = 3⁄5 (“5 to 3 against”) is useful in practice, for example because bayes’ rule reduces to plain multiplication for odds ratios.
‘5 to 3 against’ is 3⁄8, not 3⁄5. Odds of ‘N to M’ or ‘N to M against’ are always between 0 and 1.
5 to 3 against is 3⁄5 (as odds), which is a probability of 3⁄8. You are muddling probability and odds ratios in an unacceptable way.
Wikipedia:
Yes, that’s exactly what I said. There is no way to express a fraction greater than 100% using odds notation; Saying that odds are “1 million to 1” is 99.9999%, still under 1.
In the Wikipedia article, take a look at the table below the words “These are worked out for some simple odds”. The odds that TobyBartels is talking about, which one gets by dividing the numbers in an “n to m” expression, and which go from zero to infinity, are shown in the second and third columns of that table (o_f and o_a). Probabilities, which go from 0 to 1 or 0% to 100%, are shown in the fourth and fifth columns (p and q).
You said ‘Odds […] are always between 0 and 1’, while Wikipedia said ‘Odds range from 0 to infinity’, so you didn’t say the same thing.
Did you actually read the article you linked? It says the exact same thing as I did, phrased differently. Their “Odds range from 0 to infinity” means that any number from 0 to infinity can be used in the odds ratio, but still always represent a probability between 0 and 1. Which is precisely what I said.
No, that’s not what you said. I am now done with this conversation.
Um, representing a number between 0 and 1 is not the same as being a number between 0 and 1. The representation of p = 3⁄8 as odds = 3⁄5 (“5 to 3 against”) is useful in practice, for example because bayes’ rule reduces to plain multiplication for odds ratios.