I find it interesting that you lack familiarity with log-odds? What field are you in? Statisticians will usually be familar with them, as the logit is the canonical link function for the binomial function when using general linear modeling. Cut of (some) jargon, if I have a data set with binomial outcomes, and I wish to model my data as having normal errors, and the predictors as having linear effect on the outcome, I'd convert my data by using log odds. So, for instance, if I was looking at age as a predictor for diabetes (which is a yes no outcome)
I have a very strong competition math background from high school, but my primary field is chemistry.
(I wrote this post for my own blog, and given the warm reception, I figured it would also be suitable for the LW audience. It contains some nicely formatted equations/tables in LaTeX, hence I've left it as a dropbox download.)
Logarithmic probabilities have appeared previously on LW here, here, and sporadically in the comments. The first is a link to a Eliezer post which covers essentially the same material. I believe this is a better introduction/description/guide to logarithmic probabilities than anything else that's appeared on LW thus far.
Introduction:
Our conventional way of expressing probabilities has always frustrated me. For example, it is very easy to say nonsensical statements like, “110% chance of working”. Or, it is not obvious that the difference between 50% and 50.01% is trivial compared to the difference between 99.98% and 99.99%. It also fails to accommodate the math correctly when we want to say things like, “five times more likely”, because 50% * 5 overflows 100%.
Jacob and I have (re)discovered a mapping from probabilities to log- odds which addresses all of these issues. To boot, it accommodates Bayes’ theorem beautifully. For something so simple and fundamental, it certainly took a great deal of google searching/wikipedia surfing to discover that they are actually called “log-odds”, and that they were “discovered” in 1944, instead of the 1600s. Also, nobody seems to use log-odds, even though they are conceptually powerful. Thus, this primer serves to explain why we need log-odds, what they are, how to use them, and when to use them.
Article is here (Updated 11/30 to use base 10)