# Logistic regression for paired comparisons

I am not a statistician; I'm an engineer, so much of this is a foreign language to me, though it seems like it wouldn't be that hard to understand if explained in a different way.

I am trying to learn how to combine lots of paired comparisons of items into a unified ranking of the items. I can understand things like Elo and Glicko, but the Bradley-Terry model is supposed to be the more accurate, more general method that they are based on, so I am trying to learn that. I've been reading many different references and I just get lost trying to get an intuitive understanding of it.

If it's possible to Explain Like I'm 5 the Bradley-Terry model in a single answer (preferably using more plots and graphs than equations), please do that. If that's too much for a single answer then I will ask a more specific question:

This modeling is based around "logistic regression". To me, that sounds like finding the best fit for a logistic function to some data points? Is that correct? If so, what are the data points in this context, and what do we do with the fit information after we have it?

• What are you trying to do? Are you trying to infer rankings on a known set of items, or are you trying to predict comparisons on possibly new items? If the first one, logistic regression doesn't actually have to enter the picture at all, which will make it somewhat simpler to explain. Commented Dec 6, 2014 at 22:19
• Your question seems rather general and vague. Are you able to identify specific things you need explanation of? Commented Dec 7, 2014 at 0:05
• Logistic regression isn't simply fitting a logistic function to some data points (you can do with with nonlinear least squares, for example, but that's not logistic regression). The response in the case of paired competition (which I assume you want since you mention Elo) would be the cases which were won(1) or lost (0) for the member of the pair you are focused on. The predictors would be whatever features you want to consider in your model. Commented Dec 7, 2014 at 6:29
• @Glen_b That would make a good answer if you could go into more detail. I don't understand your first sentence, for instance. Is one thing a subtype of the other, or are they completely distinct? The intro to en.wikipedia.org/wiki/Logistic_regression says that it involves modeling outcomes using logistic functions, so what's the difference? Commented Dec 9, 2014 at 1:28
• Okay, let me address that part of your question in an answer, since it would be much too long for a comment. Commented Dec 9, 2014 at 3:58