# Logistic regression with arbitrary labels

I am doing logistic regression on some team stats for March Madness, where my response is 1 if "team A wins" and 0 if "team A loses". The problem with that is that the label "team A" is arbitrary. Indeed, my data are naturally labelled as winning team and losing team. However, the winning team can't be defined as "team A" because then my data is all 1s! How do I reformulate my problem to resolve this?

• Probably better asked on stats.stackexchange.com. Anyway, how can you hope to do any kind of inference without keeping track of the identities of the teams? A more natural model is that to each team you assign some parameter or parameters that describe how "good" the team is, then update these parameters in some way for two teams whenever they play and one beats the other. This is e.g. how the ELO rating system for chess works. – Qiaochu Yuan Mar 14 '17 at 8:30
• If you insist on doing logistic regresssion, you could collapse your data into a table with each team having listed wins and losses. Software such as R is able to model this using the $\texttt{glm}$ function. – Lundborg Mar 14 '17 at 8:32
• @Quiochu, in your chess analogy, you might want to, given two players' ELO, estimate a probability that player A beats player B. Logistic regression would be a natural first model for that. The independent variables, then, are the two ELOs... How does one define the response variable for this problem? – Scott Mar 14 '17 at 8:37