Machine Learning and Pattern Recognition Assignment Feedback

Integer player identifiers (p1, p2) are a natural and compact way to specify which players met in a game. However, logistic regression assumes that the probability of the output depends only on a linear combination of the input features. Using the (p1, p2) inputs in logistic regression would mean that the probability of player 2 winning a game would always have to be between the probabilities of players 1 and 3 winning against the same player. However, these integer identifiers are arbitrary! Encoding the inputs in feature-vector x gives logistic regression a separate parameter for each player, so it can learn an arbitrary ordering of their abilities.