I understand that most statistical methods focus on predicting common occurrences, but are there any tests that would predict outliers? Essentially I would want to know what outside variables stand out for outliers as opposed to "normal" values. An improvised example being predicting a stellar performance on a game (10+ points) rather than 0-9.9 points. I would then want to figure out which physical traits (out of lets say, 200) are abnormal for individuals with a stellar score rather than anything less.
I've gotten some significant results that lower AIC using logistic regression (1 = outlier, 0 = not), but I'm not completely sure if it will hold up in the long run or if it is even appropriate to recode the continuous variables into binary ones.