Multinomial Regression & Multi-colinearity

Hi All,

Question regarding multi-collinearity and multinomial logistic regression. I am trying to generate a model that can determine the winning probabilities of each horse in race. Quite simple, my data has 1 denoting Win or 0 lose for each horse in my collected data. I obviously have a bunch of independent variables to go with it.

I have two variables that are highly correlated (~IVF of about 12), when I include them both in my model the R^2 of the generated model is noticeably greater then when I omit one of them to remove the collinearity.

My question is, considering I am interested in only the predictive ability of the model (i.e probability of each horse winning a race) and I don't really care about analysing the independent variables can I leave them in? My only concern is overfitting when I include both them. Should I remove one at the cost of predictive ability?