I'm also one of the geeks that likes to math out the comparisons in games for efficiency. Your take is very interesting, but I can see you've really limited your scope for obvious reasons. You've got a solid handle on the statistical analysis, but I think one of the reasons your results are coming out rather skewed is your choice use only base stats.
I know including item stats opens a huge set of it's own problems, but I'd suggest including runes and/or masteries in your comparisons. There is certainly some variation amongst players, but I think generalizing the builds for role/position would be standard enough to be relevant. The normal builds could be developed through popular guides like Mobafire and other sites and cross referenced with pro players. This might help "fix" things like your role predictor which I noticed it has a particularly difficult time with ADCs in the early levels.
I know you're looking at abilities next, but I suspect that including typical runes/masteries and even including a way for users to build their own selections would be relatively easy and fairly informative.
Overall, I can tell you're smart enough to do this and ambitious enough to do it right. I've thought about trying to quantify some things in LoL myself like I have other games, but the variables are pretty mind boggling to come up with something realistic enough to be useful. I really, really want to do some work on how jungle pathing affects successful ganks and gold generation, but I don't have the time with university and work to even come up with a way to collect data. Actually, finding a way to record the massive quantity of data generated in an individual game in an easily accessible way would be a massive project in it's own right.
Good luck and keep it up!
