Okay so I've looking over the great responses so far, and I thank you all for commenting. It looks like this could actually happen.

From here it gets a bit technical. Most of the flaws pointed out with the method deal with how large the dataset needs to be. And it needs to be pretty damn big. I did some simple calculations which I think are accurate, stating that with 84 different champs, there are as many as 3.7 billion or so different possible team comps in LoL. Most of these will of course be bad, about a quarter should be all AD champs, so there goes a billion, another quarter all AP champs so theres another billion etc. I'm unsure about the exact numbers there but whatever, the point is this: Even if you only look at the most "viable" picks for each of the roles in the standard meta, I still calculated there to be over 22000 different team comps.

What this means is that it's impossible to make a statistical model which compares entire teamcomps. There simply isn't enough data, at least if you factor in patches and how the game changes every three weeks, plus the fact that me and my possible collaborators probably aren't gonna get much help from Riot (but I haven't asked, man who knows).

What should be doable however is a very simple system which only factors in what champions are on the two teams, and which team won. What you then do is you have a long line in something like an excel document for each champion, and you log data points in four categories: Win against champion X, Win with champion X, Loss against champion X, loss with champion X. For each champ, you log one of these four options for every other champion in the given game.

With 84 champs, meaning 83 champs OTHER than the one you are currently coding results for, and four options for each of those champs, that excel line should come to something like totalling something like 332 different boxes. And for every game that gets logged, 9 out of those 332 boxes are checked for every champ. I know this is probably hard to follow, sorry about that, but there is a point to this so bear with me. Every game that gets logged into the spreadsheet should then total 90 separate data entries, 9 for each participating champion. What is really required is some way of automating the procedure; if a database of games is amassed, can someone on these boards write an algorithm that translates that data into points in this hypothetical excel document? Also, is there a better way to do this?

The end result would of course be, that from this spreadsheet you would (automatically or manually) be able to infer win percentages for any champ vs any other champ, or with any other champ. And with a sufficient number of games added to the database, there should be statistically significant patterns popping out of this eventually. I am no statistician, or at least I have very little formal training, so I wouldn't exactly know how to know when a pattern becomes statistically significant. But maybe someone on these boards do, and thats the entire point of this. It would be a community effort, and it might produce very interesting results. What if it as an example turns out Udyr wins a whopping 60% of games when he has a Veigar on his team? That's when the theorycrafting comes in, and people can try and explain the statistics.

Now, the question of how to aquire a database. RiotStats looks really promising, they have a large number of games logged. What I worry about there is whether there is someway of making sure that A: the games we log are only high lvl games. and B: they are never the same game twice, because that could mess with the numbers. I will try and contact them, and possibly Riot as well. The third option as I see it would require a lot of manual coding and collecting by a lot of community members before the dataset grows large enough.