The idea here is that you have a 5 vs. 5 game where each player is using a unique character (henceforth 'hero'), and thousands of matches of this game have been played. The goal of the analysis is to look for the best 2-hero combinations- those that perform better than their expected value.
Some heroes work better when combined with other specific heroes, and some get in each others' way and perform worse. Without normalization, the best two-hero combination is unsurprisingly simply the #1 and #2 heroes in terms of solo win percentages. This doesn't yield any meaningful result, so we need to normalize/standardize the data.
Here is the data set in question: Spreadsheet. It's 97 choose 2, but doubled due to duplicates. In short, my question's goal is to determine the correct formula to be used for Column E. Keep in mind that it's a 5 vs. 5 format, so the other 3 heroes that are teammates of the combination and the enemy 5 heroes are undetermined (but can probably be assumed at a value of 50% win).
So for example, what is the expected normalized win percentage for a team which contains heroes which when used alone have 61% and 59% win percentages (along with any other three unknown heroes)?
My initial thought was .59+(1-.59)*.61, but that gives an overly high expectation of 84% win, likely because it doesn't account for the other 3 team members bringing the expectation down. I'm unsure of how to proceed- I've tried a half dozen other methodologies but none come very near the actual figures.
Thanks.