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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.

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  • $\begingroup$ Just trying to understand the data, is "Hero combinations" (column A) the name of Hero 1? $\endgroup$
    – Peter Ellis
    Commented Feb 12, 2013 at 10:27
  • $\begingroup$ @PeterEllis I actually just made a new spreadsheet with the same data; the original was poorly defined and had some unnecessary information. Updated the link. $\endgroup$
    – Decency
    Commented Feb 12, 2013 at 15:13

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I think you need some kind of weighted average - eg $w_1 p_1 + w_2 p_2 + w_3 p_+ w_3 p_3+ w_4 p_4+ w_4 p_4+ w_5 p_5$ where the sum of the $w$s is 1; in fact, all the $w_i = \frac{1}{5}$ as a starting point.

This basically ignores the interaction of "Player X is particularly good with Player Y" but I think will give you a very good start.

If you don't know $p_3$, $p_4$, $p_5$, etc just increase the $w_1$ and $w_2$ accordingly (so they add to 1).

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  • $\begingroup$ There's not really a "player" in this scenario. The data set is pulled from 1000's of matches where each match and all players are assumed to be independent (not true, but definitely true enough). Hopefully my edits have made this more clear. $\endgroup$
    – Decency
    Commented Feb 12, 2013 at 16:26
  • $\begingroup$ ok, I think my answer is still ok, albeit too general. I would start with looking at actual win percentage of the pair minus the average individual win percentage of the two of them. $\endgroup$
    – Peter Ellis
    Commented Feb 12, 2013 at 17:40
  • $\begingroup$ That's what the original spreadsheet did, but it unfortunately doesn't come anywhere close to expected results. $\endgroup$
    – Decency
    Commented Feb 12, 2013 at 18:00

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