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I'm trying to analyze some factors contributing to win rates of a game, there are several hundred factors but each game will only have a small subset of them (10-20).

Some of the factors may be correlated (picking one ability will tend to blend well with other abilities, and some may be antagonistic and so will not often be picked together). Ultimately I want to know the correlation these factors have on winning, which is obviously a binary value.

I have a database of several hundred thousand games so scale is not an issue, but I'm stuck at what sort of test to use. I've used ANOVA tests in university for data before so my thinking is maybe that would work, but I've never had so many variables to fit, and I'm not sure my data is normally distributed, I just wanted to check to make sure that a one-way ANOVA would make sense in this situation, or if I should be looking for another way to figure out the correlation on factors and winning.

Thanks!

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  • $\begingroup$ What are your independend replications? Player's results? Then how many players do you have? $\endgroup$
    – Horst Grünbusch
    Commented May 23, 2014 at 15:46
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    $\begingroup$ Given you want to look at the relationship between your factors and win/loss I think you should use logistic regression. This will tell you which factors are more likely to result in a win/loss. $\endgroup$
    – ThatGuy
    Commented May 23, 2014 at 20:12

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That's an interesting question, I presume you are using the data from all the recorded online Dominion games. If so, you have enough data to do some very complex modeling.

Here's something to think about: You probably can't identify a single card that's better in isolation from the rest of the 9 cards in the current set. You could take the set of other cards into account by multilevel modeling, where each set of 10 cards nests the "card of interest" variable. One way to do this would be to do logistic linear mixed modeling.

If you only look at counts of wins for each 200 cards, you will ignore how the cards influence each other within the currently playable set of 10 cards. The very least you should do, as suggested by others, is a logistic regression.

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  • $\begingroup$ yeah this is the problem I'm trying to deal with. Previous statistics looked at winningness ignoring the potential effects of the other 9 cards. I'd like to correct that but have been unsure how to go about it. $\endgroup$
    – serakfalcon
    Commented May 28, 2014 at 16:07
  • $\begingroup$ To do this analysis properly, I suggest taking a look at Andrew Gelman & Hill's "Data Analysis using Multilevel/Hierarchical Models." However, it seems that the number of different 10 card sets is too big to take into account individually. $\endgroup$
    – Lost in transcription
    Commented May 28, 2014 at 19:54
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You seem to have many types of games, each with its own set of "factors". Based on the little you wrote, I doubt there can be one solution for all games, since the factors you think are relevant are so different for the various games. That argues against using one omnibus analysis and in favor of doing an analysis for each type of game. If your data is in terms of win rates for individuals (i.e., multiple game plays by each individual resulting in a win rate for each individual) then an ANOVA might be reasonable. If your data is in terms of win-lose, then a logistic regression approach might be in order.

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  • $\begingroup$ OK logistic regression looks like what I'll go with then. The issue with the factors is this: a limited set of them is picked randomly before the start of the game, so ideally each factor will show up more or less equally over a large enough number of games. There are about 200 factors, so with 200C10 being rather large, it makes analysis by type impractical. $\endgroup$
    – serakfalcon
    Commented May 27, 2014 at 17:53
  • $\begingroup$ I do not understand what you mean by "factor" and "game" so it is hard for me to comment further. Can you give some examples of factors and games? (Perhaps use hypothetical examples if you consider the information to be confidential.) $\endgroup$
    – Joel W.
    Commented May 27, 2014 at 20:03
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    $\begingroup$ It's a card game, Dominion. Players start with a generic deck, and have the choice to purchase cards to make their deck more powerful, and eventually buy cards that give points. There are over 200 cards with different abilities/synergies/antisynergies, however in any one game 10 cards are chosen at random to be available for purchase. Obviously, some cards are better than others and contribute more to winning, but I'd like to have an objective, statistical way of knowing which ones are better. $\endgroup$
    – serakfalcon
    Commented May 28, 2014 at 3:32

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