Ok I like the idea of the long form data with a match ID effect. My goal is to capture the correlation between players in the same match. Ideally the sum of the individual player kills in a sample would match the total team kills. I dont think that’s guaranteed in this approach but you could always normalize back to the total team kills.
The part I’m struggling with now, in this framework, is how to make predictions for future matches. In that case you’ll have a brand new match ID. You could sample the match effect from the prior but that assumes you know nothing about the collection of 5 players, which I dont think is true. Maybe instead of doing a match ID effect you assign a unique identifier to any match that has the same collection of 5 players. I think that probably catches some of the correlation between players in a given match, but less so than the strictly match ID. But it becomes more obvious how to do future predictions given your new collection of 5 players. You’ll either have an ID that matches that collection, or you could do a similarity analysis and assign the ID associated with the closest collection.