Rethinking this, stacking won’t work as you need to preserve the marginal counts vs total counts for each match.
There is a kind of similarity to the baseball batting abilities example in Kruschke’s book: Doing Bayesian Data Analysis see p253 (I hope this is a kosher link, I have a hardcopy at home). Suggest you get your head around that, in case useful?
I’m not at all familiar with League of Legends, but is it a reasonable modelling assumption to assume that proportions of kills in each match relate to a players abilities (expressed via “effect” from baseline)? Does the composition of the group matter, i.e. if you have 5 average players in a match together, how would the data differ from if you had one superstar and 4 average joes? I think the upper bits of your hierarchical model may need thinking through in this respect, and could then inform what the lower bits (seen here) look like.
Interesting problem though!