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For types my battle system does this. Each type has a reference number 1-17 I think they are. I noted down on pieces of paper what number each type is and then each pokemon has 2 variables assigned to it. One for type one and one for type two. If type 2 is 0 then it's no type. Then in the damage formulae I have the usual conditional branch checking what the variables are and stuff.
OMG I only use 7 per party pokemon (6*7=42) and 3 per box pokemon and 2 extra((3*6)+2*3=60, 6 pokemon per box, 3 boxes) so that is 102 variable for me almost 11 times less then you :\ .
oh well hope you can pull it off, you got a lot of varibale to use :P