Well spoken. You (OP) could also try this:
Roll one save for your defenders. Compare it to the spell DC. For every point of save success, 5% more (than 50%) of your defenders succeed (assuming a fairly homogenous group of defenders). For every point of failure, 5% less than 50 fail.
Joe PC casts Turn Green on 3 goblins (the black kind, not the green kind). His spell DC is 13. The goblins get +1 to their saves. The GM rolls 15, total 16. Since 16 is 3 points over 13, the GM adds 5% for each point (or 15%) to 50%. That's 65%, or fudgingly, 66.66%. Two of the goblins (66% of 3) succeed on their saves.
Mathematically flawless? No.
Time-saving? Hopefully.
True to the 5e rules? Beats me, the rules aren't out yet.