Statistically, what you're describing is actually the probability that at least one partner does something batshit. This can't be done by simply multiplying by the number of partners you have; if the probability is 10%, and you have 11 gfs, you'd get 110%, which doesn't make sense. What you need to do is use a cumulative binomial probability.
These are kind of annoying to calculate, so to avoid it, I'll use binomial manipulation wizardry to convert it to its equivalent: calculate the probability that all partners don't do something batshit, and take the complement
where p is the probability of a single partner doing something batshit and N is the number of partners. Graphing different values for N and p (valid only for x≥2)
However, this assumes that the drama is generated independently from a single person alone. If the drama is interpersonal, then it is dependent on the number of interactions, which increases as the square of the number of partners.
For simplicity, let's assume all interactions have the same probability of causing drama. The probability of at least one interaction causing drama is equivalent to the complement of no interactions causing drama.
At a 10% chance of conflict arising between any two people, with five partners, the probability of drama increases eightfold to 80%
To account for both single person and interpersonal drama, you can combine the two, with different values for p1 and p2, but the change as a result of p1 is small compared to p2, especially for p1<10%
1 - (1-p1)^N · (1-p2)^(N(N-1)/2)
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