I have a supervillain game where players earn points in various ways: some for being assigned tasks, some for volunteering for tasks, and many as fanmail.
There are two types of points: Story points and Fan points. If you get 4 FPs, you get a bonus scene for your villain. If you get 4 SPs, you get to direct a bonus scene for someone else's villain.
I have found that 3 bonus scenes is a good number per villain; 4 is okay too; 2 is okay, but not as good as 4; 5 is too many; 1 is too few. If the group wants a quicker game, then 4 is too many.
I have come up with various ways of putting points in circulation which I estimate at anywhere from 10 to 19 per player. However, when I look at those, I realize that I don't know how many bonus scenes to expect because of remainders.
Let's say the average player earns 14 total points. That's 3.5 scenes. But it isn't, right? We shouldn't actually expect that the most typical outcome (median or mode; I'm curious about both) for your villain is 2 bonus scenes you control and 1 or 2 bonus scenes someone else controls (or the reverse), right? Because with 14 points, you CAN'T get 4 scenes. In fact, if you have 11 SPs and 3 FPs (or the reverse), you could wind up with only 2!
Can anyone give me a formula that I can plug my expected points into that will turn out likely numbers of scenes?
Re: the tweaks I'm considering for what points to put into circulation, they include SPs, generic points that could become FPs or SPs at equal rates, and generic points that are likely to become FPs 2 to 3 times as often as SPs (just based on how people tend to award fanmail).