Consider doing things with Dire Lions, (depending on party level). They've been blamed fro many a TPK in Pathfinder.We would just agree on percentage rolls to arbitrate everything, based on what was thought reasonable and likely. One of us might bring a TI-84 and use some homebrew calcs for some things. One example was using a compound interest formula to calculate hit probabilities based on distance and skill.

This is the nerdiest thing I have ever heard of. I don't suppose you remember the formula?

I just called him and asked.

He said that he doesn't recall the exact digits he used, but his method was that you take the general compound interest formula, and set the current principal to a skill level up to 100 (for perfect skill. 80 would be something like mediocre to intermediate skill), and set the annual addition to zero and the interest rate to a negative number slightly less than or equal to -1%, such as -1.15%, to account for difficult conditions of the shot (such as fog, camouflage, movement, a bad gun, et cetera. Again, sort out your own data for this since neither he nor I ever bothered doing the research to make a truly representative formula). The years to grow is the distance from target variable, but you'd have to work out what units you wanted to use for yourself, since a shooter with perfect skill and perfect firing conditions only has a 66.9% chance to hit at 40 distance units, so make some kind of conversion formula to convert that to hexes or feet or metres or what have you.

ETA: The formula spits out a hit probability.