TL;DR: Try rerolling attributes for a character only if the geometric mean is too different from that of the standard array.

---

I gather that lots of people like to randomly generate their player character's attributes ("roll for stats"). As most players/DMs have probably realized, this can cause problems:

• One or more players might roll lower than the rest. Either they're stuck with an underpowered character or they'll want to reroll until they like the results. The latter kind of defeats the purpose of rolling for stats.
• One or more players might roll higher than the rest. The resulting characters can outshine the rest.
• The average randomly generated array makes for more competent characters than the standard array. Players who prefer the standard array might not like this.

Folks on r/onednd have described a number of solutions, including rolling one array of attributes for the whole table and rolling a whole bunch of arrays and letting players pick from those.

I suggest an approach that's a bit mathier, for those who like that kind of thing. If you take the geometric mean of an array of numbers, you'll get an average that isn't sensitive to outliers. For six attributes, you multiply them all together and raise the product to the power of ⅙. The standard array's geometric mean is this:

(15×14×13×12×10×8)^(1÷6) = 11.74

When randomly generating a character's attributes, try taking the geometric mean of the result. If it's too high or too low (say, greater or less than 11.74±0.5), reroll. This should keep arrays pretty similar on average while allowing for some decent variety. It also lets people use the standard array or point cost methods without being left behind.

Here's an example of some randomly generated attributes for a party of four:

Character 1: 16 14 13 12 10  9
Character 2: 14 13 12 11 10  9
Character 3: 15 13 13 12 11  8
Character 4: 16 16 14 13  9  5

You can do this with some six-sided dice and a calculator, but I also slapped together an R script that does this and put it on Codeberg if you're interested. I can write instructions on how to use it if anyone asks for it, but right now it's just a bit of code and a free software license.