The trouble I've had with ability scores in the past:
- Too much variety between characters: one character will have really high stats and another will have very low stats...one character didn't have a single stat lower than 15, and another didn't have a single stat higher than 13. This happened when we were using the 4d6 method.
- Not enough variety between characters: every character at the table will have the same numbers, often in the same abilities: everyone had a 14 Constitution and a 13 Wisdom regardless of class, and half the group had the same numbers in all six ability scores. This happens every time we use the Point Buy method.
You're probably reading this and thinking to yourself, "Ah yes, I can see how
one of those is a problem, but the other one is perfectly fine." And you're right! Unless you're me.
We tried a number of methods to fix it. First, we got rid of any "choose your numbers" rules like Elite Array or Point Buy, because we learned rather quickly that "everyone can choose your stats" will always mean "everyone will choose the same six numbers and put them in the same order." I suspect this is why the authors of the 5E rules made them an optional rule: their playtesters must be very similar to my gaming group. And the players who prefer rolling at random were really happy with the change...they loved the thrill of rolling a high stat and the anguish of rolling low, and how each new set of stats became a puzzle to solve.
But there is a certain brand of player who really enjoys the character creation mini-game. And fair enough, creating a character for an hour is a great way to pass the time and 'play D&D' by yourself (it's more fun than Solitaire, anyway.) These players need to be able to generate stats without the DM witnessing their rolls. And they need a level of predictability, too, so that they can tinker with different builds from a level starting point. So there was a lot of pushback from these players.
Eventually, we settled on rolling at random but with a few adjustments (I mentioned them
upthread). In a nutshell, we use magic items and bonus feats to balance out really high and really low stats. The added layers of customization you can get from a starting magic item or a feat really help soothe the burn of rolling poorly...and having to decide whether to start with a nice stack of ability scores or a nice magic item can be very compelling.
It absolutely will not work for every group, but it works for mine.
Unfortunately, we haven't found a way make it work for the "character creation mini-game" players. Until we think of something better, we have a standing rule that in the absence of a DM to witness your rolls, you must use your previous character's stats. It gets the job done.