I am about to start running a new game in 5e and I hate all of the ways of determining ability scores.
I have always felt that we play RPGs at least in part for the opportunity to pretend to be more than we are in real life and no one wants to play a character who's just average. So I feel like characters should have the ability to become world-class in some area.
Using either standard array or point buy, you cannot start at level 1 with greater than a 15 in any ability. This means that you can't have above a 17 with racial mods and that, in order, to achieve the highest possible level of 20, you must plan to use at least two feat opportunities to improve to 20, and you have essentially no chance of improving a secondary ability to anything significant if you want to take any non-ability feats at all.
And with rolling dice, you may have some chance of starting in a better position, but you have a significant chance of starting in a much worse position. If the consequences of such a catastrophe were a few sessions of difficulty, that would be one thing, but leaving to chance the possibility of playing, for months or a year, a character whose negative modifiers outweigh their positive ones seems unacceptable to me.
For this reason, I think, some DMs (including Matt Mercer from Critical Role) put lower caps on rolls, saying, for example, that if your total rolls for all six stats are below 70, you can roll again.
I like this idea, but I'm not sure it's sufficient for what I want (giving my players a chance to be exceptional).
I know that there are 1296 possible results for rolling 4D6, and I know that the average result of rolling 4D6 and dropping the lowest number is 12.2446, which means (I think) that the average score for doing that six times is 73.46759.
I'm thinking about making 73 the "floor" for my players (so that they are at least hero-average so to speak) but I'm not sure I have a good enough grasp of the math to know that that is the right decision.
What I'd like to know is "what is the probability of getting a total of under 70 on these rolls?" So, if you roll 4D6 and drop the lowest one six times and total the six results, what is the probability that it is below 70?
I'd also like to know that for 71, 72, etc... up to 78. And I'd like to know what the probability of getting above about 80 is, and 81, 82, etc.. up to about 90.
I'm not a mathematician and I don't know how to figure this out. I don't even really know how to phrase the question. I hope this was clear enough to get an answer.
Wow! This is my first time asking a question here and I had no idea to expect such amazing responses so fast. I really appreciate your efforts in educating me on this issue. Thank you very much.