See, I really don't get the point of die rolling the character stats.
As [MENTION=6801845]Oofta[/MENTION] pointed out, the difference between a low rolled character and a high one is significant. As in a level, possibly 2 levels worth of significant.
So, would die roll fans be okay with this - We all start with standard array, then everyone rolls a d20. The highest roll gets +2 levels. Next up gets +1. Next starts at baseline level (presuming 1st) and lowest gets -1 level (use the effects from Raise Dead until you gain "first" level, 150 xp later).
Would that be considered fair?
Probably not granting levels, since levels grant so much more, but bumping stats up and down, I don't really see why not. But it also might be missing the point, depending on the group.
For us, there are two aspects to rolling stats. And it's not about having a large difference between the "good" and "bad" characters.
First, we roll in order. That's the part that makes the character creation most interesting. Because you don't get to pick and choose the most optimal mix for a class. But we do want people to be able to play the class they want (if they have something in mind). So our general rule is roll at least 3 characters at a time, or roll 6 sets of stats and pick one. This is really the bigger of the two parts. It's very rare that we need to go beyond either of these limitations to get to a block of stats that's workable. Again, the goal is not optimal, if anything it's how to optimize something that might be less than optimal.
The second aspect is the power curve. While rolling does periodically result in very powerful or very weak characters, most of the time it trends toward average. If you roll 4d6 drop one it trends higher. If you roll 3d6 it trends lower. We decided that we wanted something between the two, and came up with re-roll 1's, but only once. This sets a baseline (average) for the campaign. Most characters (and NPCs) fall in the just above average category. That's part of what we're trying to accomplish. If we want to play a more (super) heroic campaign, we adjust the power curve. But we use the same approach for PCs and NPCs.
We have pretty severe level limits too, because it's part of the world-building aspect of the game. A 15 in your Prime Requisite allows you to get to 5th level, and up to 3rd level spells. Of course, you'll gain ASIs so you can grow beyond that. But we also make ASIs more interesting, with more options, and most of them time we're more focused on developing the personality side rather than the stats.
One of the reasons why the personality becomes more of the focus is because level advancement is very slow. It's not uncommon for a character (who survives) to be 4th or 5th level after 2 years of actual game time, or about 100 sessions. We spend a lot more time exploring the characters themselves, within their world, than the next ability and so on. This is similar to most TV and movie shows, where the characters tend not to gain lots of power over time, we just experience more stories. The power curve tends to rely on magic items more, in terms of special abilities, although these are also tied closely to the setting as well.
We admittedly aren't the power-gaming types. And it's very hard to develop an "average" or "flawed" character when you have absolute control over the entire creation process. Even if you don't get deep into the "character build" approach, it just feels weird to tweak the stats manually to say, "I'm a fighter, but I'm going to take a STR 13, CON 14, INT 15, DEX 12. But as a randomly rolled character, this is a very viable fighter. It's certainly doable, but it's much harder when everybody else is stacking the stats in their favor, and it also just feels different. When you roll randomly, and you know you're making a fighter, and this is the best mix you have, then it's trying to make something suboptimal better. But when you start with optimal, and deliberately make it suboptimal, the psychological feeling is different. As a result, with point buy, suboptimal characters are rare or non-existent in most campaigns.
There's nothing wrong with that. One of the "truisms" of D&D for many years is that the PCs are "different, a step above the norm, the stuff of heroes." But to me, the greatest heroes are not the ones that are born, but are made. The ones that overcome not only the challenges of the world, but the weaknesses and flaws within. Why do the PCs have to be above the norm? Maybe they're just average people that rise above the crowd by their actions, not their abilities.
If needed, though, we can easily adjust for personal preference. Swap any two scores. Rearrange as desired. Switch to the standard point buy, whatever. We'll do what we need to to accommodate a player. But since I'm pretty old school, most non-combat involves very little dice rolling. I know your skills, and use both your passive scores and your maximum (20 + modifiers) combined with modifiers based on what you tell me you're doing to adjudicate many situations. It doesn't mean I won't ask for a die roll, and your ability scores and skills matter a lot here. Not being proficient in many skills in my campaign means that you can't attempt anything with a (base) DC of 20 or higher. All DCs are typically 5 higher than 5e as written.
Combats generally fall in the difficult category when they happen, largely because of the rules, and because when a combat does break out, it's generally the last option chosen. Combat is unpredictable, and the risk of death (or even long-term injury) is relatively high in the campaign. So there has to be a really good reason, but it also means that it's probably a significant threat. Monsters in general are much more dangerous in the campaign, although armor works better, and you can actively parry as well. So they tend to be more strategic, looking for ways to set up advantage for the right people at the right time considering the terrain, the opponent, the current state of the party, and what is most advantageous for them. Our rules modifications are in part to encourage teamwork.
Which goes back to the idea of rolling as a group. Survival usually requires teamwork, and rolling and developing characters from the start encourage that sort of teamwork. It's not a question of whether Bob is a better fighter than me. It's a question of how the two of us fighting together might be better than either of us alone, because we may not survive otherwise.
Ironically, one thing we don't like, is the concept of "roles" or trying to fill a missing spot in the party. The random rolling makes us think outside the box about what would make a cool character. So instead of deciding to play a rogue because we don't have one, you might have an idea sparked by the results of the dice, and decide to be another wizard, even though we already have two. You might still make a rogue, since the campaign is designed as a home-base campaign where you can switch characters in and out at many points, and the others are busy doing downtime activities, or might be on a different adventure that happens every other week since the group of players is different on those weeks.
As I was making some modifications to the system, I made a couple of NPCs to see how certain things worked (and whether they were overly complicated). I have a table of traits, about 40 of them, that you roll randomly for. Everybody gets one, although humans get 1d3+1. Anyway, the very first character I rolled (a fighter) ended up with one of the traits that's a 1% chance - blind. We talked about what we'd do if a player rolled that, and decided we'd leave it up to them. In the case of the NPC it worked out great. It's a grizzled old veteran that trains many of the younger folks in town for the militia. He was blinded in battle many years ago, but overcame his disability and is still a tough warrior, and usually underestimated because of his blindness. He's an awesome ally to have sitting in the corner of the tavern when a fight might break out. And something I probably wouldn't have done otherwise.
All of these rules have been developed over decades of playing, and updated to work with whatever edition we're playing. Everybody has their favorite approaches, and that's perfectly fine. All I can say is I've gotten decades of enjoyment out of our playstyle, which we continue to tweak. And while I'm happy to play in other groups in the way they choose, my time is limited enough, and my expertise is built around a given style as DM, that we simply play to
our strengths. If it's not the right group for you, no hard feelings.
So rolling ability scores is more than just deciding it's "better" for us. It's kind of baked into our system as a whole.