Just sharing a houserule I have for increasing ability scores as a character gains levels. Note I use 3d6 in order, (roll 5 sets, choose your preferred set) and a fixed 15, 14, 12, 11, 10, 9 array (assign as you like), the latter method is for those players of mine who don’t like “chance” in character creation. I also let players raise any score (not just the character’s requisite) by one at the cost of lowering another score by two, but no score can be lowered below 9.
Each time you gain a new level, you receive 1 ability point. This point is used to increase your ability scores. Ability points cannot be saved. Raising a score to the next higher score costs as follows:
4-12 = 1 point
13-15 = 2 points
16-17 = 3 points
18 = 4 points
I’m not a friend of increasing attributes simply by leveling up. It is too powergamey for my taste. Anyway, if you would do it i would not allow raising attributes to above 18 if you are still a mortal (only magic may do so - permanently or temporarily depending on type). Instead of giving an attribute increase which affects ALL actions related to that attribute (to much for my taste) i would allow an additional proficiency or something along those line.
[blockquote]If ability points can’t be saved, how do you spend two at once?[/blockquote]
I simply ask players to record points spent next to the ability of their choice (most players just make a small mark next to the ability score on their character sheet). Once they’ve spent enough points, that score increases by 1.
[blockquote]The fixed one gives +1,+1,0,0,0,0 or better if you allow redistribution. Are you sure anybody would take 3D6 in order given that choice?
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As Thomas Weigel said, the random method has a fairly high probability of getting overall higher scores… you just can’t put them where you want to. I have a couple players who do not like randomly rolling for ability scores, or randomly rolling for hit points, so I just give them numbers I’m comfortable with.
[blockquote]I’m not a friend of increasing attributes simply by leveling up. It is too powergamey for my taste. Anyway, if you would do it i would not allow raising attributes to above 18 if you are still a mortal (only magic may do so - permanently or temporarily depending on type). Instead of giving an attribute increase which affects ALL actions related to that attribute (to much for my taste) i would allow an additional proficiency or something along those line.[/blockquote]
I know this idea is not for everyone, but this is the only practical way to increase ability scores in my campaign, in a permanent form. And 18 is the cap.
Substantially?
From playing in two games and GMing a large group myself thats not my experience. I didnt run the numbers though and my sample might still be too small so who knows.
Remember the effects of multiple passes:
Though the average won’t change, the chance of not having a pass with +1 (+2,etc) decreases with every extra roll. Thus the chances of having a decent character to pick increases.