A comment from Restless resurrected an old post on improving abilities, proposing a change to a Runequest-like system of improvement: train, with or without a teacher, and roll 3d6 over your current ability score to get a 1-point increase in that score. The reasoning: the method I proposed of rolling 3d6 and taking the result as your new score if it's higher than your old score would allow the possibility of an enormous jump -- Dultar the Dullard, with Int 6, could get lucky and roll a 16, becoming a genius.
I like the enormous jump.
The problem with the Runequest-y style of improvement is: a mere 1-point increase in an ability suggests more of a slow-and-steady advancement, assuming you can train multiple times and improve 1 point at a time forever (if it's a one-time improvement, it hardly seems worth it...) It becomes merely a matter of time and money, so everyone would train whenever possible, moving all scores inexorably towards the high end. It becomes a mere grind, something you do to optimize your character.
Whereas what I was thinking about was something that only works once, and is unpredictable, because that's more fun. Think how fun it would be if Dultar the Dullard does, in fact, become a genius after a month of intense study. That's something every character in the game world would notice. Dultar would become the talk of the town! Rivals who didn't hear the news could be in for a humorous surprise! And if Wizzbang the Wise tries to improve an Int 13 and only rolls a 14, there would be loads of potential envy in the game world, not to mention lots of laughter around the game table.
And getting a teacher would make a high score more likely... but I envision the process of locating a teacher as an actual adventure itself, not just a routine downtime action. With or without a teacher, the score will only increase once... so if Wizzbang really needed a 16 or higher and only rolled that 14, the next step is to find magical assistance or a wish, which means yet another adventure.
Always think about the adventures! Rules that generate new amusing or exciting things in the game world are good; rules that set up some kind of grind are boring and best eliminated.
(This is one reason why I like to give players the option to reroll their hit dice between adventures and erase all damage. It's not just a way to boost hit point recovery, because the player might be unlucky and roll low. The unpredictable results means that sometimes the character will be brave, and sometimes extra cautious, which creates variety.)