Determining D20 Attribute Scores

Nobody ever seems to be happy with how a given group likes to generate their D&D/Pathfinder ability scores.

Three 18's‽ BULLSHIT!

Rolling for stats can generate unplayable or overpowered characters and, in some cases, opens the door to cheating on the players' part. The classic choice is 3d6 per score, but more kind alternatives such as 4d6 drop low are also popular. The latter could still result in a character with 4 in all ability scores. A system that generates characters that are patently invalid seems poorly designed. (I know, I know, Traveller - but that character generation system is basically it's own mini-game.)

I get that D&D is built around random mechanics, but attacks, saves, skill checks, etc. are moment to moment concerns. Often fun and drama result from unexpected failures. The same can not really be said for a bad roll that sticks with you for 20 character levels, or requires a character to self-abort.

Point Buy systems are popular because they, theoretically, eliminate and possibility of cheating and generate equally balanced characters. The latter is, however, bullshit, as min/maxing ability scores goes hand-in-hand with point buy. The vast majority of point-built characters I've seen have a +4 ability score in one stat and a -2 in another. The traditional point buy system doesn't really promote well-rounded characters, due to no real fault in the math but simply because the classes don't support this.

Had no "dump stat."

So, allow me to propose an alternative method which I've not seen proposed:

- The DM consults [Table 1], determining the initial values of the ability scores (X) and the number of times each player will roll on [Table 2] (Y). (I'd go with ability scores starting at 8 or 9 myself, if only because that generates valid characters, with strengths and weaknesses, but not too much rolling.)
- Players roll on [Table 2] Y (See: [Table 1]) times, adding 1 to the designated ability score each time. If the score would go above 18, they re-roll that die.

Table-1 (Assumes power equal to 3d6/Score)
X = Initial scores, Y = Rolls on Table 2
X Y
10 3
9 9
8 15
7 21
6 27
5 33
4 39
3 45
2 51
1 57
0 63

Table-2
1-STR
2-DEX
3-CON
4-INT
5-WIS
6-CHA

-----Benefits over 3d6 & Point Buy
Always generates a completely random scores (especially with lower initial scores), eliminating min/maxing
Always generates a valid character (especially with higher initial scores)
Always generates characters balanced with one another (within the limits of the class design)
Tends to create well rounded characters, while leaving the possibility of extreme examples
Easily scaled to DM's tastes (min ability scores, can modify # of rolls for games of different power levels)
Doesn't require the complex tables of point buy, can easily be done from memory

-----Weaknesses
Can require lots of rolling
Requires a "Max 18" meta-rule if rolling more than 9 times
Allows sneaky players to fudge rolls

Thoughts?