For years now, I've been an advocate of point-buy (PB) instead of random-roll (RR) for generating attributes in RPGs, especially D&D. One of a number of things I loved about 3rd Edition (3e) when it launched was that it included a PB system (for the first time in D&D core rules) as an alternative, and I even liked the specifics of the stepped costs (so it costs more per point the higher the attribute is). I've even been known to comment that 4e, by making PD the standard method, is where D&D has “finally seen sense”.
And yet, for Labyrinth Lord (the Basic D&D retro-clone), I'm going to have attributes be created by RR instead of PB. Why the U-turn?
I'll explain first why I opposed RR for attributes in the first place. That came from AD&D, which had big stat modifiers squeezed in the top and bottom ends of the 3-18 scale. Back when I first began running AD&D 2e for my current group, I allowed the option of RR or PB. The results were uneven to say the least, and thanks to AD&D's eccentric attribute bonus charts (which, as an aside, I loathe to this very day) the effect allowed the players with better scores to dominate the game, completely overshadowing those who the dice had been less kind to.
Besides (I thought), surely it's just common sense – apart from keeping things balanced so that everyone is on level ground with each other, PB gives players (not pure chance) control over creating their own character. Case closed in favour of PB, surely? Not so fast – RR has merits of its own. Some of these come down to the specifics of the game it's used for.
One of the arguments that some use for RR is that it's one of D&D's traditions. “Rolling up a character” is an expression that's entrenched into all of RPGs; it's even part of the vocabulary of some MMO players who have never played any pen-and-paper RPG. However, I don't believe in following any tradition just because it's traditional.
Old-school D&D, unlike new-school games (including 3e and especially 4e D&D) doesn't assume that the character you create when you sit down to your first session will necessarily be the same character that you'll be still playing months or years later. This is very relevant to character creation issues: in new-school games, you might have a detailed bio prepared for your character, and maybe a character arc in mind. For something so specific, PB gives a control you might really want. Also, in new-school games, “building” a character to develop game-mechanically over time can be an end in itself (3e really pushed this to the forefront), and being able to put an attribute array together predictably is pretty important to this, which PB enables well.
With old-school, this is turned on its head. When death is a real possibility for characters (permanent death in the case of low-level characters), PB enables players to simply remake the same character again, just like an MMO avatar respawning after death. Needless to say, this can take away any tension and become very silly. With RR, the rules change. Did you roll up a great set of stats? Then your character can't simply be remade the same, so danger to his life takes on some importance. Or maybe you rolled badly in making up your character? In that case, you can get the chance to beat the odds with him by surviving and prospering... or secretly enjoy his violent death and the chance to roll up something better. Characters made by RR are unique, for good or ill.
RR also gives unpredictability, in a good way. Hands up anyone who ever invested a serious amount of points in Charisma for a plain Fighter in a PB system. ... Anyone? Not many, I bet. With RR, you can end up with a smooth-talking magic-user or a wise thief, or various other combinations that you wouldn't normally get, just because the dice fell that way. Obviously, numbers aren't the main ingredient of a memorable character, but this kind of thing can be grist for the roleplaying mill.
Unpredictability also helps RR to avoid one of PB's pitfalls. In PB, a system can either charge extra for top-end scores (like in 3e, where scores of 15-16 cost 2 each and 17-18 cost 3 each), or not (for example, “spread 80 points between 6 attributes any way you like”). The latter is open to major min-maxing, like Fighters with all physical attributes at the absolute maximum, using the mental attributes as “dump stats”. The former solves this problem to a point, but only at the cost of encouraging either a broad spread (like Paladins having lots of 13s and 14s in 3e's system) or heavy focus in a single attribute (like Wizards having maxed Intelligence in 3e); and either way, it still allows for “dump stats”. The problem is that there tends to be a best way to build a particular type of character in PB systems; optimisation works against originality. With RR, well... good luck optimising the dice roll.
The last point is that Classic D&D is much friendlier to RR because the attribute bonus charts are more evenly set up than AD&D's. Basically, an 18 gives a +3, 16-17 is +2, 13-15 is +1, 9-12 is no modifier, 6-8 is -1, 4-5 is -2, and 3 is -3. So unlike D&D, you only need a 13+ to get a bonus (not 15/16+), and that +1 isn't hopelessly behind even the best possible +3 from an 18 score. This bonus progression means that characters don't become either totally dominant or totally ineffective from a bit of randomness in creation, but it has enough of an effect to still matter. I wouldn't be in favour of RR character creation in all games, but for this one, I think it works.