Let’s talk about methods of generating RPG characters, both stochastic and deterministic.
When creating character attributes, there are two broad approaches to generating them: stochastic and deterministic. The stochastic method involves chance, while the deterministic method does not. Most any other method is going to be one of the other, whatever the details. The pros of one method tend to be the cons of the other.
Stochastic
The classic method is rolling dice, usually D6, sometimes an alternative like percentage dice. There are various ways do this. For example, some of the old methods were to sum the roll of 3d6 six times in a specific order of six character abilities. A variation was 3d6 and change the order as desired, another was roll 4d6, don’t count the lowest die, and then you might be able to change order or not; and so forth.
What are the pros of rolling the dice? First of all and primarily, variety (barring cheating). You get a big range of dice rolls. Dice rolling promotes realism, you get a big variation in numbers so you get some 3s, in fact you get as many 3s as 18s, and with some methods you have the opportunity to play characters with “cripplingly bad" ability numbers. Further, it's always exciting to roll dice, whether you like it or not. (Keep in mind, when I first saw D&D I said “I hate dice games.”)
One of the cons of rolling dice is that it's unfair in the long run, a player can get big advantages lasting for years of real-time throughout the campaign just by getting lucky in the first dice rolls. This can be frustrating to those who didn't get lucky. Perhaps even more, rolling dice encourages cheating. I've seen people roll one character after another until they get one they like - meaning lots of high numbers - and then they take that to a game to use. That’s not possible with point buy. Another con is that you may want to play a particular character class yet the dice just won’t cooperate (when you’re rolling in specific order).
Deterministic
The other method which I believe has been devised independently by several people including myself (I had an article for my system published a long time ago) is the one used in fifth edition D&D. A player is given a number of generic points to buy ability numbers. The lowest numbers can be very cheap, for example, if you are using a 3 to 18 scale, when you buy a 3 it may cost you one point, while an 18 may cost 20-some points. You decide what you want, for which ability, and allocate until you run out of points.
Point buy is very fair (FRP is a game, for some people). No one need be envious of someone who either 1) rolled high or 2) rolled many characters and picked the best one. It prevents the typical new character with sky-high abilities, it prevents cheating, so the player has to supply the skill, not rely on bonuses from big ability numbers. Of course, the GM can choose the number of points available to the players so he/she can give generally higher or lower numbers on average as they choose.
But point buy lacks variety for a particular class. The numbers tend to be the same. It's not exciting, it’s cerebral, and as such it takes a little longer than rolling dice. That's all the cons I can think of. Keep in mind I'm biased in favor of point buy. It's clean, fair and simple.
I haven’t spent much time trying to figure out yet another method of generating a character. The only other method I can think of that isn’t one or the other is to have some kind of skilled contest determine the numbers, such as pitching pennies or bowling. Then the question becomes why use one kind of skill over another?
Do you favor one method over the other? And has anyone devised a method that is not stochastic or deterministic?
When creating character attributes, there are two broad approaches to generating them: stochastic and deterministic. The stochastic method involves chance, while the deterministic method does not. Most any other method is going to be one of the other, whatever the details. The pros of one method tend to be the cons of the other.
Stochastic
The classic method is rolling dice, usually D6, sometimes an alternative like percentage dice. There are various ways do this. For example, some of the old methods were to sum the roll of 3d6 six times in a specific order of six character abilities. A variation was 3d6 and change the order as desired, another was roll 4d6, don’t count the lowest die, and then you might be able to change order or not; and so forth.
What are the pros of rolling the dice? First of all and primarily, variety (barring cheating). You get a big range of dice rolls. Dice rolling promotes realism, you get a big variation in numbers so you get some 3s, in fact you get as many 3s as 18s, and with some methods you have the opportunity to play characters with “cripplingly bad" ability numbers. Further, it's always exciting to roll dice, whether you like it or not. (Keep in mind, when I first saw D&D I said “I hate dice games.”)
One of the cons of rolling dice is that it's unfair in the long run, a player can get big advantages lasting for years of real-time throughout the campaign just by getting lucky in the first dice rolls. This can be frustrating to those who didn't get lucky. Perhaps even more, rolling dice encourages cheating. I've seen people roll one character after another until they get one they like - meaning lots of high numbers - and then they take that to a game to use. That’s not possible with point buy. Another con is that you may want to play a particular character class yet the dice just won’t cooperate (when you’re rolling in specific order).
Deterministic
The other method which I believe has been devised independently by several people including myself (I had an article for my system published a long time ago) is the one used in fifth edition D&D. A player is given a number of generic points to buy ability numbers. The lowest numbers can be very cheap, for example, if you are using a 3 to 18 scale, when you buy a 3 it may cost you one point, while an 18 may cost 20-some points. You decide what you want, for which ability, and allocate until you run out of points.
Point buy is very fair (FRP is a game, for some people). No one need be envious of someone who either 1) rolled high or 2) rolled many characters and picked the best one. It prevents the typical new character with sky-high abilities, it prevents cheating, so the player has to supply the skill, not rely on bonuses from big ability numbers. Of course, the GM can choose the number of points available to the players so he/she can give generally higher or lower numbers on average as they choose.
But point buy lacks variety for a particular class. The numbers tend to be the same. It's not exciting, it’s cerebral, and as such it takes a little longer than rolling dice. That's all the cons I can think of. Keep in mind I'm biased in favor of point buy. It's clean, fair and simple.
I haven’t spent much time trying to figure out yet another method of generating a character. The only other method I can think of that isn’t one or the other is to have some kind of skilled contest determine the numbers, such as pitching pennies or bowling. Then the question becomes why use one kind of skill over another?
Do you favor one method over the other? And has anyone devised a method that is not stochastic or deterministic?
It's a world. It's big. It has tremendous variation. The world has changed overtime (and I've advanced it's history with new editions). With complex social systems, cultures, a well developed history, and interesting NPCs I don't see how someone couldn't find more to explore in it. I've plowed in detail and my players seem to enjoy that about it. The fun is in exploring a world and "living" in it. 
