Statistics (not the mathematic kind)

Nearly every video game has statistical models determining the outcome of any random event.  Did your attack hit?  How much damage did you do?  Did they save against that spell?  Games that display these statistical models to their players are typically what people mean when they label a game an RPG.  Your character has this many health points, this much energy/mana/magic points, does this much damage, has this percent chance to hit, etc.  These type of games are ideal for the min/maxers out there (like myself) because they know exactly how and what to put their emphasis in to maximize their effectiveness in their play style.  This has gotten to the point for me where being able to put an extra point in one my stats is infinitely more rewarding than getting a new weapon that does extra damage or hits more frequently.

Many RPGs that let you create your character from scratch let you determine the starting stats of your character to help define how you are going to play from the beginning.  They can determine these values in a few ways.  Some games work like D&D where a number of dice are rolled to determine your starting stats, you may then swap those numbers around or take points from one stat to put into another, but you will never have more points than what you rolled.  Another method is where you are given a set number of points and must distribute them all yourself.  Some games will mix these two styles and make sure that (unlike the D&D method) you always have the same total number of points distributed, but the computer can randomly distribute them for you.  I don't remember if I've played a game that does this, but another method I've thought of is having the player start as a blank slate and based on how they deal with the first few opening situations in the game, that determines their stats.

Each method has its pros and cons: the D&D method feels a lot like gambling, so when the player gets a bunch of high numbers, they feel like they win already.  However, since the total number of points is determined by the numbers rolled, not every one of their characters will be as good as the others (which is more realistic).  The point distribution system has a psychological con (at least for me) where I feel like I'm failing at something already since you can't make all your stats as good as possible (although I did learn years ago that making every stat slightly above average is no good either), but it gives you the most control over your stats letting you really maximize your play style.  The game determined method completely takes away any control over your stats, but it means the game designers, who know what all those stats mean better than you do, can allocate the right amount of points so you will be as good as you can be at your play style as possible.