This post is a follow-up to Leveling and skillpoints & statpoints.
As i wrote in the earlier post points are used to simulate the abilities of the character.
This is needed for two reasons.
One is that the player can't perform the actions to determine whether the character suceeded because the abilities are to a great degree physical and/or impossible in our universe.
This type includes everything from swordfighting and damage to lock-picking and spell-casting.
Damage and lock-picking is extra noteworthy. Damage since there is multiple stats involved, not only is there usually one or more stats involved determining whether damage was done at all, but there is also hit-points that ensure that what would kill in real life does not in the game. But it works for both the opponent and the player so it is acceptable mostly.
Lockpicking is noteworthy because computer-games have started including a challenge that the player can do to determine whether the lock-picking succeeded (even tho it is easier then real lock-picking and may still include some stats to determine how difficult the challenge is).
The other reason is to automate parts of the game instead of letting the DM/GM determine everything as he wills. That may make it easier to control and guide the story and thus making that better but it also makes it less of a game and more an interactive story.
Pure statistical gameplay can however remove some of the fun and for some types of games it is not fitting (such as superhero games where it might be better that the hero can beat the odds). Therefore some games include mechanics to go around the stats but these are in the hands of the players, not in the hands of the DM/GM.
