"Levels" Game Design Pattern

Summary

If you've heard of a term "Level Design", this is much simpler than what they say.
Level essentially is an act of converting a Variable into higher dimention equation.
Let's say there's a variable called "game experience points", which you earn every time you beat enemies.
If that's the only points you can collect during the game, what it produces is a really "severe" competition.
When you align all the players by how much they've earned game experience points, you soon realize that there are people who's earned too high for you to beat, since they devote so much time into game playing.
That limits the motivation of competition, or motivation to grow as a player.

Here comes in a level system, which will "convert" the points into fewer goals a player can pursue: levels.
Level sets this rule where the higher level a player reaches, the more points you need to level up 1 more step.
This will essentialy soften the competition, with less steep curve.
Implication is that this will make the game live longer, as players are evaluated less harsh each other.

Think about a Dragon Warrior or a Final Fantasy which only gives you experience points, not converting to levels.
First of all, it would be really hard to see how strong you become when game progress.
And since character's strength directly relates to the experience points, when you play longer, you character becomes too powerful to design game balance(e.g. enemies parameter).
Because there's a level which gives you clear view how strong you character becomes, you can be aware/pround of your progress in the game. If often results more word-of-mouth spread among their friends.

In recent games(especially online), it's common that you can "buy" levels under the name of "items".
Reason why I consider those items as "levels" is that any conversion that will end up with less variables are influenced by the logic above.
And lastly, advice from me: Always set the converting ratio higher than previous level. That's the golden rule of level up system.