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Level scaling is a gameplay conceit used in some RPGs to provide a continuous, consistent challenge to the player.  As the player's character rises in level, aspects of the world will change to accommodate that character's growth.  The most basic form of level scaling will increase the level of the enemies encountered, allowing their power to grow in step with the player.  However, level scaling may also influence other aspects, such as the type and quality of loot found or the availability of certain quests.
At its core as a design choice, level scaling is meant to keep the challenge of the game at roughly the same level from beginning to end.  In theory, as the player character grows in power, he or she should be able to tackle increasingly powerful enemies; the game will make adjustments based on the character's current level, thus maintaining an even playing field.
Though the idea of level scaling is fine in concept, its execution in some instances has left it open to criticism.  The primary and most pervasive being that when the enemies grow in step with the player, it prevents the player from feeling any true sense that the player character has grown in power.  Level scaling also negates the effectiveness of level grinding; a tactic by which players unable to surpass an obstacle may spend time in the game working purely to increase the character's level.  Such is done in order to become powerful enough to best the obstacle through brute force if nothing else, but in games with level scaling, this is no longer an option.
Another criticism of level scaling has to do with the effect that it has on the game world's verisimilitude.  For example, in The Elder Scrolls IV:  Oblivion, the player will at times encounter bandits on the country roads.  At low levels, this seems like a natural occurrence, as the bandits are typically armed with nothing more than simple swords, bows, clubs, and leather armor.  However, as the player's character level rises, the bandits become better equipped.  Eventually, the level scaling results in the absurdity of these simple bandits attacking the player while equipped with their own powerful magic weapons and armor.

Examples of Level Scaling

Final Fantasy VIII

Unlike previous games in the series, Final Fantasy VIII introduced a form level scaling that tied the enemy's own level to that of Squall, the game's protagonist.  The greater Squall's level, the more powerful the game's enemies, up to and including the final boss.
To counter the effects of this scaling, players are encouraged to power up their characters not through pure level progression but by effective use of the Junction system; a system that allows the player characters to receive stat bonuses by tying spells drawn from enemies to the characters' equipped Guardian Forces.  Unlike the basic character levels, the Junction system is not tied to the level scaling mechanic.

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