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Evasion is the stat that governs the mechanic for dodging enemy damage. Evasion is directly stacked up against the enemy's accuracy, and due to this, stacking lots and lots of evasion has diminishing returns as the chance to dodge versus the investment for a lot of evasion does not increase significantly enough.
Do note that certain enemy attacks do not have an evasion check (thus they will never miss). This means that evasion does not affect the dodge chance for those attacks (which is 0%).