From Dungeons of Dredmor Wiki

"Enemy Dodge Reduction affects how likely an enemy is to not dodge your attacks. Because Heroes never miss - but sometimes their attacks are dodged."

For all intents and purposes, this is your hit chance. The higher the number, the more likely you are to hit an enemy.

Increased Nimbleness will increase Enemy Dodge Reduction. (Base Enemy Dodge Reduction is equal to Nimbleness/3 rounded down. To be confirmed.)

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