The roleplaying game Champions worked like this
Your dex/3 was your combat value, CV. Attackers would add offensive skill levels to CV to get OCV, your offensive combat value. Defenders would add defensive skill levels (or maneuver bonuses like dodge) to CV to get DCV, their defensive combat value. To find your 'hit' roll, you would add to the number 11 the value (OCV - DCV). Then you would roll 3, 6-sided dice and add them up...if you were under that number you hit them.
So offense in that system increased your liklihood of hitting.
THis game is a lot different though. Things like dodge add avoidance which reduces damage received, not your odds of being missed.
My best guess is high offense values reduce mitigation from things like shield block, unbreakable, or avoidance, and let more of your damage land.