Margins, Called Shot Criticals, Expertise, and Power Attack.

Matt Miller 

Before DnD adopted d20, 2d6 was the default rolling mechanism. But the 2d6 also included a margin mechanic, when how much you won by was important. Working on Mayhem, which also has a margin mechanic (for criticals) big margins were a nightmare. 

I recall there being a feat in DnD that let you take -x to rolls to get +x to damage. I don't recall it being particularly exciting. Part of what made called shots exciting was that the pay-off was big: Big risk, big reward. A -1 to hit for a +1 to damage is just...tactical.
But the idea of margins doing more damage recalls to me Called Shit Criticals, from Skills and Powers (DnD), where you could take a -4 penalty to attacks, and then enjoy ridiculous damage bonuses. Thematically, I think I prefer the 'push your luck' mechanism of Called Shot Criticals. 

Rob Hicks 

Power attack. reduce your base attack bonus by 1 to get 1 extra damage. (2 extra damage for two-handed weapons.) Power attack was amazing.

Matt Miller

Ok, so expertise must have been -x damage to get +1 to hit.