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To be honest I would say this is is significantly more bulky. A level 10 fighter will have a damage save bonus somewhere in the 50-60 range. This would not be in the spirit of bounded accuracy of 5e where a horde of goblins is still a threat in large numbers to a high level character. But to...

I really like the damage save idea and it's been stuck in my head for a little while now. What I was thinking was using, d20 + Proficiency + CON mod + a Class bonus. The class bonus would be a +1 modifier gained every few levels depending on class. So fighter types gain 1 every two levels...