I'm able to out lift big muscular men, how much does actual muscle mass contribute to strength?

Some relation: Muscle mass has to do with hypertrophy of muscle fibers. Muscle fiber hypertrophy has more to do with the consistency of training routine, not single episode of power. Someone who is not a regular lifter can still have significant strength. This scenario isn't common, but possible...... You may also have short arms and legs, which allows you to power weight over a shorter distance.

Less than workouts: While muscle mass is important, muscle conditioning and training plays a large rôle. I can't quantify how much each contributes, but at any gym, the men who work out consistently always do better.