The Bloodied legendary effect is described as "Does more damage the lower the users health is".
How big is the bonus and at what amount of hitpoints does it max out?
Fallout – How does the Bloodied legendary work in Fallout 4
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Best Answer
After a bit of testing with a Bloodied Shishkebab and a Kneecapper Shishkebab (Both with the extra flame jets modification), it does about double damage when you're on the low end of the health bar. If i'm not mistaken, the bonus goes all the way to 1 hp. My tests ended at 3 hp because that's as far as I could get.
Big Leagues Rank 5 + Strength 4 with Kneecapper Shishkebab = 84 + 40 (Energy Damage)
BL Rank 5 + Strength 4 with Bloodied Bab (3 HP) = 165 + 79 (Energy Damage)
Hope this helped you somewhat! I was actually curious about these stats.