Well asking for proof usually gets folks to stop talking out of their ass, good day sir.
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A 40% reduction would make a 32 damage headshot deal ~20 damage. There are videos of Level 4 players with the starter Auto Rifle, which normally does 32 damage to the head in the normal Crucible (or Iron Banner when you hit the cap), dealing 29 headshot damage to Level 28 players. That's not even a 10% damage reduction and that's the largest gap in gear you can get, pretty much.