Hero Damage is one of ten stats that every hero has. It affects how many damage points your character will inflict to monsters. Hero Damage only affects physical damage.
The way your damage increase depends on your hero's weapon and Hero Damage stat. This increment is called scale of progression.
Formula
The weapon damage is simply multiplied by a logarithmic damage multiplier. The formula to calculate the approximate damage your character inflicts is:
$ \mathrm{Damage} = (0.75 \ln(x + 20) - 1.2) \cdot y $
Where "x" is the Hero Damage stat, and "y" is the weapon damage, dropping all fractions, never round. The
result will not be the DPS (Damage Per Second), but the median damage inflicted by your hero per hit. To find your hero's minimum damage multiply this value by 0.84, and to find the maximum multiply by 1.17. This is very approximate and does not apply to all heroes equally for every animation. For example, the Countess' 3rd swing is two possible stronger hits than the first two swings.
The results are approximated, so the margin of error can be more than 6% above Hero Damage 100.
This formula was discovered by "Cel" on 03-Nov-2011, in Dungeon Defenders Forums.
The Summoner doesn't carry a weapon, but his Hero Damage stat will increase the damage of his familiars of HEROIC, Mythical and higher quality.
Class Damage Scaling
Different hero classes do different amounts of damage, even with the same Hero Damage stat and exactly the same weapon. For example, for a given Huntress weapon, a Jester with the same Hero Damage stat will do about 80% of the damage, the Series EV about 70% (but check the math in your tavern). For Apprentice weapons, it seems that the Jester does the same damage (100%), but Series EV again about 70%.
This applies to the PC version at least; not certain about console and mobile.
Nightmare Damage Reduction
On Nightmare difficulty (PC only), hero damage is reduced to 20% of normal, while hero HP is increased. Pet and tower damage are increased (by about 20%, I believe). This makes pets like the Mega Chicken a more useful companion than the Propeller Cat.
Easy Damage Calculator
Point your browser to WolframAlpha, and change X by your Hero Damage, and Y by your weapon damage.
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