-25% to Target Defense

A special attribute, the most common source of '-XX% to Target Defense' are Eth runes when placed in a weapon. You can also get this from the barbarian's Battle Cry, Taunt, the assassin's Cloak of Shadows, and paladin's Conviction aura, but because we're just focusing on bowazons, we'll just stick to Eth runes.

Eth is a common clvl-15 rune, but when you put one in your weapon, your target's effective defense rating is reduced by 25% per rune, making them much easier to hit. The reduction of the DR of the bowazon's target would be:

DR × - XX% to Target Defense (decimal form)

So let's suppose your bowazon with 1,000 AR has an Eth rune in her bow. If she's attacking a monster with 2,000 DR, then her Eth rune would remove 500 DR. This is because 2,000 × 0.25 = 500. Thus, the monster now has 1,500 DR remaining. With Eth runes, the To-Hit formula should look like this:

100 × 1,000/1,000 + 1,500 × 2 × alvl/(alvl + dlvl)

For the sake of simplicity, you should figure out the target's adjusted DR before you calculate the 'new' To-Hit formula. As an example, with a single Eth rune in a weapon, your chance to hit would look like this:

100 × AR/(AR + (DR - 25%)) × 2 × alvl/(alvl + dlvl)

This bonus to hit isn't listed on the character screen.

As another example, if your target was struck with a slvl-12 Conviction Aura (-83% to Target Defense), your chance to hit would look like this:

100 × AR/(AR + (DR - 83%)) × 2 × alvl/(alvl + dlvl)

And finally, because this bonus is additive, if your target was struck with a slvl-12 Conviction Aura (-83% to Target Defense) while being attacked by a bowazon with an Eth rune in her weapon, her chance to hit would look like this:

100 × AR/(AR + (DR - 108%)) × 2 × alvl/(alvl + dlvl)

Yes, that last example pretty much means that you're attacking a normal monster as though you were using an ITD weapon; however, the "-XX% to Target Defense" cannot make a monster's DR negative, so it's automatically set to -100%. However, Eth runes (and only Eth runes) operate at half-effectiveness (-12.5% defense) when used against other players, champions, unique monsters, or super unique monsters, so the previous example would look like this when attacking any of those monsters.

100 × AR/(AR + (DR - 95.5%)) × 2 × alvl/(alvl + dlvl)

This defense reduction is static: it doesn't slowly chip away at a monster's defense. Note that this defense reduction applies only to the attacker holding the weapon with the Eth runes in it, so if a bowazon with two Eth runes in her weapon and a hireling with one Eth rune in his weapon are attacking a monster with 2,000 DR, the bowazon will be attacking the monster as though it had 1,000 DR (a 50% reduction) but the hireling would be hitting it as though the monster had 1,500 DR (a 25% reduction).