Bonus on skill damage or raw damage, which is better in this case?

I'm playing a Wizard and my main skill is Disintegrate.

My wand gives me 21% bonus damage on Disintegrate. I found another want that doesn't give me that but has more damage and intelligence.

Which one is going to do more damage when using Disintegrate? Why? How can I calculate that?

If you have no other source of increased disintegrate damage then the first wand should be better, seeing as the other wand increases general damage by 20.2%.

However, you could still reroll the vitality, or reduced resource cost, on the second wand for a damage based prefix (especially a socket) and it would then surpass the first.

I'm pulling this explanation mainly from this wiki, but it's consistent with every explanation I've seen for how damage in Diablo 3 works.

When calculating damage, the game first multiplies together your "basic" stats, like your weapon damage (after modification from the skill being used, if applicable), primary stat and critical hit damage (if applicable). Once it has that number, it will further increase it by special stats applied to that particular attack, such as increased damage for the ability. What this means is that you can generally use the strategy VanBuzzKill suggested - compare the percent damage increase given by the game, and flatly add in applicable skill or elemental bonuses. With that said, there are more damage related things to consider between the two items -

• The Slorak's Madness additionally has +17% Area Damage on hit - this effect triggers on 20% of attacks, meaning that this grants about (.17 * .2) = 3.4% extra area of effect damage to your spells

• Even ignoring the Wand of Woh's legendary affix, the increased damage applies to all of your abilities. Assuming you don't have other legendary items significantly increasing the damage of disintegrate, you probably still rely on damage from your other abilities - it looks like you have black hole and hydra, which do not do insignificant damage.

• Echoing VanBuzzKill, you can enchant the Resource Cost Reduction off of the Wand of Woh in favor of more damage or a socket (into which you would put a critical hit damage gem, so, more damage)

• Given the legendary affix on the Wand of Woh, you will probably find that using Explosive Blast with either Unleashed or Obliterate will do significantly more damage than disintegrate. Assuming you are using Hydra because you have Etched Sigil in your offhand, I'm not sure but I would guess Explosive Blast also counts a spender for it.