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https://www.poewiki.net/wiki/Shock
Basically, Overcharge Support is *lowering the threshold* required to apply larger amounts of Shock to enemies. It does this by causing supported Skills to apply Shock to enemies "as though dealing 500% more damage".
Also, to clarify, Shock is not a guaranteed 50% increase in damage to a target, nor is it a per-hit effect. Rather, you are *applying* a percentage of Shock to an enemy (up to 50%), and the Shock status may linger on the enemy for a certain amount of time (base duration is 2 seconds). This means multiple hits within that 2 second window can apply damage at the increased rate.
I'm fairly confident that Overcharge Support requires being linked to a Skill Gem that applies Lightning Damage. Otherwise, no Shock will be applied, considering 500% of 0 is still 0.
Basically, Overdrive is a support skill to support a setup that inflicts shocks. It's not really ideal to use in your main skill. You could use it on Orb of Storms and then reap the benefits (hopefully potent shock on enemy) with your main skill.
"Supported Skills deal 25% less Damage" is a significant drawback, 0.75*1.5 (for default-max best case) is still only 1.125, so 12.5% higher damage, and if you had shocks before, this is lower in practice as well. And other increases of "damage taken" reduce the effectiveness as well. A (damage number oriented) support gem that doesn't grant you 30% more damage isn't usually worth it.
edit. they get more sexy with more crit chance it seems.
You are correct - Shock is a Status Effect that increases damage from all sources. You are also correct that some Skills can inflict Shock without dealing damage. However, your original example in your first post is an incorrect interpretation of how Shock works, and your calculations are not entirely correct either.
I'm bored at the moment, so please excuse me while I write a book about applying Shock to enemies - At least, how I understand it, based on the Wiki.
Consider the following -
You are about to hit an enemy that has 10,000HP. You are hitting them for 1,000 damage, with a Skill that has a 100% Chance to apply Shock.
First, we need to know the enemy's "Ailment Threshold".
According to the Wiki, every enemy in the game (with the exception of Pinnacle Bosses) calculates its Ailment Threshold as being *equal* to its Maximum Life. Therefore, we can assume that the Ailment Threshold for this enemy is 10,000, because it has 10,000HP.
A quick look at the formula, assuming a 1,000 damage hit, without increases to Shock Effect -
E = 1/2 * (1000/10,000)^0.4 * (1 + 0)
E = 0.199
I'm not entirely sure about this next part, so maybe someone with a better understanding can feel free to comment -
The minimum amount of Shock is 5%, and the maximum amount is 50%. Shock is rounded down (in the enemy's favor), so in this case, we are just shy of inflicting 20% Shock. Therefore, we consider the first hit to apply only a 15% Shock (rounding 19.9% down to the nearest 5% leaves us with 15%).
Finally, Shock effects do not stack. Only the highest value of Shock applied is considered valid, and subsequent Shocks (if they are lower) will not overwrite that highest value until it naturally expires.
All that being said, we can look at how damage would be calculated in this scenario (again, we are assuming 100% Chance to Shock) -
WITHOUT OVERCHARGE SUPPORT
TOTAL DAMAGE: 1000 + 1150 + 1200 + 1200 = 4550
WITH OVERCHARGE SUPPORT (500% increase to Shock damage)
TOTAL DAMAGE: 750 + 975 + 1013 + 1013 = 3751
So, there you have it - This is a prime example of why you *would not* want to socket Overcharge Support in your main Skill Gem setup. It's exactly as The_Driver specified -