Critical Stacking & Average DPS Increase

[Evozer]

If i have Riftshards lvl 4(24% chance 2.2x damage) and Swifblades crit (36% chance 3x damage) the crit chance will be 1-(1-0.24)(1-0.36)=51.36% ?

And the damage will be 36% chance for 3x damage and 15.36% chance for 2.4x damage?

Is this correct?

[[S2]ElementUser]

The percentage is right, but Swiftblade's critical adds an extra 100% to your attack, thus it's 2x damage not 3x damage.

The second part involves critical probability for average damage increase (which I'm still not good at). So your second line is not ture.

[Evozer]

Oh well im glad the % is right

Average dmg is like this i think:

Damage * (CritMultiplier - 1) * Chance

So a swiftblade with 200 damage would gain: 200*1*0.36=72 avg dmg increase

The second line was mostly to ask if it first tries the 1st crit then if that fails, the 2nd

[[S2]ElementUser]

No.

See hr_tastive's post in this thread: it covers it pretty well. Calculations show that it's a 56.8% average damage increase overall.

http://forums.heroesofnewerth.com/sh...ad.php?t=98189

Here's a post (from which I quoted Malle) on probability & average damage increase with Scout's Disarm & Riftshards. The concepts still hold:

http://forums.heroesofnewerth.com/sh...2&postcount=20

I'll simply substitute the values of Scout's Disarm with Way of the Sword's values and compare the new numbers using Malle's template:

With three different triggers, we can have 8 possible outcomes:
1. Normal attack happens, Riftshard doesn't trigger, Way of the Sword doesn't trigger.
2. Normal attack happens, Riftshard doesn't trigger, Way of the Sword triggers.
3. Normal attack happens, Riftshard triggers, Way of the Sword doesn't trigger.
4. Normal attack happens, Riftshard triggers, Way of the Sword triggers.
5. Normal attack doesn't happen, ...
6-8: As 5, but with different combinations of Riftshard and Disarm.

These are all the possible outcomes. One and only one will be selected whenever you attack. We know that the probability for 5-8 are 0, since an attack always happens, if we disregard any probability for missing.

The probability for each point to occur is the product of the probabilities of each of the sub events.
1. 1.00 * (1-.2) * (1-.36) = 0.512
2. 1.00 * (1-.2) * .36 = 0.288
3. 1.00 * .2 * (1-.36) = 0.128
4. 1.00 * .2 * .36 = 0.072

We then look at how they interact when multiple things happen at once, so we can decide what happens in each of the events. We know that the highest multiplier is applied, so we get:

1. 1.0x
2. 2.0x
3. 2.4x
4. 2.4x

Since event 3 and 4 have the same effect, we can add up the probabilities and state that we have 51.2% to get 1.0x damage, 28.8% to get 2.0x damage and .128 + .072 = 20% to get 2.4x damage.

So the average damage increase is 1*(0.512) + 2*(0.288) + 2.4(0.2) = 1.568x damage or a 56.8% average damage increase.

So just read either hr_tastive's post or this post - both say the same things, just in a slightly different way.

[Hax]

To the above:

His percentage was not damage increase, but crit chance.

[Evozer]

(C1*CM1) - C1 + (C2*CM2) - C2 - (C1*C2*CM2) + (C1*C2)

Made it a *little* shorter and easier too look at.

C1: Chance to proc by the item with the highest crit multiplier
CM1: The highest crit multiplier

C2: Chance to proc by the item with the lowest crit multiplier
CM2: The lowest crit multiplier

__________________________________________________

Inserting
C1: 0.2
CM1: 2.4

C2: 0.36
CM2: 2

Gives the answer 0.568, which means 56.8% more damage (matches with hr_tastives calc)

Yes its already been done, but i think its simpler to have it like this. Maybe someone else will too

[[S2]ElementUser]

To the above:

His percentage was not damage increase, but crit chance.

Did you read my first post?

I said the % chance was correct.

[[ASPI]Gio`]

Is the damage increase substantial if Swift is holding 4xRiftshards, one at level one, another at level two, etc?

[[S2]ElementUser]

No, as the effects will diminish even more than a 15.3% relative increase. Riftshards level 4 only gave a 15.3% relative increase in damage (when it's supposed to give a 28% relative increase in damage on its own), so weaker versions of Riftshards further added in will diminish even more in terms of relative DPS increase (critical-wise, not talking about the static damage bonus included per Riftshard).

[sieneh]

Reading threads in the mechanics section with posts made by ElementUser really make me feel stupid. :/