Scout + Riftshards

[[4cXD]RealTechN9ne]

I know that Scout cannot doublecrit any longer, but how are % chances calculated if you buy Riftshards?
Is there a separate 25% chance and a separate 20% chance on each hit for a crit to occur? And which of both does overwrite the other if they both procc simultaneously?

[[S2]ElementUser]

It depends on the level of Riftshards & the level of Disarm.

Generally, the highest critical multiplier will take effect if multiple sources of critical proc at the same time.

The percent chance on criticals stack diminishingly, so the formula would be:

% Critical Chance = 1 - [(1 - %Chance_Riftshards) * (1 - %Chance_Disarm)]

Note that the % Chance is the chance to get at least 1 of the critical sources to proc; because of this, the probability of the the critical with a higher %_chance proc would proc more.

[[4cXD]RealTechN9ne]

So with Max Riftshards I get 40%, right? Im not good at maths.
So buying Riftshards is more proficient than I expected.

[[S2]ElementUser]

So with Max Riftshards I get 40%, right? Im not good at maths.
So buying Riftshards is more proficient than I expected.

Yeah 40% chance for at least 1 of the critical sources to proc. You're correct in saying that there's a separate 25% chance for Disarm to proc & 20% chance for Riftshards to proc (assuming max level of skill & item).

[[4cXD]RealTechN9ne]

If both effects procc, you say that Riftshards dominates. Is the Disarm applied nevertheless in this case?

[[S2]ElementUser]

If both effects procc, you say that Riftshards dominates. Is the Disarm applied nevertheless in this case?

Yeah it does.

Ability.entity:

    <onattackimpact />
    <onattackstart >
        <cantarget targetscheme="enemy_units" effecttype="Physical">
            <chance threshold="0.10,0.15,0.20,0.25">
                <condition test="target_type hero">
                    <condition test="not_hasstate State_Scout_Ability3_DisarmImmune">
                        <addattackimpactactions>
                            <applystate name="State_Scout_Ability3" duration="1000" />
                            <applystate name="State_Scout_Ability3_DisarmImmune" duration="2000" />
                        </addattackimpactactions>
                    </condition>
                </condition>
                <addattackimpactactions>
                    <playeffect effect="effects/impact.effect" source="target_entity" />
                </addattackimpactactions>
                <playanim name="ability_1b" speed="source_attackspeed" target="source_entity" />
                <addcritical chance="1.0" multiplier="1.25,1.5,1.75,2.0" />
            </chance>
        </cantarget>
    </onattackstart>

As you can see, the critical multiplier & disarm applications are at different portions of the code.

[[4cXD]RealTechN9ne]

Well, I had informatics in school.
Needless to say I sucked.

Would Riftshards stack in a different way with Swiftblade/Madman than it does with Scout? (Apart from those two having higher crit percentages)

[[S2]ElementUser]

Swiftblade's crit & Madman's crit don't have any other special effects on them.

So it would stack in the same way that 2 Riftshards would stack and Riftshards + any other critical source would stack.

[[4cXD]RealTechN9ne]

Riftshards dont stack with each other, do they?

[[REBL]Vulpes]

They stack the same way as with Disarm.
If both Proc at the same time, just one is applied. But the overall Proc% goes up regardless.
Just go in Practice Mode and attack a bit, once with 1, once with 6 Riftshards.

[awayish`]

it's not 40%. it's 20% of 2.4x crit, then .8 .2 chance of x2, which is 16%.

[[S2]ElementUser]

it's not 40%. it's 20% of 2.4x crit, then .8 .2 chance of x2, which is 16%.

Wait, are you talking about the actual average damage boost of Riftshards?

RealTech was talking about the % Chance to proc at least 1 of the criticals, not about the average damage boost. So was I.

[awayish`]

yes, 36% chance to proc at least 1, not 40. i did the cumulative calculation above, the simpler calculation of neither procing is just .8^2 = .64. 1-.64 = .36

[[S2]ElementUser]

Ok so:

% Critical Chance = 1 - [(1 - %Chance_Riftshards) * (1 - %Chance_Disarm)]

%Chance_Riftshards = 20% = 0.2
%Chance_Disarm = 25% = 0.25

% Crit = 1 - (1 - 0.2)(1 - 0.25)
% Crit = 1 - (0.8)(0.75)
% Crit = 1 - 0.6
% Crit = 0.4
% Crit = 40%

So I still don't see exactly what you're saying awayish`.

If you visit Malle's thread on Criticals on the DA forums, it uses the same formula I posted above: http://forums.dota-allstars.com/inde...howtopic=34345

Of course I'm making the assumption that HoN's system is the same for Critical stacking, but then again it's hard to "test" probability.

EDIT: I think I see the problem, For some reason you thought Scout's Disarm had a 20% chance to proc, not 25%. O.o

[awayish`]

wat. it's 25? ok. it should be changed to .2

[[S2]ElementUser]

Yeah I thought it was 20% chance at first too, until I checked.

Oh well lol

[[4cXD]RealTechN9ne]

And how much average damage boost would Riftshards 4 on Scout give now? Still 16%?
Because on a hero without skills, it is 28%, amirite?

[[REBL]Vulpes]

Doesnt it stack diminishingly?

It does. With two Riftshards, the first gives you a 20% Chance to Crit.
The second one can only Crit in the 80% where the first doesn't,
so the 2nd one only adds another 16% CritChance. A fifth less Crits is "diminishingly stacking".

For Swift, it gets even worse since he has an inherent 36% Chance.
2nd one can only Crit in 64% of Hits (and there with its 20% Chance),
that reduces the RiftshardsCrit probability to terrible 12.8%;
Thus it's not worth to buy them at all. Much better Damage/Gold Items for Swiftblade.

[MichaelBurge]

How much damage do you need before Riftshards is the best DPS increase for Scout? Or does Shieldbreaker always take priority?

[[S2]ElementUser]

Ok, here's a probability response by Malle (I hate probability ). It makes perfect sense after he explains it:

While each crit does indeed have the same independent probability to trigger regardless of how many crit sources you have, it is not so that they always add to the damage as much as they normally would if you had only one crit source, since only the highest multiplier will be used.

To clarify: If you have Disarm level 4 (25% for 2.0x damage) and Riftshards level 4 (20% for 2.4x damage), then if Riftshard triggers its multiplier will always be used, but if Disarm triggers, there's still a 20% probability for Riftshards to trigger and override the multiplier of Disarm.

In this scenario, you would then have

• 20% for 1.4x extra damage
• 20% for 1.0x extra damage
• 60% for 0.0x extra damage

That is, on average, .2*1.4+.2*1.0+.6*0 = 0.48x extra damage, or a damage factor of 1.48.

Without Disarm (only Riftshards) you would have .2*1.4 + .8*0.0 = 0.28x extra damage or a damage factor of 1.28.

Only Disarm (no Riftshards) would give .25*1.0 + .75 * 0.0 = 0.25x extra damage or a damage factor of 1.25.

Thus, when adding Riftshards when you have Disarm, you only get an extra .23x of base damage instead of .25x of base damage (you go from 1.25 to 1.48 instead of 1.00 to 1.28), which corresponds to that 20% of the times Disarm would trigger, it does nothing, since Riftshards overrides it due to higher damage multiplier. If you want to count it as a separate damage factor, then you get 1.48/1.25 = 1.184 instead of 1.28 / 1.00 = 1.28.

In case you didn't understand where the 20% chance to proc Disarm comes from (like me), here's an in-depth explanation:

If we first look at the items independently, then we have 25% for Disarm to trigger, 20% for Riftshards to trigger and 100% for an attack to happen.

With three different triggers, we can have 8 possible outcomes:
1. Normal attack happens, Riftshard doesn't trigger, Disarm doesn't trigger.
2. Normal attack happens, Riftshard doesn't trigger, Disarm triggers.
3. Normal attack happens, Riftshard triggers, Disarm doesn't trigger.
4. Normal attack happens, Riftshard triggers, Disarm 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-.25) = 0.6
2. 1.00 * (1-.2) * .25) = 0.2
3. 1.00 * .2 * (1-.25) = 0.15
4. 1.00 * .2 * .25 = 0.05

That is, on average, 60/100 attacks are normal, 20/100 attacks have Disarm trigger but not Riftshard, 15/100 attacks have Riftshards trigger but not Disarm, 5/100 attacks have both Riftshard and Disarm trigger.

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 60% to get 1.0x damage, 20% to get 2.0x damage and .15 + .05 = 20% to get 2.4 damage.

This apparent decrease in Disarm's triggering rate is simply because (on average) out of every 5 times it triggers, it will not have any effect 1 time, since Riftshards has a higher multiplier. Thus, it is reduced to 4/5's (average) efficiency and is as if it was 20% instead of 25%.

TL;DR: Scout gets an average damage increase of 148% with level 4 Disarm & level 4 Riftshards. Or you can say that Riftshards only directly adds 23% average damage increase to Scout.

In response to this question:

How much damage do you need before Riftshards is the best DPS increase for Scout? Or does Shieldbreaker always take priority?

Disregarding any IAS, orb-effects (including procs from things like Thunderclaw) and current level of damage; ie, looking purely at the damage coefficient increase:

We just learned that level 4 Riftshards gives a 18.4%% average damage increase (0.18 on the following graph) if Scout already has level 4 Disarm. We also know that the average damage increase is constant (meaning it is a horizontal line on the graph below at 0.48) if compared to armor because it is unaffected by that. However, the average damage increase of Shieldbreaker is not a constant & fluctuates based on this graph:



As you can see, the damage coefficient of Shieldbreaker goes above 18% (or 0.18) between certain intervals . Thus, Riftshards is superior to Shieldbreaker in terms of average damage increase (but remembering that once again, we're not accounting for IAS, orbs and damage).

The more units hitting the target affected with Shieldbreaker though, the faster it dies because the damage from your allies are also increased by a certain damage factor, whereas Riftshards only increases your own damage factor.