Chance to Freeze & Cold Snap

Hello everyone. I'm trying to work out the chance to freeze an enemy, but I've been having issues with the mechanics; I don't really know how to add everything up.

1) The passive skill Freeze adds a "chance to freeze enemy on cold damage" (5%)
2) Elemental weakness says it increases the chance for an enemy to be frozen by cold damage (14% at lvl 20)
3) The "chance to freeze enemies on hit with cold damage" that is displayed on the description for Cold Snap... does that mean that the skill itself has that additional chance to freeze when cast, or is it that a monster that's been hit by Cold Snap now has an increased chance to be frozen by further cold damage?
4) Cold skills themselves have a chance to crit, which causes freeze

An example of trying to add things up... Are the chances for Elemental Weakness and Freeze additive, or are they independent events? i.e., if i have both in effect, is my chance to freeze an enemy with cold damage:

1) .14 + .05 = 19%? (additive chances)
2) .14 + .05 - .14*.05 = 18.3%? (different dice throws, independent events)

The same goes for Cold Snap, assuming that the skill itself has an increased chance to freeze when it hits enemies. Would the 44% (lvl 20) be an addition to the previous number, or is it an independent dice throw?

Regarding criticals, can a critical and a "chance to freeze" occur at the same time? Is one calculated after the other?

Thanks to anyone who can shed some light on this :) Sorry if it's been posted before, if it has, I haven't been able to find it.

Cheers

The only time something can freeze is when the attack/spell is a critical strike.

Spells like Cold Snap, however, always have a chance to freeze whether they crit or not. They are the exception.

If you make a critical strike with cold damage and do not freeze your target, it is because you did not do enough cold damage. There is a minimum freeze threshold (a specific minimum % of the target's maximum life must be removed via cold damage for them to be frozen for any length of time).

I'm not sure how "% chance increase for freeze" on elemental weakness works, whether it does anything to spells that aren't like Cold Snap, but I suspect for a spell like cold snap, is simply multiplies its current freeze chance by that percentage.

When you attempt to freeze something, you always need to do a sufficient amount of cold damage for it to do anything. This is why getting a +% chance to freeze passive (near Shadow start) and freezing pulse spam - aren't inherently powerful. Although it will allow you to freeze without ever critting, your non-crit freezing pulse needs to do pretty hefty damage to freeze, even when it rolls the chance to.

I can't begin to imagine why they would have things like "chance to freeze on cold damage" or "chance to shock on lightning damage" if these things were the same as critical strikes. And I don't believe they're that rare as to call them exceptions, although I do admit the passive skill tree isn't exactly abundant with them. But you do have a few.

You also have the equivalent for lightning damage (see passives "Shock", "Static Blows", "Chance to Shock") and to me, they seem to be something different, separate from chance to crit.

If these were the same, I wish they would just change it to things like "5% increased critical strike chance for cold damage". It would certainly make it easier to understand. In any case, I still don't understand how you can calculate the total chance to freeze or shock.

Spells like Cold Snap have, on the one hand, their critical chance. And on the other hand, a separate (at least in the description) chance to freeze. I suspect they would simply add that second bonus to the critical chance if they were the same thing. My main question would be: OK, I have a critical chance, and also a chance to freeze on regular damage. What's my total chance to freeze?

And to answer that question, you need to know if the two can occur at the same time, if they're independent, etc. In other words, how they are calculated.

I didn't know about this freeze threshold. That's very interesting. Are there any concrete numbers on that?

That's not how they work.

Critical strikes ALWAYS attempt to inflict a status effect.
X% chance to inflict status effect (as seen near the Shadow start) doesn't make the attack a crit, it just inflicts the status effect on hit - or at least, it tries to.

A spell that crits always tries to freeze, that's my point, there's no "chance" involved anywhere. It always freezes. If a spell that crits doesn't freeze, it's not doing sufficient cold damage to the enemy (who either has high cold resist or high max life). The only other possible reason as to why your crit cold snap didn't freeze (for instance) is if the target has "immune to freeze" or "avoid freeze" effects on them (which you will see in PVP).

"

fmoss3 wrote:

I didn't know about this freeze threshold. That's very interesting. Are there any concrete numbers on that?

Burning, Chilled, Frozen, and Shocked are collectively known as Status Ailments. The duration of the chilled, frozen, and shocked statuses is related to the amount of cold/lightning damage dealt:

Shocked: 276ms per 1% max life dealt as lightning
Chilled: 138ms per 1% max life dealt as cold
Frozen: 100ms per 1% max life dealt as cold

All three are capped at considering 1/3 of max life - if you deal more than 1/3 max life as that element, the status ailment occurs as though you did exactly 1/3.

The maximum unmodified durations are therefore:
Shock: 9.2 seconds
Chill: 4.6 seconds
Freeze: 3.33 seconds

If the duration would be less that 300ms, it's ignored entirely (the effect is not applied). For characters using Chaos Inoculation, these durations are calculated based on what the character's maximum life would be if they did not have Chaos Inoculation.

edit: format

"

anubite wrote:

That's not how they work.

Critical strikes ALWAYS attempt to inflict a status effect.
X% chance to inflict status effect (as seen near the Shadow start) doesn't make the attack a crit, it just inflicts the status effect on hit - or at least, it tries to.

A spell that crits always tries to freeze, that's my point, there's no "chance" involved anywhere. It always freezes. If a spell that crits doesn't freeze, it's not doing sufficient cold damage to the enemy (who either has high cold resist or high max life). The only other possible reason as to why your crit cold snap didn't freeze (for instance) is if the target has "immune to freeze" or "avoid freeze" effects on them (which you will see in PVP).

I understand what you've said and I agree on it. That's why I'm confused in the first place, specially regarding calculations. On the one hand, chance to freeze. On the other, chance to crit. So how do they come together, mechanics-wise? Same thing with shock.

"

Ladderjack wrote:

"

fmoss3 wrote:

I didn't know about this freeze threshold. That's very interesting. Are there any concrete numbers on that?

Burning, Chilled, Frozen, and Shocked are collectively known as Status Ailments. The duration of the chilled, frozen, and shocked statuses is related to the amount of cold/lightning damage dealt:

Shocked: 276ms per 1% max life dealt as lightning
Chilled: 138ms per 1% max life dealt as cold
Frozen: 100ms per 1% max life dealt as cold

All three are capped at considering 1/3 of max life - if you deal more than 1/3 max life as that element, the status ailment occurs as though you did exactly 1/3.

The maximum unmodified durations are therefore:
Shock: 9.2 seconds
Chill: 4.6 seconds
Freeze: 3.33 seconds

If the duration would be less that 300ms, it's ignored entirely (the effect is not applied). For characters using Chaos Inoculation, these durations are calculated based on what the character's maximum life would be if they did not have Chaos Inoculation.

edit: format

Thank you, you've cleared that up.

Well, chance to crit is chance to crit.

If you're using freezing pulse, which I think has a base crit chance of 6%, then, that means, you need almost 2000% increased critical strike chance to reach 100% chance to crit, which would be 100% chance to freeze.

If you're using freezing pulse with +5% chance to freeze on hit, then you have two separate things going on. When you make an attack against an enemy, the game should roll 2 different random numbers. It probably rolls crit chance first. If it's a crit, it will attempt to freeze the target based on cold damage done. If it's not a crit, the second random number will tell ie whether it should attempt to freeze the target for the cold damage done on the attack.

In regards to EW effecting this chance to freeze...



If I assume I'm reading the description right, and given the fact it's only 10%, I imagine it means EW is applying an actual 10% chance to freeze, as in, it will stack additively with cold snap and the shadow passive. However, the description in the skill does not say "10% additional chance to freeze" like you see on the stave block passive skill "additional chance to block with staves" so I guess it could be multiplifying your existing chance to freeze by 10%, but that would seem pretty weak, given its low prevalence as a stat.

Elemental Weakness is losing this ability next patch, by the way. Three new element-specific curses are coming.

"

anubite wrote:

Well, chance to crit is chance to crit.

If you're using freezing pulse, which I think has a base crit chance of 6%, then, that means, you need almost 2000% increased critical strike chance to reach 100% chance to crit, which would be 100% chance to freeze.

So, 6% base chance. Assuming a lvl 20 Increased Critical Chance Support gem, you've got a 105% increased critical strike chance, which adds up to 0.06 + 1.05*0.06 = 12.3%. To get to 100%: 0.123*x = 1; x will be approximately 8.123, which means you'll need at least 812% increased critical chance strike from Passive Skills, which is not doable without the help of items that greatly boost your critical strike chance--I'm talking 300% critical strike chance bonus from items.

"

anubite wrote:

If you're using freezing pulse with +5% chance to freeze on hit, then you have two separate things going on. When you make an attack against an enemy, the game should roll 2 different random numbers. It probably rolls crit chance first. If it's a crit, it will attempt to freeze the target based on cold damage done. If it's not a crit, the second random number will tell ie whether it should attempt to freeze the target for the cold damage done on the attack.

In regards to EW effecting this chance to freeze...

Unavailable

If I assume I'm reading the description right, and given the fact it's only 10%, I imagine it means EW is applying an actual 10% chance to freeze, as in, it will stack additively with cold snap and the shadow passive. However, the description in the skill does not say "10% additional chance to freeze" like you see on the stave block passive skill "additional chance to block with staves" so I guess it could be multiplifying your existing chance to freeze by 10%, but that would seem pretty weak, given its low prevalence as a stat.

This is what I've assumed so far, additive chances. However, if it does work this way, I'm not sure non-crit freeze is very helpful.

Assume you've got a skill like Freezing Pulse, with a 6% chance to crit, and the support gem that brings it up to 12.3%.

On the other hand, assume the monster has been hit with lvl 20 Elemental Weakness (its bonus by the way is described as Additional % Chance to Freeze/Ignite/Shock in the wiki), and you have taken the Freeze passive, and assuming they are simply additive:

0.05 + 0.14 = 19% chance for the monster to be frozen on hit with cold damage.

Now, assuming critical strikes and non-critical freezes are independent events, the global chance for a monster to be frozen is, according to the laws of probability:

Freezing chance = Chance to crit + Chance to freeze - Chance to crit and freeze at the same time
Freezing chance = 0.123 + 0.19 - 0.123*0.19 (let us assume they are independent events that can overlap)
Freezing chance = 28.96%

And this does not take into account the freeze damage threshold, so possibly not all of those cases can effectively freeze.

Doing the same calculations for Cold Snap:

Cold Snap crit chance = 0.04 * 2.05 (assuming lvl 20 Increased Critical Strike chance support gem) = 8.2%
Chance to freeze on Cold Damage by Cold Snap = 0.05 (Freeze passive) + 0.14 (lvl 20 Elemental Weakness) + 0.44 (lvl 20 Cold Snap) = 63% (assuming they are additive)

Global freezing chance = 0.082 + 0.63 - 0.082*0.63 = 66%

Which is nice and all, but unreliable. Since they are independent events, you'll never have a 100% freezing chance unless one of the non-mutually exclusive events has a probability of 1.

In conclusion, if you want to freeze 100% of the time, you either have to crit 100% of the time or you have to have a non-crit chance to freeze on cold damage of 100%, which is as of now, impossible.

So why bother with the passive skill Freeze, or a skill like Cold Snap, when the only possibility to freeze 100% of the time is with Ice Spear? Only with the obscene critical strike bonus of 600% that comes with the second form of Ice Spear can you even come close to critting 100% of the time. Although if I recall correctly, you have a 95% critical strike chance cap, but it's the closest you can get.

"

anubite wrote:

Elemental Weakness is losing this ability next patch, by the way. Three new element-specific curses are coming.

I'm aware of this. The more reason to know exactly how it works! The equivalent of "Cold Weakness" will certainly have the "chance to freeze" mod, so naturally I'm interested to know how it works in order to know if I'll want to use it or not.

In light of the previous conclusions however, even if elemental weakness loses its Chance to Freeze on Cold Damage bonus, I'll still use it for the damage bonus. On the other hand, the other curse that adds a chance to freeze will be useless if you want to freeze all the time, given that it's highly unlikely that will add up to a 100% chance to freeze, and even then, you still need a certain amount of cold damage for an effective freeze.

Again, Ice Spear comes out on top, so why bother with anything else?

It'd be interesting if the Cold Weakness curse had a substantial amount of chance to freeze on cold damage. If with the additional freezing chances of the Freeze passive skill and the one from Cold Snap you could get to 100% chance to freeze an enemy on cold damage, I'd definitely consider using it.