How stun works

[KillerKea]

I just learned that stunning in this game doesn’t work the way most of us thought/assumed it did. The way I thought it worked was

Bard with Nightmare set 15 + 8 = 23% stun chance (31% with arena frozen hide set)

Samurai with Grand Slam set
Chance not to stun = .92 * .92 * .92 = .779 Therefore chance to stun = 22.1%

Samurai with Grand Slam set and frozen hide set
Chance not to stun = .84 * .84 * .84 = .593 Therefore chance to stun = 40.7%

The chance to stun bonuses are not added to the regular chance to stun, but instead are a separate chance to stun. Therefore the correct numbers would be:

Bard with Nightmare 21.8% and if you add the frozen hide set it is 28.1%
.85 * .92 = .782
.85 * .92 * . 92 = .719

Samurai with Grand Slam is 22.1%, but if you add the frozen hide set it is only 28.4% not 40.7%
.92 * .92 * .92 * .92 = .716

I guess this lowered chance could be a good thing because a Samurai, Bard and Lightning bird with all these items would be too deadly of a combo in the arena.

Topic

[t_russell]

Is it just me or does stunning the banner when you have Matilda with the nightmare set not work. The bonus damage occurs at the beginning of the stunned objects turn. Since the banner does not get a turn the damage never occurs.

[mich]

@tigerussell Yes, I observed this too.

[Valtyron]

This is quite self-explaining: Stunned pigs receive 200% damage at the beginning of their turn. SO this ability only does damage to Pigs(Birds) while all other abilitys do damage to >targets< or >opponents<

[dr_ishmael]

Abilities that proc on attack always work like this – the chances are multiplied, never added together. I remember back in Guild Wars (the first one), it took a lot of explaining to convince people that wielding two items that gave a 20% chance to reduce skill cooldowns only gave you a 36% overall chance, not 40%.

[t_russell]

@valtyron — It seems to work for the AI when the situation is reversed. At the beginning of my turn the banner takes a large amount of damage. The unfortunate choice of wording in the description should not matter.

[burbman]

Not sure if anyone has the answer, but I see my banner get stunned quite often in Epic, but since it does not have an attack, does anything really happen?

[Anonymous]

@burbman Nope nothing happens when the banner is stunned. All the skills on it still works.

[raziel29a]

not all the skills work with stunned banner. Marksmen skill used on banner doesn’t work when opponent is targeting blues, because usually target bird jumps in front of blues, since jumping banner is silly in arena enemy is forced to attack banner when targeting blues. However if banner is stunned it no longer works. (With my favorite bird set enemy always starts by killing blues)

[KerrAvon]

@dr_ishmael I am aware that killerkea’s calculations are just a simple way of getting to the answer by determining the probabilities of every stun missing. But I presume the game actually processes each attack and calculates whether each attack causes a stun?

Do all the attack bonuses and shielding work in the same way?
So for samurai’s shield, multiply damage by 0.5 or 0.6?. And multiply by an extra 0.9 if he’s armed with protectors aura?

[dr_ishmael]

This is weird. The forum really doesn’t like the post I wrote for some reason. It’s not too long (I posted a longer one in the mastery thread), but I tried posting the first half, and that worked. Then I tried editing and adding the second half… and my post disappeared. Something wiggy’s going on here.

[edit] Okay, I seem to have found some random string that makes the forum choke. I have no clue what it could be, because there’s nothing all that unusual in what I wrote. I’ll try rewording it to see if I can get the forum to accept it.

[edit2] Got it to work. For @admins reference, here’s the paragraph that was making the forum delete my posts: http://pastebin.com/wzSmHxXv

[dr_ishmael]

@kerravon “I presume the game actually processes each attack and calculates whether each attack causes a stun?” Yes, and the mathematical representation of this is that you multiply the probabilities.

Think of it this way. On a single attack, you have two abilities that give a chance to stun – one is a 15% chance, the other is 8%. The abilities trigger independently of each other, so it doesn’t matter which one is calculated first, but we’ll start with the bigger one. A 15% chance means that 15 times out of 100, the first ability stuns the target, and it doesn’t matter whether the second ability triggers or not (because stunning something is binary, i.e. there are only two outcomes: either you stun the target or you don’t). The other 85 times, the first ability doesn’t trigger, but now the second ability comes into play. In 8% of those 85, or 6.8 times, the second ability will trigger. Adding those together, you have 15 + 6.8 = 21.8% chance overall to stun the target.

(Proof that order doesn’t matter: starting with the 8% ability, you have 92 times that the other ability matters, and 15% of 92 is 13.8, and 13.8 + 8 = 21.8% again.)

Going back to my point about this being a binary outcome, the actual math behind this is more complicated. You have to start with a matrix of all possible combinations of outcome. Then, you multiply the A and B probabilities together to find the chance of each of those combinations occurring.

A triggers  B triggers  A%  B%  Chance
----------  ----------  --- --- ------
Yes         Yes         .15 .08   1.2%
Yes         No          .15 .92  13.8%
No          Yes         .85 .08   6.8%
No          No          .85 .92  78.2%
                                ------
Total                           100.0%

Here we see that there is a 78.2% chance for nothing to happen, and a 1.2 + 13.8 + 6.8 = 21.8% chance to stun the target. The same number we got above, just from a more thorough examination of the problem.

This thorough examination becomes important when you are working with a non-binary outcome, i.e. when the combination of A and B triggering together does make a difference. Instead of stunning, let’s imagine the abilities deal 100 bonus damage, and they can stack with each other. When either triggers alone, you deal 100 bonus damage, and this would happen 13.8 + 6.2 = 20.6% of the time. However, in the 1.2% of the time when both trigger, you would deal 200 bonus damage.

[dr_ishmael]

(This was intended as a separate post, even before discovering the forum bug.)

@kerravon “Do all the attack bonuses and shielding work in the same way?” The math may look the same, but those are actually a completely different type of effect. Instead of being probabilities, they are scaling factors: e.g., rather than having a 10% chance of reducing damage, Protector’s Aura scales the received damage by 0.9. Attack bonuses are the same: rather than having a 15% chance to increase damage, the Tricksters’ Cheer ability scales your outgoing damage by 1.15.

When multiple scaling abilities are combined, they are all multiplied against the base damage value together. Samurai’s shield (target) and Protector’s Aura together gives you 0.5 * 0.9 = 0.45 damage reduction. (100 damage is reduced to 45 damage.) Cheer + Arrr! gives you 1.15 * 1.25 = 1.4375 damage increase. (100 damage is increased to 144 damage.)

[AMslimfordy]

@dr_ishmael We’ve bumped up our moderation requirements due to recent spam attacks.

[Strategia55]

Silly question and it may not be related to this topic:

Is anyone finding their “stunned” Birds are actually stunned for an extra round in comparison to the Opponents’ Birds?

[dr_ishmael]

@strategia55 Were you stunned by Red using the Grand Slam set (Titan’s Wrath/Titangrip)? The set bonus increases the hammer’s stun duration to 2 turns.

Otherwise, I have noticed some oddities in the way that turns are counted in arena battles. Sometimes I’ll knock out two birds in one round, but their respawn counters will be out of sync (one won’t progress the counter immediately when your turn ends while the other does). This might affect stun timing as well.

[KerrAvon]

@dr_ishmael Thanks for the explanation. Something I may have done many many years ago in high school – before Uni.
The stunning table gets really complex with Samurai and his three attacks so, as long as there are no combination effects, using “100% – chance of missing” is the simplest way to get to the final result.

[Zeke Kaiser]

@dr_ishmael If the opponent’s bird is knocked out by a DoT (damage over time), they do not receive the first count on their revival since it does the turn count before the damage.

[GrauGeist]

One oddity that I have seen is that Stun (1) replaces Stun (2) (e.g. Bard/Nightmare after Grand Slam). That’s really annoying.

[dr_ishmael]

@zekekaiser Hmm… I seem to remember it happening when my team had no DoT (Wizard/Sea Dog/Spies), but I might be mixing things up. I’ll watch and see if I notice it again.

@graugeist That happens outside the arena, as well. I remember someone pointing it out when discussing stun-lock strategies for the Maelstrom level.

[Strategia55]

It’s happened several times with different Birds. From the sound of it, you’re probably correct in regards to turns counted in Arena Battle; some are askew.

Not all the time, but a little annoying…

[t_russell]

I got to attack with a stunned Red yesterday in the arena. I saw the ring of stars and stupidly sat there waiting for the other team to go. Not realizing the blue ring was still active and waiting for my input. On their turn the AI knocked him out so I don’t know if he was really stunned or not.

[mich]

@tigerrussell
I have seen this a couple of times when the banner’s stun is activated during Chuck’s rage attack. Birds that have not used their attack when using the chili on Chuck can still attack afterwards even when stunned. The game still shows them as stunned, and in your next turn, they cannot attack.