Stats, breeds, mechanics, and math

Discuss pet battles, strategy and theorycrafting.
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Poofah
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Re: Stats, breeds, mechanics, and math

Post by Poofah » February 22nd, 2013, 3:47 pm

Time for another eyesore, just in time for weekend reading. There should be some things of interest regarding 5.2 balance, at least indirectly, if you can make it through section 8. Definitely reread section 4 if you're fuzzy on the notion of ATK, as that will feature throughout.


6. How the mechanics lead to balance:

From the first sections, hopefully I convinced you that pet battles seem to be balanced around the assumption that on average, 1 pet versus 1 pet will last 5 turns, ie that 1 turn = 20% of a pet’s health. This is apparent in all of the basic attacks, which have an ATK ratio of 1 and deal 20% of an average pet’s health. Although I have no direct evidence to support this next assertion, I am willing to bet that pet battles were designed around these basic assumptions as a way to maintain balance while still having a large diversity of abilities and movesets. Basically, I think that abilities are all designed to provide a benefit that’s roughly equivalent to 1 turn/1 ATK ratio/20% health; and if this leads to abilities that are balanced in isolation, then any 3 of those abilities (ie a moveset) should also be balanced.

There are some fairly glaring examples where balance has broken down, e.g. Ghostly Bite, Fluxfire Feline, Tiny Snowman and more. I’ll try to explain how those fit into this putative balancing scheme in the next section or so. So please bear with me.

First I want to convince you that attacks are all designed around providing a benefit equal to or very close to 1 ATK ratio/20% health per turn. The basic attacks (Punch/Claw/Scratch/etc.) clearly adhere to this. Slightly less basic spammable attacks also seem tied to this: such as Flurry (1.25 ATK ratio if going first/0.75 ATK ratio if going 2nd) and Arcane Blast (1st use = 0.75 ATK ratio, 2nd use = 1 ATK ratio, 3rd use = 1.25 ATK ratio, etc.) and Arcane Explosion (0.5 ATK on the frontline and 0.25 ATK on the backline, for 1 ATK total) and Alpha Strike (1.2 ATK if going first/0.8 ATK if going 2nd) and Tail Swipe (1.25 ATK if going 2nd, 0.9 ATK if going 1st—actually slightly high) and Absorb (0.5 ATK of damage and 0.5 ATK of heal) and Death Coil (0.75 ATK of damage and 0.375 ATK of heal).

Any attack which exceeds this 1 ATK ratio comes with a drawback, in the form of a cooldown, or in the form of some negative effect, or in the form of a condition that needs to be met, or by delaying or spreading out the benefit over multiple turns. Consume deals 0.65 ATK and heals for 0.65 ATK, for a total of 1.3, but it has a 1 round cooldown to compensate; Demolish deals 2 ATK of damage but with 50% accuracy, for an expected damage of 1 ATK; Flamethrower deals a total of 1.2 ATK, but takes 3 turns to do it; Agony deals 1.5 ATK over 3 turns and is backloaded; Wild Magic adds 0.25 to each attack for 5 turns, which is 1.25 ATK total if you use basic attacks; Spectral Strike deals 2 ATK of damage but requires the target to be blinded; Lift-Off takes 2 rounds, avoids an attack (1 ATK), and then deals 1.75 ATK with an accuracy of 80% (1.4 ATK expected value), for a total of 1.2 ATK per turn over two turns; Surge of Power deals 2.5 ATK but costs you 3 turns; Wind-Up deals 2.25 ATK but takes 2 turns; etc.

Defensive moves such as heals, avoidance, and CC seem to have a slightly higher ATK ratio—closer to 1.5. I think this is because heals are reactive—they are only worth using if they heal more than the average damage you take (otherwise you should always choose to attack instead). Avoidance and CC is anticipatory, and due to the turn system gains value with speed. So for example, Healing Wave heals for 1.5 ATK, with a 3 round cooldown (1.125 ATK per turn on average). Dodge and Crystal Prison are 1 ATK if slower and 2 ATK if faster and have 5 round cooldowns: averaged over time this is neutral (1 ATK) if slower and 1.17 ATK per turn if faster.


7. Adding stats to the system: health beats power beats health…

How do the pets’ stats interact with this balancing system? On the surface, it seems that things will get out of control pretty quickly if we just choose the highest power pet with the highest ATK ratio abilities. I would say that this actually is the case currently, but it’s due to a failure of implementation. That is, if abilities are all balanced properly compared to one another based on always yielding ~1 ATK or 1 turn of benefit, then you can allow stats to vary while still maintaining balance. That is, I submit that the system as a whole is well-balanced, and the current overpowered pets are the result of a failure to properly adhere to the balancing system. Hopefully this will become more clear after I explain the exceptions to the rule.

But, if every ability provides exactly 1 ATK of benefit per turn, then every moveset must provide exactly 1 ATK of benefit per turn as well. Under this condition, every turn provides the benefit of a basic attack, and in this case it’s also clear that average pets (breed 3s or breed 5s) will necessarily kill each other in 5 turns on average. From section 3, we also know that breed 4s will kill each other in 4 turns on average, and breed 6s will kill each other in 6 turns on average.

We also know from section 3 that in a fight that’s less than 5 rounds, health is a better choice than power. That is, in the case of a breed 4 vs breed 4 where the fight lasts only 4 rounds, then your opponent can gain an advantage by choosing health over power, and the best way to do this is with a breed 6. In a fight longer than 5 rounds, the opposite is true; so if you have breed 6 vs breed 6 (6 round fight), then your opponent can gain an advantage by choosing power over health, ie a breed 4. And notice that when you battle a breed 4 versus a breed 6, you get:

Breed 4 (1400 health/325 power) vs Breed 6 (1725 health/260 power)

Breed 4 kills the Breed 6 in 1725/345 = 5 rounds
Breed 6 kills the Breed 4 in 1400/280 = 5 rounds

The main conclusion here is that: if your opponent stacks power, then you can counter by stacking health, and you will return to the 5 turn break-even point; if your opponent stacks health, then you can counter by stacking power, and you will return to the 5 turn break-even point. Thus if the metagame swings toward high power, the natural counter is to choose health, and this in turn will push the average fight length back up to the ‘average’ fight length of 5 rounds. If the metagame swings toward high health, then the natural counter is to choose power, and this will push the average fight length back down to the average fight length of 5 rounds.

So to summarize: as long as abilities provide 1 ATK of benefit (on average), and as long as pets trade 1 power for 5 health, then the system will remain balanced. If people try to stack power, then the system self-corrects by allowing savvy players to gain the upper hand by choosing health instead. From section 5, we also know that stacking speed is not ideal: instead you want the speed that beats your opponent by as little as possible. Thus speed is also self-correcting: a savvy player can gain a benefit by choosing the speed that’s just barely higher than the opponent, and past a certain speed, the opponent can counter by sacrificing speed entirely in favor of power or health. Therefore the stats are in dynamic balance with one another: if they deviate from the mean, they will be pushed back toward the mean.


8. Where it all goes wrong.

In section 7 I made the claim that the ‘broken’ pets are a failure of implementation, and not a failure of the system itself. Now I’ll try to convince you of that, case by case. The failure in all of these cases is that somehow or other, the pet (or team) in question is able to break the fundamental rule that 1 turn equals 1 ATK equals 20% health.

(i) Reflection.

I’m sure a lot of people love Reflection and a lot of people hate it. It’s very broken. It 1) dodges all attacks for the turn (this is worth 1 ATK, like Dodge) and 2) returns the most recent attack (this is worth another 1 ATK, on average). So you spend 1 turn for 2 ATK, which is double what you should get. I’ve seen people argue that you can ‘play around’ Reflection, but even if you do, the best you can generally hope for is a wasted turn. That is, you almost never come out behind on a turn that you use Reflection. The upside, on the other hand, is enormous.

Case 1 – I Reflection, you pass: I’ve spent 1 turn to prevent you from dealing damage, and you’ve spent 1 turn to do nothing, so I essentially used Dodge, and the turn is neutral (1 ATK).
Case 2 – I Reflection, you use Punch: I’ve spent 1 turn to prevent your attack (1 ATK) and deal 1 ATK to you (total of 2 ATK).
Case 3 – I Reflection on the turn that Elementium Bolt is going to land, you pass because you know I’m going to Reflection: I’ve spent 1 turn to prevent you from dealing damage (1 ATK) and hit you with Elementium Bolt (2 ATK plus a stun, which is another 1 ATK).
Case 4 – I Reflection, you Explode: ok ok, you genuinely outplayed Reflection in this case.


(ii) Wish.

If 1 action is supposed to be equivalent to 20% health, then Wish gives you 2.5 actions’ worth of healing (2.5 ATK). More on this in part (v).


(iii) Ghostly Bite

Ghostly Bite does 2.5 ATK of damage, then stuns you for a turn afterward (ie it costs you 1 ATK on the next turn). Normally this is a net gain of 1.5 ATK for 1 turn, which is pretty high. But of course you can just swap the Biter out. Swapping also costs 1 turn or 1 ATK, so if you were going to swap out anyway, then you completely avoid the ‘cost’ of being stunned. Also, Ghostly Bite is upfront damage. Compare this to two separate attacks of 1.25 ATK each: Ghostly Bite gets to deal the 2nd batch of damage 1 round earlier—it essentially gets to ‘go first’ for the 2nd batch of damage, regardless of speed. If this is the killing blow, then Ghostly Bite has given the Biter the advantage of going first, without having to be faster. In section 5 I tried to quantify the value of going first—it’s generally at least 1 ATK. Needless to say, Ghostly Bite gives you enormous value for such an easily avoided drawback.


(iiii) Stacking Multipliers (Fluxfire Feline, Anodized Robo-Cub, Chrominius, Mr. Bigglesworth, Spectral Tiger Cub, Feline Familiar)

In section 6 I said “if abilities are all designed to provide a benefit that’s roughly equivalent to 1 turn/1 ATK ratio/20% health; and if this leads to abilities that are balanced in isolation, then any 3 of those abilities (ie a moveset) should also be balanced.” What I really meant was “… if this leads to abilities that are balanced additively in isolation…”

If you take two abilities that deal 1 ATK of damage on average, and combine them additively, then you always get 2 ATK of damage. For example, take Chew (1.25 ATK) + Wind-Up (2.25 ATK over 2 turns): this is just 3.5 ATK over 3 turns, or 1.17 ATK per turn. No big deal.

If you take two abilities that deal 1 ATK of damage on average, and combine them multiplicatively, then the result depends completely on how that damage is spread out: high ATK abilities will combine to give higher-than-average damage. In this case take the PTR Supercharge (also 1.25 ATK, just like Chew, but it multiplies rather than adds) + Wind-Up (2.25 ATK over 2 turns): now you get 2.25*2.25 = 5 ATK over 3 turns, or 1.67 ATK per turn.

For reference, Wind-Up+Supercharge is 5.6 ATK on live; Supercharge+Demolish is 5 ATK; Howl+Surge of Power is 5 ATK; Prowl + Ice Tomb is 5 ATK; Prowl + Spectral Strike is 5 ATK; Prowl + Call Darkness is 3.75 ATK.

This is speculation, but I don’t think it’s coincidental that 4 out of 6 of these problem pets are from 5.1. I suspect that somebody decided to push the envelope a bit. It’s also possible that they simply forgot their own balancing rules between MoP and 5.1, but I doubt that.


(v) Shields and double-dipping.

Let’s look at Shell Shield, which is the same as Emerald Presence: it blocks 0.25 ATK per hit, and lasts 5 rounds. Against 5 Punches, this yields a total ATK of 1.25—only slightly above 1, and takes 5 turns to provide its full benefit. On the surface this looks fine.

However, like stacking multipliers, the details of how the damage is dealt makes all the difference. Against Punch, Shell Shield is 1.25 ATK. Against Slicing Wind, Shell Shield blocks twice per turn on average—since you get the benefit of the shield twice, this is called double-dipping, for a total of 2.5 ATK. Against Stampede, which is broken into 3 hits per turn, Shell Shield blocks 3.75 ATK.

Any time damage is split into chunks that are less than 1 ATK each, Shell Shield will overperform its apparent 1.25 ATK. Conversely, any time damage comes in chunks that are larger than 1 ATK (e.g. Wind-Up, Elementium Bolt), Shell Shield will underperform. The former are far more common than the latter, however, and includes all DoTs, all multi-hit attacks, and a few abilities that deal bonus damage if particular requirements are met: Tail Whip, Alpha Strike/Pounce, Conflagrate, and Early Advantage.

For a more concrete example let’s take Lil’ Ragnaros’ moveset of Sulfuras Smash (1 ATK)/Conflagrate (1.25 ATK, plus 1.25 ATK if burning)/Flamethrower (0.75 ATK upfront, plus 0.15 ATK per turn for 3 turns). If Lil’ Rag uses a cycle of Flamethrower, Conflag, Smash, Smash, Smash, then here is his ATK over 5 turns, with each turn split into its own parentheses:

(0.75+0.15)+(1.25+1.25+0.15)+(1+0.15)+(1)+(1) /5 = 1.34 per turn.

This is pretty high, which just confirms what we already knew--that Rag is a pretty strong pet. If the opponent has 5 ATK worth of health, it will die after 4 turns.

But, here’s what happens to that moveset versus Shell Shield:

(0.5+0)+(1+1+0)+(0.75+0)+(0.75)+(0.75) /5 = 0.95 per turn.

So Shell Shield prevented 0.39 ATK per turn over 5 turns in this situation, for a total of 1.95 ATK for the cost of 1 action. From this example it’s pretty clear that shields have the potential to prevent a disproportionately large amount of damage, even under fairly routine circumstances. In this case, if the opponent has 5 ATK worth of health, it takes a full 6 turns to kill it, as opposed to 4 turns without.


(vi) Heals scale too well with power and/or the length of the fight.

In part (ii) I promised I’d come back to Wish; now that we’ve talked about Shell Shield, we can discuss Magical Crawdad and his friends Emerald Proto-Whelp and Anubisath Idol.

In section 7, I claimed that power and health are balanced because stacking power makes health more valuable (and vice versa). This is because stacking power increases incoming damage and shortens the fight, which means you get to take fewer actions and therefore get fewer opportunities to convert power into damage. But this idea is based on the assumption that pets are using their power to deal damage. What happens when a pet decides to heal instead? Two related and potentially bad things happen. First, healing necessarily makes the fight take longer, which makes power more valuable: and second, since most heals scale with power, stacking power makes the fight take longer. So whereas damage+power pushes the balance toward a 5 round fight and balanced stats, healing+power reinforce each other and push the balance toward longer and longer fights, and higher and higher power (or health, in the case of Wish).

As noted in section 6, heals tend to have ATK ratios that are higher than 1. Wish is an extreme case, at 2.5 ATK. Emerald Dream is (0.5+1+2) = 3.5, and costs 3 turns, for an average of 1.17 per turn. Anubisath’s healing is 4% of his health each time he attacks (which is only 0.2 ATK), but it doesn’t cost any actions. Emerald Dream scales with power; Wish and the humanoid passive scale with health; but importantly, they all scale with the length of the fight. This is because as long as your healing per action is higher than your opponent’s damage per action, then you always gain a health advantage by using your heal. Healing per action is ATK*power (or 0.5*health for Wish), and since heals get ATK>1 whereas damaging abilities typically have ATK=1, then healing per action tends to be higher than damage per action. So healing is generally advantageous, and if using a heal once is an advantage, then using it twice is double the advantage: the longer the fight, the more heals you get, and the more health advantage you get.

Note that the humanoid passive doesn’t cost any actions, so healing per action is always a net positive, regardless of power or health.

Now, most heals have longish cooldowns (Wish, Emerald Dream) or are very weak (humanoid passive), and so by themselves they’re not enough to lengthen the fight to the point where healing is overwhelmingly strong.

This is where shields come into the picture. Since shields are an overly efficient way to lengthen the fight, they compound the effect of heals. Let’s revisit the Lil’ Rag versus Shell Shield example from part (v), but now let’s give Lil Rag’s opponent the humanoid passive and 5 ATK worth of health.*** The opponent’s health looks like this, split into turns as before:

Without shield
5 - (0.75+0.15)+0.2 - (1.25+1.25+0.15)+0.2 - (1+0.15)+0.2 - (1) = -0.1
ie, the opponent just barely dies on turn 4, before their humanoid passive can kick in and save them. In this case the humanoid passive has provided 0.6 ATK, or 12% extra health, but the pet dies on turn 4 with or without that extra healing.

With shield
5 - (0.5+0)+0.2 - (1+1+0)+0.2 - (0.75+0)+0.2 - (0.75)+0.2 - (0.75)+0.2 - (0.5+0)+0.2 - (1+1+0) = -1.05
now the opponent dies on turn 7, and the humanoid passive has provided 1.2 ATK or 24% extra health: the shield allowed the heal to provide 0.6 ATK or 12% more health. And, whereas the shield alone bought 2 extra turns, and the heal alone bought 0 turns: the shield+heal bought 3 turns.

That is, shield+heal is more than the sum of its parts. They synergize by lengthening the fight and providing more opportunity to gain health.

Since they’re nerfing Conflagrate down to 1.5+0.5 ATK, instead of the current 1.25+1.25, let’s try one last example.

5.2 Conflagrate vs Shell Shield, with humanoid passive:
5 - (0.5+0)+0.2 - (1.25+0.25+0)+0.2 - (0.75+0)+0.2 - (0.75)+0.2 - (0.75)+0.2 - (0.5+0)+0.2 - (1.25+0.25+0) = -0.05
It still takes 7 turns to kill the opponent, same as in 5.1, but you’ve dealt 1 ATK less damage and are very close to letting them live an extra turn.

This is a good reason why people are beginning to worry about the strength of shield/heal teams in 5.2. Burst damage is being nerfed across the board, and at some point incoming damage is just not enough to ever kill these tank pets. Whether we hit that point in 5.2 remains to be seen.


(vii) Weather and the cost of swapping

Weather and team buffs have a fundamental problem: they require a pet swap to take advantage of, and that costs a turn. If you believe me so far, then a turn is worth roughly 20% of a pet’s health, or 1 ATK. That’s pretty huge. So in order for a weather+pet swap to be worthwhile, you have to get a pretty large advantage from it—in fact, you have to get exactly 1 turn or 1 ATK worth of benefit in order to break even. For example, look at Nocturnal Strike, which is 2 ATK with 50% accuracy, but 100% accuracy if the target is blinded. So Nocturnal Strike is 1 ATK without Darkness and 2 ATK with Darkness. If you cast Darkness, then swap, then Nocturnal Strike, you’ve lost a turn to gain 1 ATK later, which is a fair trade.

But what if you can Nocturnal Strike twice? Now you are ahead by 1 ATK. If you can Nocturnal Strike 3 times in 1 Darkness, then you’re ahead by 2 ATK, etc.

The issue here is not so much that Darkness gives you an advantage, but the size of the advantage. Since swapping is so costly, that forces the benefit of swapping to be large. That in turn means that any time you can pay the cost once but get the benefit multiple times, you are gaining an extremely large advantage. If Darkness+swap+Spectral Strike is balanced, then Darkness+swap+Spectral Strike+Spectral Strike is way too strong.

And what if you can Nocturnal Strike without swapping, ie if you’re a Gilnean Raven? In this case you get all the benefit and none of the drawback. Gilnean Raven has an absurd moveset: Darkness is 1.5, Nocturnal Strike is 2 under Darkness, and Alpha Strike is 1.2 if faster—a slightly non-optimal cycle of Darkness, Nocturnal, Alpha, Alpha, Alpha is 1.42 ATK per turn on average, which is even higher than Lil’ Rag. If you had to set up Darkness with another pet and swap, then you’re down to 1.183 ATK per turn, which is worse than just Alpha Striking.

You might recall that sometime prior to 5.1, weathers such as Darkness and Call Blizzard had their damage buffed from 9 base damage to 30. I suspect that they realized nobody was using weather, because the cost of swapping was so punitive, and decided to make weather a worthwhile button to push regardless of its longterm effects. I think this also inadvertently gave Feline Familiar a decent nuke to use with Prowl, whereas before they had avoided Prowl/Supercharge + nuke.

For another example let’s look at the team buff Uncanny Luck. The downside here is that Uncanny Luck only lasts 4 rounds, and it does zero damage by itself (0 ATK). The upside is that you can use it with spammable attacks like Demolish (1 ATK normally; 2 ATK with +50% hit). But the result is more or less the same. Let’s consider a sequence of turns, assuming your opponent always does something productive on their turn (ie something worth 1 ATK on average):

Turn 1. Uncanny Luck (behind by 1 ATK)
Turn 2. Swap (behind by 2 ATK)
Turn 3. Demolish (behind by 1 ATK)
Turn 4. Demolish (break even)
Turn 5. Demolish (ahead by 1 ATK – Uncanny Luck fades at this point)


(viii) Backrow cooling and degenerate combos

Prior to 5.1, abilities only cooled down on the frontline pet. This made the cost of swapping even worse than it is now, however it also prevented stupid combos such as double Basilisk or double Snowman or triple Turkey.

How does this relate to ATK and the value of a turn? Well, CC abilities are worth one extra turn if you’re faster (e.g. Dodge is worth 1 turn or 1 ATK if slower; 2 turns or 2 ATK if faster). As discussed above, the cost of 1 turn is pretty much fixed at 20% health, which is rather large. So in order to make CCs balanced, they need to have their advantage spread out over multiple turns. Ie, they need cooldowns. So for example Dodge has a cooldown of 5 rounds, meaning that if you’re faster, that 2 ATK is spread out over 6 rounds and is worth 1.17 ATK on average. This is no big deal.

What does backrow cooling do? It allows you to circumvent cooldowns by playing multiple copies of a pet—now you can pay the cost of a pet swap (1 ATK) in order to get a fresh copy of the pet with a fresh cooldown. To take advantage of that, you need to find an ability worth more than 2 ATK.

Let’s look at double Snowman. Snowman, incidentally, has the same issue as Gilnean Raven: he has Call Blizzard (1.5 ATK) and Deep Freeze in the same moveset (1.5 ATK, plus a stun if under Blizzard {2 ATK if faster, 1 ATK if slower}). One snowman is bad enough, but if you have two, then you can pay the cost of a pet swap in order to retrieve the fresh snowman, who can immediately pay one turn to Deep Freeze (3.5 ATK if faster, 2.5 ATK if slower). From above, we know that if you can swap pets in order to gain an extra 1 ATK later, then it’s worth it. In this case you gain 1.5 extra ATK if slower and 2.5 extra ATK if faster. And since the cooldown of Deep Freeze allows it, you can Deep Freeze, swap, Deep Freeze, swap, Deep Freeze, swap, and on and on.

This problem is made worse by the fact that if you’re faster, you get a full 2 turns worth of stun. So you can pay 1 turn and 1 action to get a 2 turn stun, which conveniently keeps the opponent stunned forever.

*** for this example, I'm also technically replacing Shell Shield with Sandstorm -- the only difference for the purpose of this example is that Sandstorm triggers the humanoid passive.
Last edited by Poofah on March 7th, 2013, 4:54 pm, edited 1 time in total.

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Re: Stats, breeds, mechanics, and math

Post by Gendou » February 22nd, 2013, 4:36 pm

Good lord.

... maybe I should stone a second and third snowman ... Image
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Re: Stats, breeds, mechanics, and math

Post by Adorich » February 22nd, 2013, 8:12 pm

Being a devil's advocate on poofah's posts:

While a P/P might on average do more damage than a H/P, it's possible for a H/P pet to do more damage than a P/P pet, because abilities hit for a range of amounts rather than the same amount each hit. Health/speed also impact survivability, thus damage as well. It's entirely possible that H/H, H/P, P/S, B/B, S?S (and so on) is better than a P?P or visa versa. Plus, your opponent's stats and abilities will impact your pet's overall damage/survivability as well. The importance of pet speed, health and power will vary with each pet and opponent in every battle.

Poofah's has posted some interesting formulas, but has no data supporting them. At this point all we have is personal experience to evaluate their accuracy. Keep this in mind before dumping a pet that might be very good. Also, please beware of anyone who claims [insert pet] or [insert pet breed] is best in every situation.

Statistically, pet breeds may not be significantly different at all-- we just don't know at this point-- so posting 1(power0+5(health)/1(speed)= "best pet" formulas will only confuse players more than help us. :)

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Re: Stats, breeds, mechanics, and math

Post by Gendou » February 22nd, 2013, 9:01 pm

Adorich wrote:While a P/P might on average do more damage than a H/P, it's possible for a H/P pet to do more damage than a P/P pet, because abilities hit for a range of amounts rather than the same amount each hit.
But over time, the average will be be the same.
Health/speed also impact survivability, thus damage as well. It's entirely possible that H/H, H/P, P/S, B/B, S?S (and so on) is better than a P?P or visa versa. Plus, your opponent's stats and abilities will impact your pet's overall damage/survivability as well. The importance of pet speed, health and power will vary with each pet and opponent in every battle.
No one is denying that - certain pets and builds are better using different breeds.
Poofah's has posted some interesting formulas, but has no data supporting them.
The data is available to anyone playing the game.
We don't need an API pull to know how much an ability hits for relative to power stat.
At this point all we have is personal experience to evaluate their accuracy. Keep this in mind before dumping a pet that might be very good. Also, please beware of anyone who claims [insert pet] or [insert pet breed] is best in every situation.
I don't believe anyone has claimed that anything is best in every situation, or else there would just be a post saying, "Use Breed 4 Yellow Moth for every fight." But there's nothing like that - instead, there's a great deal of theorycrafting about what makes a particular breed superior in a particular situation against a particular opponent. Just reading over the information about the 5 round breakpoint for health vs. power belies your assertion that particular breeds and pets are being advocated for every situation.
Statistically, pet breeds may not be significantly different at all-- we just don't know at this point-- so posting 1(power0+5(health)/1(speed)= "best pet" formulas will only confuse players more than help us. :)
You're free to ignore the data if you like, but some of us like to consider the maths behind the curtain.
It's hardly confusing, especially when it's presented in such a layman-friendly way as these posts.

It seems as though you have an issue with theorycrafting in general.
That being the case, this may not be a thread you'd particularly enjoy given the focus on numbers.
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Re: Stats, breeds, mechanics, and math

Post by Ryazan » February 23rd, 2013, 2:30 pm

Good stuff again Poofah, I actually had stop doing my pet battles for a while and focus to reading :)

Keep'em coming!
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Re: Stats, breeds, mechanics, and math

Post by Lilhottie » February 24th, 2013, 12:18 am

I think poofah just found another major Payne killer. Tomorrow I will test Kun-lai Runt + Tiny snowman. :twisted:

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Re: Stats, breeds, mechanics, and math

Post by Ryazan » March 7th, 2013, 12:52 am

I've so far noticed few mechanic changes in 5.2 and first is how the blocking abilities work. They now really block everything instead of blocking just one hit per round. Few examples:

- Moth Balls / Flurry etc. - all attacks are blocked instead of the first hit
- Acidic Goo - Dots which don't deal damage on initial hit gets now blocked too

Second change doesn't directly impact battling mechanics but to tamers instead. I noticed tamers now have fixed initial pets or me trying to get Antari's elemental come as first pet in vain for like 6 minutes was just AWFUL streak of bad luck. :P I guess this is due to the fact forfeit penalty was applied to tamers too at first.

Has anyone noticed something else? I saw someone mentioned about shields absorbing more or...?
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Re: Stats, breeds, mechanics, and math

Post by Darkke » March 7th, 2013, 3:08 pm

I love your posts and analysis! Puts common sense things into a quantitative form.

Not to be too nit-picky, but in "8.VI" you overestimate the benefit of the shield and human passive.
Poofah wrote:With Shield
5 - (0.5+0)+0.2 - (1+1+0)+0.2 - (0.75+0)+0.2 - (0.75)+0.2 - (0.75)+0.2 - (0.5+0)+0.2 - (1+1+0) = -1.05
now the opponent dies on turn 7, and the humanoid passive has provided 1.2 ATK or 24% extra health: the shield allowed the heal to provide 0.6 ATK or 12% more health. And, whereas the shield alone bought 2 extra turns, and the heal alone bought 0 turns: the shield+heal bought 3 turns.
Unless they changed it in the patch, don't you have to attack to get the humanoid passive's benefit? So if you're using a shield, it should read along more like this:

5 - (Shield used)(0.5+0) - (1+1+0)+0.2 - (0.75+0)+0.2 - (0.75)+0.2 - (0.75)+0.2 - (0.5+0)+0.2 - (Shield Used)(1+1+0) = -1.85

This is also making the assumption that:
1. You're faster than the opponent, a safe bet with the Lil Ragnoros example, meaning your shield reduces the damage of the first turn.
2. On turn 7, you would be refreshing the shield, or else the damage that turn would be higher. (Used on the first turn, up for 5 turns, and would go before the opponent on turn 7)


The heal and shield combination still provides a 3 turn benefit, but the length of this hypothetical battle would decrease if the opponent is faster than your shield user.

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Re: Stats, breeds, mechanics, and math

Post by Poofah » March 7th, 2013, 4:50 pm

Yes, you are right. I was actually thinking about Sandstorm in that example (which does trigger the humanoid passive), since you can probably guess that the example is about Anubisath Idol--I'll edit it.

The point about going first is definitely true. In general I'm assuming that we're looking at a sequence of attacks in the middle of a fight, as opposed to from the very start. That makes it a lot easier to talk about 'average' damage for a set of moves or moveset, but it doesn't capture the whole story. For the same reason, speed is the hardest stat to place an average value on, because its benefits depend so much on the specific pet you're fighting and the specific circumstances of the fight.

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Re: Stats, breeds, mechanics, and math

Post by Arcanicus » March 7th, 2013, 6:45 pm

The math here leads me to believe that Wild Magic will become a lot more valuable for off-setting abilities like Shell Shield, since it double dips offensively on multi-hit abilities. You might want to math that one out.

Considering that Ice Tomb + Stampede is still a fairly potent combo even after 5.2 nerfs, I'd say that Azure Whelpling (which has both Wild Magic and Ice Tomb) just migrated to the top tier of battle pets. Thoughts?

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Re: Stats, breeds, mechanics, and math

Post by Poofah » March 7th, 2013, 7:51 pm

Wild Magic double-dips the same as Shell Shield, that's true. That's why Wild Magic plus DoTs or Stampede or Build Turret is so mean--or the new Zandalari Raptors, which are bonkers with Black Claw + Hunting Party.* And it does offset Shell Shield--if the pets have equal power, then they precisely cancel each other out. However I don't think this makes Wild Magic a particularly good counter for Shell Shield. That's because in order to abuse Wild Magic, you have to play with gimmicky pets/abilities. Without Wild Magic, they become very ordinary, and that's exactly what happens versus Shell Shield. Put another way -- Wild Magic allows you to restore your damage output to 'normal' levels, but since your team is built to operate with Wild Magic (ie Siphon Life/Stampede/Build Turret), your normal damage output isn't necessarily very good.

If I knew I had to face Shell Shield/Sandstorm, I'd opt for damage in the largest packets possible, ie Pump/Wind-Up or similar charge-up abilities. Shell Shield 'half-dips' Wind-Up, so you gain an advantage this way, as opposed to returning to parity with Wild Magic. Ice Tomb is a good example too--it deals its damage in one big chunk of 2*(20+power), so it's minimally impacted by Shell Shield.

*The reason Wild Magic+Stampede is so nasty is that addition is handled before multiplication when calculating damage.** So Wild Magic adds its bonus damage to each of the 3 Stampede hits, and is then multiplied by 2, so you get to six-dip in this case.

** except the aquatic passive--this applies before any other damage modifiers, even though it's a multiplier--don't ask me why.

And one last point, specifically about Stampede+Ice Tomb: prior to 5.2, if you Stampeded into a Shell Shield, you would see 'block block block', but it would still apply the Stampede debuff. Now, if the damage is completely blocked, the Stampede debuff is not applied. That makes it harder to pull off an Ice Tomb+Stampede. But Ice Tomb by itself is already pretty strong against shields (unless the shield pet also happens to have Deflection).

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Re: Stats, breeds, mechanics, and math

Post by Darkke » March 8th, 2013, 11:36 am

Question for you Poofah, brought to mind by your mention of anubisath idol:

1. Do shields work together? For example, Sandstorm and Shell Shield.

2. If they do work together, do we see any of the funky multiplicative behavior, or is it just additive?


I can imagine at least one other scenario were a weather debuff could interact interestingly with an applied debuff. Darkflame and Call Darkness would be interesting to see combined, even if it's fairly impractical in the current meta.

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Re: Stats, breeds, mechanics, and math

Post by Poofah » March 8th, 2013, 12:29 pm

They do work together additively, so Sandstorm+Stoneskin with Anubisath Idol is 74+74 = 148 damage reduction per hit. This 148 is subtracted before any multipliers, which makes it surprisingly effective against burst damage that relies on debuffs (such as Prowl/Howl/Stampede -- a pet with 280 power normally can Prowl+Claw for 2.5*300 = 750 damage, but against Anubisath's double shield, it's down to 2.5*(300-148) = 380), and it subtracts from each hit of multi-hit abilities such as Conflagrate and Alpha Strike.

I've never tested Darkflame+Call Darkness -- based on the way other debuffs interact, my assumption is that it would be multiplicative, and would reduce heals down to 25% of normal.

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Re: Stats, breeds, mechanics, and math

Post by Poofah » April 30th, 2013, 7:00 pm

9. 5.3 (ptr edition)

I want to revisit this old post because if things stay as they are on PTR, then balance is going to change subtly but fundamentally in 5.3. The relevant parts to reread would be section 1 and especially section 6. But they’re long and you don’t want to do that, so I’ll just summarize those sections:

Summary – Abilities are balanced against one another according to 1 turn equals 20% health.

The fundamental reason this is true is because of the way basic attacks like Bite and Punch scale: they always deal 1*(20+power) damage, and this is 20% of an average pet’s health because the game values 1 power = 5 health (ie when you trade a breed 4 for a breed 6, you are trading 65 power for 325 health). In 5.3, if ptr stays as it is currently, this is no longer true. Here’s why:
As noted earlier, the following basic attacks have had their damage increased by 10-30% and accuracy reduced by 5-15%... (from the [url=http://%20http://us.battle.net/wow/en/blog/9425567/]pet battle accuracy change blog[/url])
Notice that damage is going up for these abilities by 10-30% while accuracy is only being reduced by 5-15%. Here are some examples from ptr:

[url=http://ptr.wowdb.com/pet-abilities/111-punch]Punch[/url] -- 100% accuracy, 20 damage, so over time you’ll get 1*20 = 20 expected damage. This is the same as basic attacks on live. No problem so far.
[url=http://ptr.wowdb.com/pet-abilities/429-claw]Claw[/url] – 90% accuracy, 24 damage, so over time you’ll get 0.9*24 = 21.6 expected damage. This is 8% more damage than Claw on live.
[url=http://ptr.wowdb.com/pet-abilities/406-crush]Crush[/url] – 80% accuracy, 28 damage, so over time you’ll get 0.8*28 = 22.4 expected damage. This is 12% more damage than Crush on live.

Why is this a problem? Let’s revisit the example from section 7, where a breed 4 fights a breed 6 using Punch or Bite or any other basic attack in 5.2.

Breed 4 (1400 health/325 power) vs Breed 6 (1725 health/260 power)

Breed 4 kills the Breed 6 in 1725/345 = 5 rounds
Breed 6 kills the Breed 4 in 1400/280 = 5 rounds

This is great: they are evenly matched, which means that power is not better than health and health is not better than power. And the fight lasts exactly 5 rounds, which means a turn really is worth 20% of a pet’s health.

Now, what happens in 5.3, if we give both of these pets Crush, which does 12% more damage than Punch? Now we get

Breed 4 (1400 health/325 power, Crush does 1.12*(325+20) = 386 damage) vs Breed 6 (1725 health/260 power, Crush does 1.12*(260+20) = 314 damage)

Breed 4 kills the Breed 6 in 1725/386 = 4.47 rounds
Breed 6 kills the Breed 4 in 1400/314 = 4.46 rounds

So a Crusher versus a Crusher are still evenly matched, which is good. But the fight only lasted 4.46 rounds, which means that a turn is now worth more than 20% of a pet’s health—in fact it’s now worth 22.4% of a pet’s health. Why is that bad? There are two reasons:

First, since the fight got shorter and turns became more valuable, going first also became more valuable. This means that whenever Crush or other low-accuracy abilities are involved, speed will be more valuable in 5.3 than in 5.2. Since speed was already situational and arguably could stand to be buffed, this shouldn’t be a major problem.

The second and larger problem is that all the pre-5.3 abilities were balanced around a turn being worth 20% of a pet’s health, and they haven’t been updated on the ptr. That means those old abilities just got a lot worse in comparison. To see that, let’s have a Punch pet fight a Crush pet:

Breed 4 with Punch (1400 health/325 power, Punch does 1*(325+20) = 345 damage) vs Breed 4 with Crush (1400 health/325 power, Crush does 1.12*(325+20) = 386 damage)

Breed 4 Puncher kills the Breed 4 in 1400/345 = 4.05 rounds
Breed 4 Crusher kills the Breed 4 in 1400/386 = 3.63 rounds

and

Breed 6 with Punch (1725 health/260 power, Punch does 1*(260+20) = 280 damage) vs Breed 6 with Crush (1725 health/260 power, Crush does 1.12*(260+20) = 314 damage)

Breed 6 Puncher kills the Breed 6 in 1725/280 = 6.16 rounds
Breed 6 Crusher kills the Breed 6 in 1725/314 = 5.49 rounds


Regardless of breed, Crushers beat Punchers. In 5.3, expect the minority of pets with these new low-accuracy/high-damage attacks to become stronger than they are now. You can check out the list of ptr abilities at [url=http://ptr.wowdb.com/pet-abilities]http://ptr.wowdb.com/pet-abilities[/url] – accuracy is shown in the righthand column. The best abilities are the 80% accuracy/28 damage ones, and note that not every 5.2 ability got updated, so don’t go by accuracy alone.

Tl;dr – In 5.3, the new low-accuracy attacks are numerically superior to pre-5.3 attacks, and not all abilities were updated. Abilities are not balanced against one another as consistently as in 5.2, and therefore the pets that have these low-accuracy abilities will be stronger than pets without them.

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Re: Stats, breeds, mechanics, and math

Post by Arcanicus » May 1st, 2013, 10:29 am

The buffs are bigger than you claim, since accuracy is effectively 90% on live, not 100%. Also, their blog seems to be understating the buffs, as I note below.

Recalculating with that in mind:
100% accuracy move with 20 power (10% accuracy increase): 11.1% buff (Keep in mind this buff is applied to almost all offensive moves, not just the basic moves.)
90% accuracy move with 24 power (20% damage increase) : 20% buff
80% accuracy move with 28 power (40% damage increase, 10% accuracy decrease): just under 25% buff.

So yes, they are accelerating the pace of pet battles, which is a stealth nerf to certain defensive abilities (and is probably where the real analysis needs to occur, to determine which defensive combos are no longer viable).

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Re: Stats, breeds, mechanics, and math

Post by Saasan » May 1st, 2013, 11:35 am

Bravo, Poofah! This is top rate stuff that I will study in detail. Thank you for your time and effort!

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Re: Stats, breeds, mechanics, and math

Post by Poofah » May 1st, 2013, 1:45 pm

Arcanicus wrote:The buffs are ...
Those are great points. I calculated the duration of a fight as being 5 turns, but you're right that on live it's actually slower due to misses/dodges. So practically we're not going from 5 turn fights to 4.5 turns fights, it's more like 5.5 to 4.5 turns.

I agree that a shorter fight will hurt defensive strategies, but I think it depends on the type of strategy. The basic issue is that offensive moves are gaining effectiveness: all moves are getting a stealth buff to accuracy, as you say, and a handful of RNG moves are getting a raw numerical increase on top of that. Defensive strategies that rely on heals will absolutely be weaker, because none of the heals got buffs to compensate for the bigger hits. The big exception to that is the humanoid passive, which will keep pace with most offensive abilities since it benefits from the same accuracy buffs. On the other hand, defensive strategies that rely on negating the opponent's turns (ie dodges and CC) should actually become stronger, because turns are worth more.

The biggest issue I see is that a select handful of pets received the new and improved RNG attacks, and these pets will have a significant numerical advantage over the others. When choosing pets, access to one of these buffed up RNG attacks is going to be a big factor, which will narrow the field of competitive pets even further than it is now.

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Re: Stats, breeds, mechanics, and math

Post by Arcanicus » May 1st, 2013, 6:48 pm

Three other things to keep in mind:

First, any Lifesteal abilities (Absorb, Leech Seed, etc.) also benefit from the accuracy buff just like the humanoid racial. While direct heals may not be viable, these will still have some usage.

Second, the undead and mechanical racials just shot up in importance, especially the former. 1-2 guaranteed extra turns in this environment is unbelievably good. Expect to see more of these families on every team.

Third, this also hurts any DOT based pets. Since most DOTs run into the same problem they do in the main game (slow ramp-up time), any pet that is forced to carry more than one just got voted off the competitive pet battle island. This already was a minor problem, but it just got elevated to a major one.

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Re: Stats, breeds, mechanics, and math

Post by Tekulve2012 » May 1st, 2013, 7:16 pm

1) I love Poofah's analysis and commitment to statistical breakdown
of moves,turn values and move set combos that
are more and less efficient and effective

2) if I ever have to face Poofah's in pet pvp I plan
to mystify and dazzle him with a senseless
team like a marsh fiddler, brown prairie dog and
sinister squashling

3) the question some may be secretly wondering is
what 2 or 3 optimal teams you'd field in the upcoming
Pvp blitz for a direhorn (feel free to mix up reasonably
Easy to acquires and rarer ones ..) I see a possible
use of new ones like spectral porcupette and animus

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Re: Stats, breeds, mechanics, and math

Post by Poofah » May 1st, 2013, 8:10 pm

Arcanicus wrote:First, any Lifesteal abilities (Absorb, Leech Seed, etc.) also benefit from the accuracy buff just like the humanoid racial. While direct heals may not be viable, these will still have some usage
Direct heals are going to be weaker than they are now, but I think it's too early to say they won't be viable. Actually, some of the best healing pets also benefit from the new RNG abilities (Emerald Bite, Crush, and to a lesser extent Snap and Metal Fist). So they'll lose a bit of tanking power but gain some offense. And anyway, Anubisath Idol for example can afford to lose some power and still be very viable.

Regarding the lifesteal abilities, Absorb and Leech Seed did get better, but for example Consume and Deathcoil have 95% accuracy yet didn't get a damage buff. This underscores another big point: in 5.2, you could trust most attacks to be balanced numerically, but you can't any more, because some got updated with the new accuracy changes and some didn't. So we have to reevaluate every pet for things that didn't matter before. Specifically, if your pet has Crush, it got a sneaky 12% buff; if it has Punch instead, it didn't (meaning that it's actually nerfed relative to the field).

Totally agree regarding UD/Mech racials. The UD racial in particular has been overpowered since the beginning, and when turns become more valuable in 5.3 it's just going to get worse--I'm going to quote myself from the first page
The way racials are balanced against each other also seems tied to this idea that a fight will last 5 rounds (ie 1 turn = 20% health). At least in some cases. The clearest example is the Mech racial -- you rez with 20% health. The humanoid racial is +4% health per attack: if a fight lasts 5 rounds, that's 20% health. The critter racial is 1 less round of cc: if you're fighting a pet that spams one of the basic stun moves (e.g. Crystal Prison, 1 round stun with 5 round cd), then you gain 1 extra turn every 5 turns. So it seems like these racials are giving roughly the equivalent of 1 extra turn in a 5 turn fight.

By comparison, the UD racial is absurd. When you die, you get to rez and complete the turn. And then you get a free turn on top of that. So if you're faster, then you get 1 free turn. If you're slower, you get 2 free turns. This does two bad things: it makes speed almost completely irrelevant for a fight involving an UD, and it grants roughly double the benefit that other racials give.

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