Re: Stats, breeds, mechanics, and math
Posted: 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.
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.