Stats, breeds, mechanics, and math

[Poofah]

People often ask which breed is best for a particular pet. I wanted to post some observations about how pet battles appear to work, how stats determine damage, and how valuable the 3 stats are compared to one another. This info should help pick out which movesets are especially good, and which stats are best for those movesets.

p.s. it’s kind of long, and I hope you like math.


1. The damage formula:

Damage = (20 + power) * (baseDamage/20)

The baseDamage is how much the ability does with 0 power—this is the case for any greyed-out pet in your pet log. Or, you can use an online source such as wowdb. You can also use this site’s ability lists to find baseDamage, *however*, for whatever reason the values are calculated for a pet with 48 power, so you have to back-calculate.
(*edit* -- today, 4.30.13, the values are calculated for a pet with 374 power -- I have no idea what determines this or why it changed
*edit* -- 6.17.14 -- as it turns out, damage values are calculated for all pets as though they were Lil' Rag, who happens to have 374 power)

Heals and buffs/debuffs work exactly the same way. So for example Shell Shield prevents (20+power)*(5/20) damage from each hit; Healing Wave heals for (20+power)*(30/20), etc.


2. How the game values stats:

A pet gets 24 total stat points spread between health/power/speed, and then between 1.5 and 2 ‘bonus’ stat points—see petsear.ch for a great summary of how breeds work.

A ‘generic’ rare level 25 pet with 8/8/8 stats and no bonus stats will have 1400 health, 260 power, 260 speed. Breed 3 gets 0.5 bonus points to each stat, while Breeds 4-6 all get exactly 2 bonus points to one stat.

Breed 3: 1481 health/276 power/276 speed
Breed 4: 1400 health/325 power/260 speed
Breed 5: 1400 health/260 power/325 speed
Breed 6: 1725 health/260 power/260 speed

So you can trade 65 power for 65 speed, or 65 speed for 325 health, etc. From this it’s apparent that the game values these stats as follows

1 power = 1 speed = 5 health


3. How the stats contribute to winning:

The game thinks that 1 power is worth 5 health, but is this really an accurate value in an actual pet battle? Let’s find out:

Suppose that we take two generic 8/8/8 pets and pit them against each other, using only Punch. With 260 power, Punch deals (20+260)*(20/20) = 280 damage. Since they have 1400 health, it will take exactly 5 turns (1400/280) for the fight to end. The length of the fight determines the value of power, because each turn you get to Punch, and Punch deals exactly one extra damage for each extra point of power. In this case, if you give one of those pets 1 extra power, it will deal exactly 5 extra damage with Punch over the course of 5 turns. So in this example, 1 power really is equal to 5 health.

Let’s see how long the fight lasts for some other breeds:

Breed 3: 1481 health, 276 power; Punch deals 296 damage; 1481/296 = 5.00 turns
Breed 4: 1400 health, 325 power; Punch deals 345 damage; 1400/345 = 4.06 turns
Breed 5: 1400 health, 260 power; Punch deals 280 damage; 1400/280 = 5.00 turns
Breed 6: 1725 health, 260 power; Punch deals 280 damage; 1725/280 = 6.16 turns

So here are the first big conclusions, assuming these simple conditions of only using a basic attack like Punch:

The break-even point for power vs health is 5 turns. If the fight lasts exactly 5 turns, then 1 power = 5 health, which is the same value that the game places on these stats. If the fight lasts 4 turns, then power is only worth 4 health; if it lasts 6 turns, then power is worth 6 health. So, if the fight lasts less than 5 turns, power is worth less than the game values it, and you should choose health over power. If the fight lasts more than 5 turns, power is worth more than the game values it, and you should choose power over health.


4. Extending to non-basic attacks: the value of a turn.

Most fights entail more than Punch. How do we know the value of power when using other abilities? The key to this is in how damage scales with power. Remember that

Damage = (20 + power) * (baseDamage/20)

In this formula, power is scaled by (baseDamage/20). I’m going to call this value the ATK ratio. For Punch, the ATK ratio is 20/20, or 1. Thus Punch deals 1 extra damage for every 1 extra power you add. But what about other abilities? Let’s take Healing Wave as an example. Healing Wave heals you for 30 base damage, ie (20+power)*(30/20), so it has an ATK ratio of 1.5. Every time you use Healing Wave, you directly convert each point of power into 1.5 points of health. In this sense, a turn in which you use Healing Wave is ‘worth’ 1.5 times as much as a turn in which you use Punch. And, this gives us a way to calculate the value of a moveset, which in turn will tell us the new break-even point of power versus health.

For example, let’s look at an Emperor Crab, using Claw (1 ATK ratio), Healing Wave (1.5 ATK ratio), and Whirlpool (1.5 ATK ratio). Healing Wave and Whirlpool each have a 3 round cooldown, so let’s consider a cycle of 4 turns – Whirlpool, Claw, Claw, Healing Wave. The average ATK ratio of this set of moves is (1.5+1+1+1.5)/4 = 1.25.

What does this mean? It means that on an average turn, Emperor Crab gets to apply 1.25x of its power – either to add to its own health or subtract from the opponent’s. If the Crab fights for 5 turns, then 1 power is worth 5*1.25 = 6.25 health to him. If he fights for 4 turns, then 1 power is worth 4*1.25 = 5 health. Therefore, the break-even point for the crab is 4 turns: as long as the crab lives longer than 4 turns, then the crab will get more value from choosing power over health.


5. The value of speed

Speed is much harder to place an absolute value on, because it completely depends on the opponent’s speed. However, you can place a value on going first.

Let’s go back to the generic pets using Punch. 1400 health, 260 power, 280 damage per Punch, and the fight lasts 5 rounds. The pet who goes first will win with 280 health remaining. Therefore in this situation, going first was worth 280 health, which is equivalent to 20% health, and equivalent to 1 turn. We can also calculate the value of that extra turn in terms of power – in order for the slower pet to win, it would need to deal 1400 damage in 4 turns instead of 5. To do that, it would need to deal 350 damage per turn, and since Punch damage is (20+power)*(20/20), that means the slower pet would need 330 power, which is 70 more power than it has. Therefore, in this simple case, going first was ‘worth’ 70 power.

Now let’s look at two other cases:

Breed 4: 1400 health, 325 power, 345 damage per punch, and the fight lasts 4 turns. In order for the slower pet to win, it would need to deal 1400 damage in 3 turns, which requires 447 power, which is 122 more than it has – so going first is worth 122 power in this case.

Breed 6: 1725 health, 260 power, 280 damage per punch, and the fight lasts 6 turns. In order for the slower pet to win, it would need to deal 1725 damage in 5 turns, which requires 325 power, which is 65 more than it has.

The main point here is that unlike power, the value of going first decreases as the number of turns increases—therefore speed scales positively with power, and negatively with health. If neither pet has abilities that particularly benefit from going first, then you can calculate the value of going first as above. This is the break-even point for speed: if this value is higher than the difference between your speed and your opponent’s, then you would benefit by sacrificing other stats in order to go first.

However, the biggest benefit of going first is in using abilities such as Dodge, Flurry, and Kick. The value of going first is easy to calculate for these abilities, in terms of ATK ratio or in terms of turns.

For example, let’s look at Flayer Youngling—he can either choose breed 4 (325 power) and use Triple Snap (ATK ratio of 1), or he can choose breed 5 (260 power) and Blitz (ATK ratio of 1.25 when going first). In the breed 4 case, he deals 345 damage per turn with Triple Snap; in the breed 5 case, he deals 1.25*280=350 damage with Blitz.

Kick has an ATK ratio of 0.5, and prevents the opponent’s action if going first, so Kick is worth 0.5 turns if going last, and 1.5 turns if going first.

Dodge is similar: it avoids 1 attack if going last, and avoids 2 attacks if going first. Going first is worth one extra turn in both of these cases.

If we make the assumption that an opponent’s turn is worth 1 ATK ratio,* then this lets us incorporate the value of going first into the average ATK ratio for a pet’s moveset. For example, let’s take Rabbit.

If going first, Rabbit would use Flurry (1.25 ATK ratio); if going 2nd, Scratch (1 ATK ratio). Dodge is worth 2 turns if going first, 1 if going 2nd. Since we’re assuming that 1 Rabbit turn is equal to 1 opponent’s turn, we can say that Dodge is worth 2 ATK ratio if going first, and 1 ATK ratio if going last. The first half of Burrow avoids an attack (ATK ratio 1), and the 2nd half has an ATK ratio of 1.75 with 80% accuracy, for an expected value of 1.4 ATK ratio.

Dodge and Burrow both have 4 round cooldowns, so let’s consider a set of 5 moves: Dodge, Flurry, Flurry, Burrow(1), Burrow(2) – this moveset has a value of (2 + 1.25 + 1.25 + 1 + 1.4)/5 = 1.38 average ATK ratio, if going first.

If going second, Scratch would replace Flurry, and we’d have: Dodge, Scratch, Scratch, Burrow(1), Burrow(2), which is (1 + 1 + 1 + 1 + 1.4)/5 = 1.08 average ATK ratio.

By going first, the faster rabbit gets 0.3 ATK ratio extra out of each of its turns – even for a breed 5 rabbit with a fairly low 222 power, this means that going first is worth 0.3*222 = 67 power, in addition to the intrinsic benefit of going first.


* this is a bad assumption, but it actually underestimates the value of speed. This is because when you use Dodge, you are avoiding damage based on the opponenent’s power and not your own. In the case of a rabbit (or any fast pet), you’ve sacrificed power for speed, and the opponent’s power is likely to be higher. It’s possible to more accurately calculate the value of a turn in terms of both your pet’s power and your opponent’s, but it gets complicated.

[Gendou]

Good stuff, Poofah.

[Breanni]

Excellent post, Poofah! I hope you don't mind -- I edited your post to bold the subheads. It's the web designer in me. I couldn't resist!

Anyway, fantastic info. Thank you for sharing.

[Ryazan]

Poofah on the loose! ( ^^)b

[Stabya]

For those of us with ADD, does this mean one breed is better than the other? or it all depends?

[Poofah]

For those of us with ADD, does this mean one breed is better than the other? or it all depends?

I'll quote the most relevant part of the OP

For example, let’s look at an Emperor Crab, using Claw (1 ATK ratio), Healing Wave (1.5 ATK ratio), and Whirlpool (1.5 ATK ratio). Healing Wave and Whirlpool each have a 3 round cooldown, so let’s consider a cycle of 4 turns – Whirlpool, Claw, Claw, Healing Wave. The average ATK ratio of this set of moves is (1.5+1+1+1.5)/4 = 1.25.

What does this mean? It means that on an average turn, Emperor Crab gets to apply 1.25x of its power – either to add to its own health or subtract from the opponent’s. If the Crab fights for 5 turns, then 1 power is worth 5*1.25 = 6.25 health to him. If he fights for 4 turns, then 1 power is worth 4*1.25 = 5 health. Therefore, the break-even point for the crab is 4 turns: as long as the crab lives longer than 4 turns, then the crab will get more value from choosing power over health.

In some cases, one breed is clearly better; Emperor Crab is a good example of that, because his moveset lets you turn power into health/damage very efficiently.

Basically, power turns into damage/health over time. The ATK ratio tells you how efficiently the pet can turn power into damage/health on a per-turn basis. Every pet will have a break-even point: this is the number of turns where you would get exactly the same amount of benefit from choosing health or choosing power. If your pet can fight longer than this, it should choose power; if it fights for fewer turns than this, it should choose health.

For the crab, the break-even point is only 4 turns. It's rare for a pet to last fewer than 4 turns, and this is especially true for the crab because he has at least one heal, which prolongs the fight. Therefore a crab is almost always better with power over health. Emperor Crabs are pretty popular and have a breed 4 and breed 6, so I bet a lot of people have a feeling which one is better from experience.

In general, we choose pets with good movesets. This means that the break-even point will rarely be shorter than 5 turns, and at least in PvE, since we can choose good matchups, pets almost always last 5+ turns. This means that in PvE, power is almost always the best choice. There are a handful of exceptions, but these involve pets who have abilities that key off of health (e.g. humanoids, magical crawdad). In an environment where pets can die in 3-4 turns, like in PvP at the moment with all the burst teams, then health is actually better for most pets.

Speed is much more complicated, but a good rule of thumb is: if you are winning on speed by less than 70, you are gaining an advantage; otherwise you would be better off with power or health. Speed loses value as the fight becomes longer, so if you're a healing pet, you should probably not care about speed at all. If you're a pet with Dodge/Kick/Eyeblast/Flurry/Blitz or similar abilities, then going first is an extremely large advantage, and it's worth sacrificing almost any amount of power to get enough speed to go first.

[Gendou]

If you're a pet with Dodge/Kick/Eyeblast/Flurry/Blitz or similar abilities, then going first is an extremely large advantage, and it's worth sacrificing almost any amount of power to get enough speed to go first.

This is a good rule of thumb, especially for PvP.

The problem with doing this in PvE, however, is that against the highest tamers, they have Epic and Legendary pets.
Unless you have one of the [url=http://petsear.ch/Breeds/Ranking]Top Speedy Pets[/url], odds are good that the speed variant of a given pet won't be fast enough to let you go first anyway - in which case, Power is still the safer bet.

At least IMHO. Poofah might have math to show up my subjective experience on the matter.

[Poofah]

Sort of, yes. The ideal speed is 1 more than your opponent's--the minimal investment that still lets you go first. The worst possible speed is 1 less than your opponent's, for the same reason. So, if you think you're going to lose on speed, then you should not invest in speed at all.

In PvE, you know exactly what speed the opponent's pets have--Warla has that info posted on [url=http://petsear.ch/Breeds/TamerPets]petsear.ch[/url]. In this case, you can get a big advantage by choosing a pet that's just barely faster than the tamer's. If you can't be faster, then the slowest/strongest pet will be the best.

A good example of this is Lil' Ragnaros and Lil' Deathwing. They completely give up on going first, but as a result they get to stack a huge amount of power. In most cases, the power more than makes up for going 2nd. If they compromised and had a little more speed and a little less power, they would still be too slow to go first most of the time, and they'd be much weaker.

In PvP, you don't know the opponent's speed, so you have to guess what speeds you might face and how much it's worth to beat those speeds. In current PvP, going first is extremely valuable because burst is rampant and pets die very quickly. But even so, a lot of popular pets are very slow. Therefore in current PvP, you can gain a very large benefit with an intermediate speed pet. If you have 260 speed (e.g. a P/B pet) and the opponent has 244 (P/P), you're at a large advantage. And of course if the opponent then chooses a 276 speed pet (P/S maybe), then the tables are turned. Speed is a very interesting metagame stat for that reason.

In 5.2, burst is getting nerfed pretty severely, so I'd expect speed and health to lose value, while power should gain value, which in turn will make healing more valuable. Certain pets such as Rabbits and Flayers will always need speed, however, due to their movesets.

[Gendou]

In PvE, you know exactly what speed the opponent's pets have--Warla has that info posted on [url=http://petsear.ch/Breeds/TamerPets]petsear.ch[/url]. In this case, you can get a big advantage by choosing a pet that's just barely faster than the tamer's. If you can't be faster, then the slowest/strongest pet will be the best.

Very, very true. Enzzo's [url=http://warpets.info/post/40253258137/thundering-pandaren-spirit-revisited]current Thundering Pandaren Spirit strategy[/url] is based around a rabbit that is just barely faster than the fastest enemy pet. Speaking for myself, I find it to be a very effective strategy, though I do need to find a slightly better rabbit than the one I'm using now.

But overall, I think that min-maxing team power/speed based on the Tamer stats is more work than I'm willing to do.
Since I personally only want one of each pet, I tend to just go for the most power I can get, unless otherwise indicated.
There are a handful of exceptions, but for the most part, that strategy has served me exceptionally well in PvE.

Certain pets such as Rabbits and Flayers will always need speed, however, due to their movesets.

I have a P/P Flayer Youngling, and I've found it to be exceedingly potent.
Is there a reason to forgo power for speed in this case (particularly for someone focused on PvE instead of PvP)?

[Poofah]

But overall, I think that min-maxing team power/speed based on the Tamer stats is more work than I'm willing to do.
Since I personally only want one of each pet, I tend to just go for the most power I can get, unless otherwise indicated.

This is perfectly reasonable--just not always optimal.

In the case of rabbits, I think most people just use a typical breed 5 (357 speed, 228 power). This works fine for the earth spirit and his rat--in fact it's what I use. Breed 5 Grasslands Cottontail (325 speed, 260 power) would be much better. If I had one I'd use it, but I'm not going to go farm it for a fight that's already easy. But if a difficult tamer fight came along with a pet like the earth spirit, you can bet that I would.

I have a P/P Flayer Youngling, and I've found it to be exceedingly potent.
Is there a reason to forgo power for speed in this case (particularly for someone focused on PvE instead of PvP)?

I should have been more specific: a Blitz/Reflection/Kick Flayer always needs speed; a Triple Snap/Rampage Flayer doesn't gain any extra benefits from speed, so power is better after the 5 turn break-even point. Flayer is kind of a special snowflake in that he has two very different movesets that are both pretty good. Because of that, he's also a great example where it's nice to have multiple breeds available: P/P or H/H for killing critters, P/S or S/S for killing dragons (depending on their speed), and S/S for PvP.

[Usaia]

Absolutely great post, worth a sticky IMHO.

As you said yourself, in some cases this simplified math does not work. For example Survival. If I pop my Survival on 2 points of health on low speed pet, I get extra 2 turns. The health after that has no relevance being it 4/5/6 turn fight. It looks like power means all after that but no - if I get my speed to increase for 1 turn after these 2, I get extra 3rd turn...The same goes for example undead racial (without extra 3rd attack). And negating effects against different attacks (multi-turn vs shield etc) have also math problem unless you know opponent stats. But generally the logic is on the spot.

[Usaia]

I have a P/P Flayer Youngling, and I've found it to be exceedingly potent.
Is there a reason to forgo power for speed in this case (particularly for someone focused on PvE instead of PvP)?

I should have been more specific: a Blitz/Reflection/Kick Flayer always needs speed; a Triple Snap/Rampage Flayer doesn't gain any extra benefits from speed, so power is better after the 5 turn break-even point. Flayer is kind of a special snowflake in that he has two very different movesets that are both pretty good. Because of that, he's also a great example where it's nice to have multiple breeds available: P/P or H/H for killing critters, P/S or S/S for killing dragons (depending on their speed), and S/S for PvP.

Another good example is Crimson Geode. Suicidal version and amplify/bolt version. H/H and P/P become handy depending what version you use and if you cannot decide, there is even H/P available.

[Poofah]

Another good example is Crimson Geode. Suicidal version and amplify/bolt version. H/H and P/P become handy depending what version you use

Definitely a good case in point. Stone Rush actually uses your own power against you, while also speeding up the fight by dealing a large chunk of damage. These properties both favor health over power.

If I pop my Survival on 2 points of health on low speed pet, I get extra 2 turns. The health after that has no relevance being it 4/5/6 turn fight.

Another interesting case. Survival operates much like Dodge (except Dodge is millions of times better) -- it prevents your opponent from getting the benefit of their turn as long as the Survival or Dodge buff is up. If you're slower, then you spend your turn to negate your opponent's next turn--it's a wash. If you're faster, you spend your turn to negate your opponent's current turn and next turn. The difference is that Survival is only effective if you would have died, while Dodge is always effective.

The same goes for example undead racial

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.

[Quintessence]

Very informative post! Bravo on all the math too! A lot of the theorycrafting goes over my head, but I learned more about breeds than I thought I could understand from your post.

[Usaia]

If I pop my Survival on 2 points of health on low speed pet, I get extra 2 turns. The health after that has no relevance being it 4/5/6 turn fight.

Another interesting case. Survival operates much like Dodge (except Dodge is millions of times better) -- it prevents your opponent from getting the benefit of their turn as long as the Survival or Dodge buff is up. If you're slower, then you spend your turn to negate your opponent's next turn--it's a wash. If you're faster, you spend your turn to negate your opponent's current turn and next turn. The difference is that Survival is only effective if you would have died, while Dodge is always effective.

Thanks for correcting, I meant 'fast' pet'. There one more major difference between Dodge and Survival - with Dodge you negate the full hit (no damage) while during Survival you will take damage for health that is above 1 hp. I agree, Dodge is superior but Survival a lot more common.

[Ryazan]

The damage formula:

Damage = (20 + power) * (baseDamage/20)

Mmm, wondering do you have any theory on how does the damage range work since we all know that an ability hardly ever hits for what the tooltip states but always a bit less or more? I haven't found anything solid so far but my wild guess it's probably some % of the damage following the formula above since abilities hitting harder tend to have more variation to both ways than dots, for example.

[Maizing]

I have a P/P Flayer Youngling, and I've found it to be exceedingly potent.
Is there a reason to forgo power for speed in this case (particularly for someone focused on PvE instead of PvP)?

I should have been more specific: a Blitz/Reflection/Kick Flayer always needs speed; a Triple Snap/Rampage Flayer doesn't gain any extra benefits from speed, so power is better after the 5 turn break-even point. Flayer is kind of a special snowflake in that he has two very different movesets that are both pretty good. Because of that, he's also a great example where it's nice to have multiple breeds available: P/P or H/H for killing critters, P/S or S/S for killing dragons (depending on their speed), and S/S for PvP.

I have 2 flayers... an S/S that I have started using vs Aki and an H/P that I am currently leveling. Should I scrap the H/P and look for a P/P? Or maybe keep it and just try to get a 3rd one that is P/P (or maybe a P/S)?

[Poofah]

Mmm, wondering do you have any theory on how does the damage range work since we all know that an ability hardly ever hits for what the tooltip states but always a bit less or more? I haven't found anything solid so far but my wild guess it's probably some % of the damage following the formula above since abilities hitting harder tend to have more variation to both ways than dots, for example.

I haven't kept track of the damage range well enough to know how big the variation is. DoTs appear not to have any variation; other damage abilities feel like they have roughly a 5% +/- range, but I have no idea what the distribution is.

I have 2 flayers... an S/S that I have started using vs Aki and an H/P that I am currently leveling. Should I scrap the H/P and look for a P/P? Or maybe keep it and just try to get a 3rd one that is P/P (or maybe a P/S)?

I wouldn't scrap him, if you're using him to kill critters with Rampage. The health gains a lot of value when incoming damage is reduced, and the Humanoid passive also makes health more valuable.

Flayer is a frustrating case where I would really like to have more than 3. I'd say that a S/S is a must-have; any of P/P, H/P, H/H are good for critters; and personally I really like having a P/S as a metagame choice, because 289 speed still lets you go first against a lot of pets, and the extra power is very noticeable.

[Maizing]

I have 2 flayers... an S/S that I have started using vs Aki and an H/P that I am currently leveling. Should I scrap the H/P and look for a P/P? Or maybe keep it and just try to get a 3rd one that is P/P (or maybe a P/S)?

I wouldn't scrap him, if you're using him to kill critters with Rampage. The health gains a lot of value when incoming damage is reduced, and the Humanoid passive also makes health more valuable.

Flayer is a frustrating case where I would really like to have more than 3. I'd say that a S/S is a must-have; any of P/P, H/P, H/H are good for critters; and personally I really like having a P/S as a metagame choice, because 289 speed still lets you go first against a lot of pets, and the extra power is very noticeable.

Thanks... I used stones on both of the flayers I have and (while I still have 2 or 3 extra humanoid stones... even after upgrading both my Argent Squire and my Argent Gruntling) would rather not waste one on a pet that I ended up scrapping.

I think I will look for a P/S flayer then... and agree with you that I would like to be able to have more than 3.

[Deepfriedegg]

Breanni, please sticky this. This is exactly the type of information that many battlers are looking for.
Great job, Poofah.