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)
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 health3. 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.