Wiki - Pet Care

Taming a pet, and controlling it are not the same thing.  To tame a pet requires Animal Taming.  The amount required can be seen on the Tamable Creatures table. 

Controlling a pet is far more complicated. 

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Control Chance Calculation
1. Taming Bonus = Difficulty Modifier * (taming skill – required taming skill)
2. Lore Bonus = Difficulty Modifier * (creature lore skill – required taming skill)
3. Skill Bonus= (Taming Bonus + Lore Bonus) / 2

Final control chance % = 70 + skillBonus;

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The difficulty Modifier above depends on the difference between your skill and the pet’s difficulty. The difficulty modifier is applied independently to each skill and then that result is averaged. Thus more importance is given to taming than lore, while still requiring you to have a significant investment in both skills to control high level pets. The way that modifiers are picked is as follows:

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Difficulty Modifiers:

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6 – if (taming/lore skill – pet difficulty) is positive (i.e. if taming/lore skill is greater than the pet’s difficulty)
28 – if (taming skill – pet difficulty) is negative (i.e. if your taming is less than the pet’s difficulty)
14 – if (lore skill – pet difficulty) is negative (i.e. if your lore is less than the pet’s difficulty)