
Avoron |
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Do polymorph spells, such as Beast Shape, give a natural armor bonus, or do they give a bonus to natural armor?
Polymorph: A polymorph spell transforms your physical body to take on the shape of another creature. While these spells make you appear to be the creature, granting you a +10 bonus on Disguise skill checks, they do not grant you all of the abilities and powers of the creature. Each polymorph spell allows you to assume the form of a creature of a specific type, granting you a number of bonuses to your ability scores and a bonus to your natural armor. In addition, each polymorph spell can grant you a number of other benefits, including movement types, resistances, and senses. If the form you choose grants these benefits, or a greater ability of the same type, you gain the listed benefit. If the form grants a lesser ability of the same type, you gain the lesser ability instead. Your base speed changes to match that of the form you assume. If the form grants a swim or burrow speed, you maintain the ability to breathe if you are swimming or burrowing. The DC for any of these abilities equals your DC for the polymorph spell used to change you into that form.
Small animal: If the form you take is that of a Small animal, you gain a +2 size bonus to your Dexterity and a +1 natural armor bonus.
Medium animal: If the form you take is that of a Medium animal, you gain a +2 size bonus to your Strength and a +2 natural armor bonus.
If they give a bonus to natural armor, does this bonus have a type?
If they give a natural armor bonus, is a creature affected by such a spell able to use their original natural armor bonus instead, if it is greater?

Gauss |

Generally, you lose any natural armor bonuses that are due to form and then gain the spell's natural armor bonus.
While under the effects of a polymorph spell, you lose all extraordinary and supernatural abilities that depend on your original form (such as keen senses, scent, and darkvision), as well as any natural attacks and movement types possessed by your original form. You also lose any class features that depend upon form, but those that allow you to add features (such as sorcerers that can grow claws) still function. While most of these should be obvious, the GM is the final arbiter of what abilities depend on form and are lost when a new form is assumed. Your new form might restore a number of these abilities if they are possessed by the new form.

Avoron |
Then why would the polymorph description say you gain "a number of bonuses to your ability scores and a bonus to your natural armor"?
Your Strength score is dependent on your original form, but that remains too, because it's not an extraordinary or supernatural ability, and the polymorph rules just say that you get a bonus to it.
I don't mean to be contrary, I just wish it made more sense.

Gauss |
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Because the rules are written from the perspective of PCs which do not (normally) have a natural armor bonus. Thus, it is a 'bonus to your natural armor' since you have no natural armor.
The Devs have stated repeatedly that the rules are written from this (PC rather than monster) perspective.
However, there have been many threads on the topic of 'is a natural armor score an ex/su ability and/or due to form and thus lost when you polymorph?'. The consensus seems to be 'yes'.
Additionally, James Jacobs has weighed in on this topic here and here.
(Edit: remembered a Dev response so changed my post.)