Quote Originally Posted by Fax Celestis View Post
...yes they do.

When backwards-extrapolating a monster's base ability score modifiers, you subtract one from its highest ability score for every four hit dice it has. Once hit dice reach zero, subtract 10 (if even) or 11 (if odd) from the creature's remaining ability scores. The resultant numbers are the creature's racial ability modifiers.
Nope!

Look at the Centaur. It has Str 18 and 4 racial hit dice. Str is its highest score. Centaurs as Characters says that they get +8 Str, not +6.

Oddly enough, when monsters start gaining class levels and/or advancing in hit dice, they begin gaining ability increases at levels that are multiples of four. This can be confirmed by looking at statblocks of classed monsters. They just don't gain increases during their initial hit dice. It's a very weird rule, but I've extensively confirmed it for a large set of examples.