There is a separate roll for hats. That's sure. When you earn a hat the time earned isn't following the 25mins pattern of normal items.

1 roll per 4 hours 17 minutes with 1.19% chance seems to be the formula.

The 0.44% might be close/equivalent to this but it's not correct since it's based on the total numbers of items founds (and hats are independent to items...)

I guess the chance is still the same but you got less chances to find a particular hat, since there are more hats now. It's common logic.


Edit:
Hm... "Valve increased the drop chance to 3.5714% on 9/1/09."
Great

Cool, now you actually have a chance of finding one.

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a bird in a bird in a bird in a bird in a bird in a pig

That is written where?

link

Yeah mini. Now you have 3x chances to get a hat! Oh wait... 3x0 = still 0

Oh wait, that's not a good thing D:

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a bird in a bird in a bird in a bird in a bird in a pig