It's not Bernoulli's theorem (it has some context but not this).
Fat head were bought in as a way to reduce luff length but keep sail wars as calculated in IRC and other fleets including Merlin's. (LL xLP )/2
thereby allowing more area on mainsails etc.
The by product of them is that too a certain extent they are aerodynamically better this is more due to leech position though.
A common problem with them when first made (and a reason for the now illegal jib bar head fitting) was that it was hard to stop the leech falling away was the sheet control runs pretty much in a straight line from clew to head point.