Each hat wearer prefers a certain profile type for a particular occasion, look or functional purpose. Whether a hat's profile is low or medium refers to the way the top of the hat sits on the head because of how high the crown rises from the brim. Sports players prefer certain profiles--some for looks and others for comfort.
The profile of a hat describes the height and slant of the front of the hat connected to the brim. This slanted area is called the crown. A crown can slant only slightly or dramatically back towards the head, creating three unique looks and functional abilities from low to medium to high profile.
The height and slant of the crown directly affects the types of situations for which a hat is used. A high-profile hat has the longest and highest crown, allowing the wearer to pull it down farthest over his eyes. The higher the profile, the greater the structure and slant in the crown to hold up the material of the crown. The lower the profile, the more shallow it will sit on the head. Higher profile hats are best at keeping sun out of the eyes. Lower profile hats fit snugly and the wearer can use them easily for sport.
Low profile hats can be structured or unstructured. The crown is short slanted, if structured, and not slanted if not structured. Structured low-profile hats keep their shape easily, even when not being worn. Unstructured low-profile hats are more broken-in and take the shape of the wearer's head.
Medium-profile hats have crowns an inch or two taller than low-profile hats. Medium-profile hats can also be structured or unstructured, slanted or not slanted, respectively. The wearer can pull a medium-profile hat down lower on his forehead, as there is more material and room because of the higher crown.