Why do the people playing American Football wear hemets as American Football is very similar to Rugby and Rugby players don't wear helmets?

Answer 1

That's how the creation of the game got about.

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When heavy body armour was introduced to American Football the heat protection was a leather helmet similar to the scrum cap used in Rugby. When the hard protection was introduced they had to add extra hard head-wear as the injuries to the face from the shoulder padding cause serious injury. Rugby boards are desperately trying to maintain a flexible body armour, which in effect reduces stud damage to the skin whilst not being made in such a way as to be used to increase tackle effectiveness.