Boxer Hats

Still ploughing through tales of sin in Melbourne in the early 20th Century. John West is now a millionaire running a Tattersal's club and a tote and owning several race courses. He's also got about half of the State Parliament on his pay roll. Wow, I say, if this is indeed based on a true story as advertised.

Something that's bugging is that John West's henchmen are described as wearing "boxer-hats". I've never heard of this before and nor has anyone I've asked. Google brings up sites happy to sell me caps with pugilist or boxer dogs on them or strange German sentences where Mr or Ms Boxer are doing something because "hat" is a verb. Does anyone have any ideas?