There are few words more British than "soccer", it's classic public school slang from the 19th century playing fields. c.f. "rugger".
"Half" as in "centrehalf" (but also left half and right half) comes from the classic English 2-3-5 system (the one before WM, it's also where the slightly odd numbering of shirts comes from.
Soccer happens to be a shortening of the word association. So ostensibly you are correct. So yes. I apologise for including the word soccer. Simple. Let's hope the origins of the one word soccer doesn't detract from the reason I posted regarding Americanisms. If people want to get exact where it comes to the etymology of a word, I'm in. Make yourself a load of sandwiches and a flask and we can chat after the game.
Soccer isn't an Americanism, but it has certainly been adopted by Americans to distinguish it from their version. And if you want to be totally accurate, football should be applied to rugby seeing as it was invented first and soccer to association football.
I think you may find the game Rugby was a sport derived from football btw. So we can leave this and allow me to complain if I choose, or, we can start a thread on the Origins of words and certain types of sport associated with them by name.