common and proper nouns questions

[jotham]

Actually, you are right. Nike used as the company name is a proper noun. It is only an issue when used for the product name, much the same way as with Coke.

[Stephen Jones]

I don't think it's incorrect, but I wouldn't use it, even in describing a high school basketball teacher.

You use the hyphen when the noun phrase is used attributively.

Thus He teaches in a high school.
but
He's a high-school teacher.

However there is little chance of amiguity in that last example so.
He's a high school teacher.
is also correct.

Google doesn't admit the hyphenated phrase as separate from the two separate words, so I can't do a comparative frequency count.

[JuanTwoThree]

With intonation it's even possible to suggest that it's a team that plays basketball in a high-school style.
"Don't worry about them, they're just a high-school basketball (pause) team"

Head: team

Modifier: high-school basketball

Could you write "They're a high-school-basketball team" ?

[jotham]

Could you write "They're a high-school-basketball team" ?

No. I would only do it if high school acts together to modify a basketball. And since the word basketball already works to modify the team anyhow — as a game, not as the actual ball — it's easiest to leave it that way. In other hypothetical contexts, however, there may be justification for the extra hyphen — if there was a difference between a high-school or junior-high basketball, then it could clarify the difference: "I want a bowling ball that is high-school-basketball size. (Some editors even put a hyphen between high school and an en dash before basketball.) But Stephen Jones has a point: the hyphen is sometimes omitted if there is no way that confusion could arise — although most of us aren't always aware just how confusing we could be without the use of intonation or pauses in our voice. I always try to use it when it can be used.
Juan, I see your point about the style of basketball, but I think you would italicize high school to emphasize the fact and to contrast it to professional or even junior-high basketball.

[JuanTwoThree]

That's exactly my point:

Talking about a university or adult team that isn't very good would be talking about a team that only plays basketball in a high-school way. "high-school" would modify basketball and "high-school-basketball" would modify "team":

"they're just a high-school-basketball team"

(((high) school)) basketball)team

If they were stoned, adults and not very good they'd be a "high school-basketball team"

[jotham]

Okay, with your context, it becomes clear. Yeah, that would work. It does require some imagination, and people who aren't really adept at the rules of hyphens...well, the nuance may be lost on them, so they may still end up reading it how they're used to and think they really are high school. It may be best to reword it for clarity in that case: the team cooperates in a high-school-basketball way.

[JuanTwoThree]

Shall we start on "a man eating tiger steak" ? Better not.

[jotham]

Google doesn't admit the hyphenated phrase as separate from the two separate words, so I can't do a comparative frequency count.

Well, even if you could, it probably wouldn't be a very high frequency, as it is a rule most people aren't familiar with (even though it could render their writing clearer). Now if you could search newspapers and magazines, like the New York Times and Washington Post, it would be immediately apparent that the rule is kept, and pretty consistently.

[Stephen Jones]

You should find the hyphenating done properly in the Washington Post. The chief copy editor there is Bill Walsh, who is a fanatic over hyphens.