What do college coaches look at?
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I emailed the OSU (Ohio State University) coach once asking and he said that anyone who tries out must carry at least a 2 handicap. That is a division 1 school who has a history of very good golfers. So, take what you want from that. Division 3 schools probably a bit more lax, but you are looking at close to or better than scratch golf at majority of all levels of play. At least that is what I take from it.
To get noticed for scholarships, especially at serious D1 levels, you need to be posting red scores in several big amateur events, as well as fairing really well in your high school state tournament. To get the necessary exposure, you really need to be playing in some sort of amateur tour. That's not to say all of these things are necessary, but a combination of those things is going to be necessary to get yourself noticed. When you get into D2, D3, and NAIA levels, the requirements drop obviously.
To walk on, you just need to be really good and prove yourself at the try outs.