I want to acknowledge what Philly says about things clicking (especially from the kid's point of view) and how critical that is. It could be classified under the comment often seen here:
You'll know when they're seriously interested.
How we understood this: After HF and Stanford, son went down a list of schools he wanted to apply to,whether baseball was part of the deal or not. He contacted each of the coaches before the camps, but did not have time to meet each of them there, so he wasn't sure he was seen by everyone. However, in the week or two after the camps, many wrote back offering to meet him on campus, and asked him to send transcript and scores for an admissions pre-read. He narrowed the list from there. What we didn't know at the time was that he would be offered at each school he visited. Maybe we could have asked ahead of time, but we didn't really expect any offers at all. It was only early August and he hadn't actually met all the coaches yet. Sure, he was personally invited with a legit email or phone call, and the HC made clear that he would be the coach there to meet with, and not anyone else, so maybe that was more of a signal than we understood at the time. We certainly didn't want to assume anything, especially since the schools were so hard o get into.
At the end of each of son's meetings with the various HCs, he would ask the coach where he stood, and the coach would look at his computer, shuffle some papers around in a file, and then say let me see what admissions says, then shuffle some more papers around and finally say something like we want you to come here and admissions does, too. I liken this part of the process to that moment when the auto salesman who's been working your sale says I'm not sure I can go that low, let me talk to my manager. The auto salesman knows exactly how low he can go, and I think these coaches know full well by this point whether a kid is a viable candidate or not. That little charade of looking through files on the computer to get an admissions report allows a moment of delicious anticipation for the uninitiated. At son's final choice school, Coach asked if he had any other questions and son said "just one. Where do I stand with you?" Coach goes, "Well, I want you to come and play here. Let's see what admissions says." Coach taps computer keys, peers at the screen, "Let' see, oh, there it is...yes, it says they think you're a strong candidate for admission. Does that make things more clear for you?" Long exhale, then "Yes sir, crystal clear."
Long story, short: the connection with the coach is huge. It may be illusory and fleeting but it can really unlock stuff.