...I'd have to put a metric down of admissions percent for a HA school. I'd say 15% admitted percent as a high water mark for starters. That would be my stake in ground. Others may think differently and I'd like to hear what they have to say.
Son's school was one of the HAs that Fenwaysouth listed in his post, but the acceptance rate is MUCH higher than 15%, mostly because it is a known backup school to the Ivys. Keep that in mind. Many of it's baseball players got in to an Ivy, or applied.
In my son's case, baseball may have gotten him in to a school that he may not have gotten in to on his own. We will never know. But, once you get in, even with the coach's help, YOU NEED TO MAKE THE GRADES TO STAY THERE. (Son did, thank goodness).
If you are teetering and your son has some good metrics, go for it. You can make final decisions on schools after an offer is made.