I can't speak for the other programs, or for anyone else who was being recruited for baseball, but our experience was that we were never told that if he applied he would be accepted. In fact, considering he had never taken the SAT and had to take the last one offered before the deadline, and after seeing his scores, we thought "oh well, it was nice while it lasted".
The coach in fact told us he had put in his recommendations, but the ultimate decision was with admissions. They aren't about to let someone in who they think might not be able to succeed there, no matter what the coach says.
Maybe in our case after only seeing him pitch 3 innings at a showcase, they didn't care if they got him or not
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BTW, I believe "observer" and "hit and run" are talking about two different coaches. Coach Baldwin has left for Michigan State, Coach Enriquez is still there.
In closing, I don't mean to sound like a broken record, but when considering Dartmouth (or any other Ivy for that matter) IMHO I wouldn't advise choosing them strictly for the sports. The Ivy league plays very competitive baseball and has many players drafted each year, but don't make that your only criteria for going there. The much used HSBBW saying applies here, "Would you go there if baseball was no longer an option?"