Thanks, #1 Assistant Coach. I think your theory is a good rule of thumb.
One other thing about the Ivy League: if a kid can clear the baseball and academic bar, it can be a much better financial deal than the typical D-1 baseball scholarship. For example, at Princeton, if your family income is <$120,000, 100% of tuition is covered by grants (no loans). From Princeton's financial aid brochure:
Yale has a similar program. Each school is a little different, but for many student-athletes, the Ivy deal can be better than a traditional baseball scholarship to another D-1.