Schools like HYPSM are high reaches for everyone. If your stats are not at least comfortably within the middle 50th percentile, don’t even bother applying, unless you are hooked. Your stats really should be in the 75th at a minimum to think of those colleges. A low reach might be a college with a sub-20% acceptance rate but your kid has stellar stats there. With match schools, your stats are probably well into the top of the middle fifty and probably above that, ideally into the 75th. What changes things a lot at this point is acceptance rates and what the college prioritizes. High matches probably have a 30% acceptance rate or lower and your stats are high, above the 75th. A low match means your stats are definitely well up there, above the 50th and heading towards the 75th percentile, and maybe the acceptance rate is a little higher, like getting towards 35% and above. Safety schools will have acceptance rates closer to 50% and your stats will be very high. There are many variations and no hard and fast rules. It’s probably easiest to just stick to reach/match/safety:-)
Many colleges that might be considered matches or safeties don’t like it when students don’t express interest. My D was accepted to a college where her stats were in the 90th percentile, but saw scattergrams that showed kids with even higher stats were denied. Colleges need to meet their yield, and they don’t want to admit kids they think won’t attend. D was WLed at a college which should have been a match. She was called off the WL, but this demostrates the need for a balanced list. I think that 8-10 is a good number to apply to, but again, this can vary depending on the colleges your kid likes. Does he love the college with a 60% acceptance rate, and are his stats high there? Then maybe he only needs to apply to a few schools. If his list is reach-heavy, he will need to apply to more.
So many factors come into play, such as essays, recs, ECs. Of course, it is a little different at many public universities where the most important criteria are definitely grades and test scores. Even then, there can be uncertainty depending on the major your kid applies to, or if he/she applies as an OOS student. Were the essay and teacher recs poor? That is never going to help, at private or public colleges.
Grades are King. Above all, your child should always aim for the best grades he can get. Test scores are also very important, and can be really helpful if a student has slightly low grades, especially at public or less selective colleges. Having said that, if your child thinks a high test score will make up for a lot of Cs, they might be in for a rude awakening. Then throw the test-optional colleges into the mix, where grades will be paramount, along with very good teacher recs and strong involvement in ECs.
Probably more info than you needed, but hopefully you have a better idea now.