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From my experience w/Yale admissions as an alumni volunteer, here are some facts for potential Yale applicants (much of which applies to Likely letters in general)
1) What's a Likely Letter? Yale and some other selective private schools will send out handfuls of letters out to their most coveted recruits for the incoming freshman class. These act as unofficial offers of acceptance and are clearly worded as such. They are "unofficial" because by Ivy agreement, "official" offers can not be made before April 1 (except by those colleges that offer EA/ED). These letters are, in a way, to keep the students from pre-maturely committing to other offers (e.g full athletic scholarship offer from a State school) and to confirm to the applicant that a spot is awaiting them. NCAA rules allow many colleges to seek "letters of commitment" from athletes. This is a way to counter that impulse.
2) How does this differ from other communiques from athletic coaches? The language that coaches use is defined and often limited in scope ("I'll talk to admissions on your behalf", "I'd like you to apply", "We're interested. Please send us a tape"). Likely letters are issued by the Admissions office and are unequivocal with words to the effect of "Unless you screw up major, you will receive an offer of admission from us in April"
3) Do only Athletic recruits get Likely Letters? No. Yale sends out about 100 Likely Letters to non-athletic applicants. These are clearly the cream of the crop amongst that year's applicants. Knowing full well that these kids will be the most sought after by peer institutions and will be the ones most showered with merit financial aid, Yale sends out Likely Letter as a clear statement that "We want you. Please come to New Haven"
4) What if I don't receive a Likely Letter? Am I sunk? Yale accepts about 1950 applicants each year. Only 200-300 Likely letters are issued. My calculator tells me that the vast majority of accepted students never get one.
5) When do Likely Letters get sent? The Joint Ivy agreement says that highly coveted athletic recruits may even receive them in the fall starting on Oct 1-- along with strong suggestions that the kids apply SCEA. It strikes me that the super slam-dunk YES, non-athlete applicants in the SCEA round won't get Likely Letters because they're informed of their acceptance in mid December. All SCEA admitees are highly courted from December until May, the formal reply date. The bulk of Likely Letters seem to go out in the early part of the year (late January to February). The last dates these could possibly go out is March 15.
6) How Reliable are Likely Letters? According to anecdote, the LL is the college's commitment to the student. Only tremendous student foul ups (grades drop off a cliff, criminal activity, fraudulent application materials, etc.) would cause a reversal. But then again, these would cause a college to rescind a regular admissions offer, too.
I hope this helps. If I'm off, hopefully someone tweak my info. Good luck all. Enjoy your senior year!
PS: I never got one. Never heard of them until a few years ago when I interviewed a girl who had one from us and Harvard. She chose them and I'm glad she did! She was quite unlikeable.