I think it is incorrect to assume that a CC at an elite NE boarding school can assess chances any more than a fuzzy maybe. Especially these days. We (a private day school) “lost” one of our below average CC to an elite NE boarding school not so long ago. And our own CC, who I think is the best at our school, and in my opinion really good, had many gaps in their knowledge for particular kinds of situations. When you really get into the weeds and probe them, they just don’t know. They often commented to us that AOs come back to them with questions about candidates that they thought were modest/marginal sometimes.
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