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[quote=Anonymous][quote=Anonymous][quote=Anonymous]
WRT an individual applicant, whose likelihood could be [b]0% or 100% at any one college[/b].[/quote]
There is a 100% likelihood of an applicant being between 0% to 100%, so that is quite a meaningless understanding of probability.

Probability is about trying to quantify uncertainty. The more complete the model, the lower the error range/standard deviation. So sure, if someone had a line of sight on acceptances based on SAT+GPA+ ECs they would have a better model than someone with just a line of sight on SAT+GPA.

But the only public data that can be modelled comes from Naviance (school level SAT+GPA) and CDS (overall acceptances accurate, SAT+GPA based on those reporting). For those who are so inclined, they can calculate their probabilities of rejection from each and multiply them.

I think the third interpretation from the math for me is very clear, if applying to reaches, apply to a whole bunch of them , it will improve your chances of acceptance to at least one. Applying only to say Harvard is quite meaningless.

[/quote]

No, I am sorry, everything you are saying is wrong.  In fact your first sentence makes exactly my point.  You cannot use game theory to get any useful knowledge of whether applying to more highly selective colleges will have a substantive increase in your odds.  It is not a reasonable way to develop an application strategy.

You can’t do the math without knowing the factors, and you have no idea what the factors are for an individual applicant.[/quote]

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