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[quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous]The amount of work in crafting essays is going to be more than you realize! My kid applied to 11 schools and the lead up to the RD submission deadline was painful.

Applying to more schools should improve your probability of admission to at least one, as long as you’re qualified. My kid applied to 4 serious reaches (acceptance rate < 10%) and got into 1, waitlisted at 1, and rejected at 2. She got into all matches and safeties.

Calculating independent probabilities, if dc applies to 10 schools, 5 with a 5% probability of admission and 5 with a 10% probability of admission, then the probability of getting shut out is 46%. Add 2 more applications with a 10% probability of acceptance and the probability of getting shut out drops to 37%. You can use an online calculator like calculator.net to play around with the probabilities. It can help you understand that the probabilities may not be what you expect. For example, if you apply to 10 schools with a 10% probability of acceptance, your probability of getting shut out is 35%. Add 2 schools with a 75% of acceptance and the probability of getting shut out drops to 2.2%.[/quote]

I am the PP above who pointed out that these are in fact independent events.  However, the flaw in your approach is that you have no idea what any one persons odds of admission are at any one school - so you can't accurately calculate your chances this way and it is foolish to try.  For example, your odds may be zero at all 15 schools.

You can't know the odds the way you know there are 52 cards in a deck, so this exacting method of calculation is useless.  Despite that, they remain independent events.  And the famous "Reach-Match-Safety" approach is essentially non-quantified game theory applied.  It remains the best one I know of.[/quote]
Seldom in risk assessments does anyone know the true probability!  This doesn’t mean that it’s not helpful to know that 10 schools with 10 % probability does not mean a 100% chance of acceptance! Playing around with a reasonable range or probabilities can help create some reasonable expectations and some guidance in if it’s worth applying to an additional school.[/quote]
I agree that calculating independent probabilities is a very good idea for people as a starting point: even well-educated folks who would not believe applying to 10 schools with a 10% chance of acceptance equals 100% seem to wrongly think it gives their kid a better than even chance of getting into at least 1. It doesn’t.

However, these independent probabilities, as a second, more intuitive step, need to be played with:

Take the “top” schools with 2-6% RD acceptance rates (RD rates are lower; don’t look at overall rates). Let’s assume your “typical” high stats kid with great curriculars who is not a recruited/semi-recruited athlete, URM, child of a long-term faculty employee, first-gen, or resident of North Dakota (the 5 huge admissions plusses; legacy only moves the needle slightly these days, and not at RD). Now take an educated guess as to the “real” probability of your child being admitted.

For this type of applicant, my educated guess is that the probability is 0. Maybe it is 1-2% for a small subset (a male humanities kid, say; but yet another male CS or female biology kid is a 0). If you, more optimistically, assume your child has a 1% admissions probability at each of these schools, 11 applications would result in a mere 10% chance of getting into 1. Far more likely, the real chance of admission is 0 at half of these schools (there is no way to know which half). Your child would then have to apply to 22 of these schools to have a 10% chance of getting into 1.

Stop doing this folks. There is a reason these schools are not timely sharing all of their admissions stats this year: they don’t want non-hooked kids, or their parents, to recognize that their RD applications are exercises in futility.
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