My colleagues and I were looking for a statistical explanation to help explain to parents why you do not increase the odds of admission to a more selective school (schools with very low acceptance rates) by applying to more of them. Here are two (slightly reworded) well-reasoned responses that I liked:
Response #1: Each event is unique. They aren’t additive. It’s called independent probability. For example, when flipping a coin, the odds of heads are 50%. Each separate time you flip a coin, the odds are the same. It doesn’t matter how many times you do it, each separate time you flip the coin, the odds are still 50%. Each time is independent of whatever happened before. The same applies to applying to college. Just because you got rejected by Harvard, Yale, Cornell, and Princeton, doesn’t mean your chances of getting accepted to Columbia improve. It is independent of what happened before.
Response #2: This is an interesting concept that I think requires logic rather than math to consider. If this were a two-sided coin with a head and a tail, each time the coin is flipped there is still a fifty percent chance it will be heads and a 50 percent chance it will be tails. If it were a ten-sided coin, there would still be a one in ten chance each time the coin is flipped that it would land on any particular side. There would not be a better chance on the tenth flip that it would land on the one side that hadn’t yet come up. This is logic or probability theory, or whatever you wish to call it. But more to the point, admission to college has little to do with pure probability like this. If a college has a ten percent admit rate and someone applies with a 3.7 GPA or even a 4.0, middling essays, a few extracurricular activities but nothing remarkable, and no legacy, athletic or other ‘hook,’ she or he would not have a 1 in 10 chance of admission in the first place. This student likely would have a zero chance of admission. No matter how many schools with low admit rates that student applies to, they have virtually no chance of admission. The point is that a ten percent admit rate does not mean every applicant has a 1 in 10 chance of admission. All it means is that of the 1000 applications received, 100 will be admitted.
My take on this issue takes a slightly different approach. Although I agree that the probability of getting into a highly selective college does not increase by applying to more of them, as the second response above indicates, the probability of admission is not the same for all students in the first place. Looking at it in terms of acceptance rather than rejection, all things being equal, if a student is accepted to one or more highly selective college, he or she is likely to be accepted to one or more other highly selective schools. This is because the student’s application had qualities that many selective schools may find attractive. Generally speaking, the odds of any applicant getting admitted have everything to do with the student’s transcript, test scores, essays, letters of recommendation, special talents, abilities or ‘hooks’ and the type of class that college is putting together that cycle, and almost nothing to do with probability per se. Thus, when I consider a student’s profile in light of the student’s actual college application list, I can often predict what schools will accept or deny the student. Understanding the mission and culture of each college as well as admission trends also helps put each student’s profile into clearer focus.
If we, as independent college advisors, could dispel the ‘more is better’ myth, and guide students toward selecting colleges that are a good match for them, families would enjoy far less stress and far better results each spring.