Stanford GSB 2013 - Calling all Applicants

Ok, I'll agree that that is the driving variable, but it's also an obvious one. I wouldn't consider a variable relevant in predicting my fate unless I know its value. I have no idea when the admissions committee read, or will read my application. I do know when I submitted it, where I live, what my major was, what my intended concentration was, what my GMAT score was, etc. Because I have to assume that the time my application is read is random, and that applications are read linearly throughout the review period, I stand by my calculation. Here it is in an easier format to understand that incorporates the above:

The probability at this point of your application having been read is 75% because we are 75% of the way through the review period. If your application was read, you were either invited to interview (100% chance), or not invited to interview (0% chance--we'll ignore waitlists). So this already-determined out come accounts for 75% of us. If we did not receive an invite, our only hope is to be in the remaining 25%.

We know that because a random variable (when your application is read) is the only driver of your odds, they remain at 14% even if your application has not been read. Therefore, your odds if you have not already been invited are 14% x 25% = 3.5%, which is similar to the 4% I provided earlier. I have some ideas of what the reconciling half percent is, but I'm not willing to spend the time to prove it out.

It is relevant. As my expectation of going to business school rises, my propensity to do certain things around home such as purchase new furniture that would be difficult to move or renew college football season tickets declines.

You are right. I can see how knowing the difference between a 3% chance of an invite that carries under a 50% admittance chance or a 7% chance of an interview that carries under a 50% admittance chance is very relevant in the decision to buy furniture and football tickets in the next three weeks.

Initial expectation of an interview is 14%, not 7%.

Yes, my personal anecdote re: a decision on whether to renew my season tickets by last Friday's deadline was not material, but there are other deadlines that are. Let's consider an applicant who is considering submitting a round 2 application to Haas (due 11/29/12):

In this case, the applicant experiences the following possible outcomes:

Admission to both schools: 1%
Admission to Stanford and not Haas: 6%
Admission to Haas and not Stanford: 11%
Admission to neither: 82%

But if the odds of admission to Stanford are reduced to 2% based on my analysis above, the outcomes change to:

Admission to both schools: 0%
Admission to Stanford and not Haas: 2%
Admission to Haas and not Stanford: 12%
Admission to neither: 86%

So in essence, there is a marginal increase of 1% in the student's probability of ultimately attending Haas. If we presume that the value of the MBA to be the simple sum of the increase in applicant salary for the number of post-MBA years worked**, the value of the Haas MBA is $88,819/year for 35 years to retirement, or $3,108,665. 1% of that would be $30,109, so the yet-to-be-invited applicant should be that much more interested in applying to Haas than before.


*I'm well aware that there is probably some co-variance between admission to various schools. I've never seen a good study on it, so we will have to just assume that there isn't any.
**This would require wage growth to equal the discount rate, which, although not necessarily accurate, is reasonable.

The point he was making was to stop obsessing. It's a meaningless pursuit and the statistical probability doesn't mean you should adjust your behavior or thinking.

Statistical probability should most definitely affect decision making. Isn't that what we do NPV analyses for investments? Isn't that how we adjust EV for risk? Isn't that how we decide what states to visit on a political campaign? Isn't that how we decide whether to continue operations in a failing company?

I would say that EVERY decision should be made based on its statistical support. Then again, I ran a multiple regression to draft my fantasy football teams this year, so maybe I'm a bit extreme.

I would think the best argument here is saying that the change in outcome is immaterial. Even in my Stanford/Haas example, it would be very easy to claim that the applicant would have already been applying to Haas, so this new information wouldn't change anything, just increased the EV of the decision already made.

You already made your decision based on the probability you saw for yourself in being accepted. You believe you had a chance, like all of us, and applied. Your probability of admission is more or less the same as when you applied.

Go take a spa day.

I don't know man. (woman?). This admissions process, just like dating, is far too subjective to put effort into doing any sort of mathematical analysis. A lot of what is involved on the adcoms' part is intuition, gut, and an overall sense for how attractive a person's candidacy is - which is not always quantifiable. Just do the best you can in your apps, apply to where you want to go, and that's it.

How ironic. I'm actually on PTO today--one of several days that I strategically scheduled in the Nov - Jan time frame for potential interviews. Sadly, I'm not interviewing today for any school.

Agreed. There are quantitative factors and subjective factors. However, the subjective factors are basically considered random noise that impairs the statistic. If there were no subjective factors, we'd all know if we were accepted before we ever applied. Instead we have to summarize them into cumulative probabilities across all applicants.

I don't do NPV analysis or adjust EV for risk. I won't even google it for that matter.

Btw Nate Silver called, he wants his stats notes back. Cheers =)

Wow...this just doesn't appear to be a valuable use of time. There is a point were the formal analysis ends and sense kicks in. No class, not even at Stanford, can teach you where that line is.

Also Nate Silver is GAY. I'm so in love.

Yes. I feel like I spent more time trying to justify the value of knowing that the odds of being invited are now at 4% than I did figuring out that they were 4%. Coming up with the 4% probably took me about 5 minutes, and I figured some folks might be curious, considering that everyone posting has been trying to figure out if they are still in the game. Maybe I'll preface any other quick and dirty analysis with a disclaimer that I'm not going to waste my time explaining it.

It would be AWESOME if someone could PM me with specifics about the interview. I tried to help others out after my Booth interview and my GSB interview is coming up in a few days. Thanks in advance!

OK, people who submitted for R1, who else got a heart attack after reading the sender and the first three words of the subject line of today's e-mail reminder about Round 2 deadlines?

I didn`t get this email!