Judging B-School Admissions Chances

I'm thinking of applying to a couple of name-brand business schools that I'm competitive for.

I assess that I'm competitive because my scores are well within the range of the schools' class profiles.  However, what would really help me out in assessing my chances would be knowing the characteristics of the applicant pool.  I am particularly interested in correlation of GMAT scores with admit rates.

For instance, say School A has an applicant pool of 10000, and admits 1000.  The admit rate is 10%.  Then the school comes out and says its admit profile has a middle 50% GMAT range of (for instance) 690-750.  This is wonderful, and with the 80% spread can give a pretty good picture of what the normalized curve for the entering class looks like.  But that tells me nothing about my chances before I get in; it merely says how I'll fit in once I get there.

If I had the applicant pool profile, then I could match up the normal curve of the applicant pool with that of the admit pool--overlay them, almost-- and see if the left end of the Applicant GMAT curve significantly overlaps the left end of the Admit GMAT curve significantly enough to rule out most of the low-end of the applicant pool.

Note that schools do not release profiles of their applicant pools.  This must be to increase the number of people applying by preventing people from seeing that they don't have a very good chance of getting in.  They can claim to be a) not basing admissions on test scores, and b) getting lots of applicants to get their admit ratios low and keep exclusivity up.  In other words, they are having their cake and eating it too.

I assess that the 10% admit rate in the example is actually closer to 40%, maybe 50%, of qualified candidates, i.e. those that  match the general class profile.  Now, to be truthful, I do not have any statistics to back that up, other than to say that the mean GMAT score nationwide is around 530, and that a lot of people apply to exclusive schools just because they are exclusive.  Assuming that 2/3 of the GMAT test-takers do actually get scores between 400 and 600, as the test is designed, and standard deviation is about 100 points... well, I would be very interested to see the applicant pool stats vs admit pool stats.  I think we'd be very surprised what the admit rate is for people who fit the class admit pool.

While the applicant pool is probably skewed high based on the caliber of school, I don't think that solely geniuses are all applying to Harvard.  Why?  There aren't enough of them for the top-20 schools.  See the next bit..

The applicant pool we're interested in are about 2 standard deviations above the mean--actually, with a 690 and above, we're talking about 1.5 STDEVs above, or in roughly the 94th percentile.  The number of GMAT test-takers last year was 267000.  We'll assume all single, unique testers for this little exercise.

With a total pool of 267000 GMAT test takers, we look at what a score of 690 means percentage-wise (set the mean to 538 and stdev to 100, then move the cursor to 690), multiply by the total GMAT population, and end up with a total of... 16000 people with a minimum 690 GMAT score.  With a 730 GMAT, it becomes 8000 people.  Are all those people applying to the same schools?  There may be some overlap, but let's posit that that all the smart people (690 GMAT and above) apply to the top 10 schools. With average class sizes being about 560, we're talking a total of 5600 top-program slots available.  Assuming that only this year's GMAT takers apply, this means that if everybody with a 690 or above--throughout the world--applied to these top 10 B-schools, we'd see a 30% admit rate.  


This isn't even counting the next 10 ranked b-schools, or other top-ranked international schools, etc.  Wow, the odds just get better and better for scores in that top 6%, don't they?  This tells me that there are a lot of people applying with sub-super GMAT scores, and that those people comprise the majority of the exclusive schools' rejects.

Now, I could be totally off base and all the normal people could be scared off by the high mean GMAT of the schools.  However, this doesn't pass the sniff test.  If I'm average Joe, I might not apply to the exclusive school... but the cost of the application (in time and money) might be worth the return, especially because I know the school admits at least a few low-end scores.  Might be my lucky day, or something.

What we do know then is that a lot of folks apply to multiple schools, and we have a lot of lower-tier GMAT applicants as well.  We also know that top schools admit mostly top GMAT performers.

Keep in mind that the GMAT takers number includes International students as well, which are taking the GMAT in equal or greater numbers to US takers.  What I am leaving out of my analysis is the folks who have legacy GMAT scores (like who keep scores on file for a couple of years and then apply) because 1) not all of the top GMAT takers apply to the exclusive schools, 2) not all GMAT takers apply to schools period, and 3) it's a rolling process, so I assume that the carry-overs from last year replace the ones who wait this year.

So what is the takeaway?  If you're applying to a top B-School or other school that requires the GMAT, and you're facing great odds... like the 10000 apps vs 1000 slots crunch... and you have a high GMAT, you probably don't have to worry about quite as much as you thought you did.  And you can still tell people you got into a really selective school.

If you had an average GMAT, then you need to be really really special, because you're competing with the high scores that comprise the majority of slots, and the low-scores are relatively rare at the selective schools.

I still want to see the applicant pool profile.  But I suspect we never will, because it would mean too much in prestige and applications revenue.

Feedback and help with my math would be greatly appreciated.

Union Theory

This will be a short post, as I am not an economist and haven't done any research on the post-topic.  Also, my jargon will be off because I haven't taken econ in years.

Here it is.
Thesis:  Adding constraints or invalidating economic assumptions creates market distortions.

No suprise there, right?

Sub-Thesis:  Labor unions are an externality caused by the invalidation of the homo economicus assumption of perfect mobility.

Explanation:  When I learned about labor markets in Econ 101, I learned that labor is a commodity (more or less) with its supply and demand curves, et cetera.  One of the things that had to be accounted for in assessing prices and elasticity and so forth was the degree of mobility of the labor in question.  Now, it seems that unions were created because workers weren't getting paid commensurate with their working conditions and labor.  The only reason this could have happened is that there were no other acceptable jobs around, and that the workers couldn't move to the jobs they wanted.

Whether those jobs actually existed is irrelevant to this point.

Now, as the workers couldn't move to a better job, there was a market distortion that benefited the employers, namely a lack of competition for labor.  The employers essentially had a captive labor pool and could pay less than competitive-market prices.  So, as the unions formed, they essentially functioned as a substitute for the perfect mobility that the workers lacked.  They acted as an indirect competitor with the original employer.  This moved the overall supply/demand curve intersection to a point closer to that of optimal efficiency.

This suggests that there is an economically optimal amount of union involvement in a given labor pool or situation.  That amount would be just enough to balance the degree of invalidation in the labor-supply-assumption, or perfect mobility, whatever you want to call it.  Further, if there's an optimal amount of union involvement, that means that there are sub-optimal levels-- too high, and too low--and those levels can be determined and compared against reality.

This is a fun academic exercise.  I think it describes why unions formed and a bit of their history.  For predictive theory, it seems that unions would thrive in environments where the facilities are fixed and labor pools are specialized (hence, they have imperfect mobility) and be unable to keep a foothold where labor is fungible and facilities are widely distributed (or where mobility is greater).  Does this accurately describe reality?

It does not describe union pension plans, however-- I think that will take a more deliberate thought-experiment to explain.

Baghdad Election Booms

This evening I heard small-arms fire (like AK-47s) and explosions (probably RPGs) in the distance as I walked to my CHU.  Over the last several days, we've seen embassy bombings and a massacre.  It seems as though there is mischief afoot.

Personally, I am glad this is happening now.  Here's why:  We are still here.  I would wager that the recent spate of violence is directly related to the recent elections and the Iraqi people's empowerment of Ahmed Allawi.  This did two things.  First, it emboldened Al-Qaeda, which now have another Sunni (and former ba'athist) on the cusp of power.  I don't think Allawi is a bad guy, as he pissed off Saddam pretty good, but he is likely tied through family and tribal relations to some bad people.  Additionally, as he takes over the PM slot, he will inevitably replace current officials with those he prefers-- and those officials are more likely to be tied to Sunni extremist groups than the current officials.  This all adds up to a political climate that might embolden Sunni groups, and I think that's what we're seeing now.

Now, the other side of the coin has the Shi'a contingent (like Nouri Al-Maliki and his contingent) not wanting to relinquish power to the newly-elected government.  So there will be shenanigans from the Shi'a side of the house and its Iranian supporters as Maliki tries to create either a) a reason for him to stay in power, or b) um... another reason for him to stay in power.

This is why I am glad this is happening now.  If Maliki had won, we would probably not be seeing the recent increase in violence.  The long-term effect, however, would be that Iraq would have to go through its first eventual transfer of power on its own and later.  Historically, transfers of power have been a hard thing for middle-eastern countries to deal with.  See: Iran, Iraq, Saudi Arabia, Egypt, Afghanistan, etc.  So for Iraq to confront this election and transfer of power now, when the US is still around to provide a stabilizing influence, is a very good thing over the long term.

There's nothing saying that the political situation won't vaporize when Allawi gets voted out of office in 4 years, but it's a lot more likely to go smoothly if we establish a positive precedent now.  The confidence of the people in the process will go a long way to making this a permanent fixture.  Then, in 20 years, we can look at this moment, right now, and say it was a defining point in Iraq's prosperity.