Since MBAs are becoming overwhelmingly popular as the post-grad degree of choice in today’s job market, being a Swiss-Army-tool-like credential for folks who don’t know what they want to do when they grow up, I decided to look at admissions rates with the goal of telling an aspiring MBA what his chances of getting into a prestigious school are. I focus on prestigious schools because they are most worth the investment of time and money, and analysis like this doesn’t cut it.
For this example, I have to make some assumptions, and I hope to list all of them. If some sharp cookie out there who knows stats or better information spots an error, please let me know. I am an amateur at this sort of thing.
There were 264000 GMAT takers in 2010. 78% of the score reports were sent to schools in the United States (page 8). The Graduate Management Admissions Council says that 2/3 (67%) of test takers score between 400 and 600. In a perfect normally distributed world, we’d take this to mean that the average score was 500, but that conflicts with this report of a mean of 540. We’ll use the 540 figure here, and assume a Standard Deviation of 100 points for the general population. I did not find hard data on that Standard Dev, but the calcs are pretty easy to adjust for and I recalled seeing that as a figure somewhere.
So, accordingly, about 83% of all GMAT takers have scores at 640 or below.
That leaves ~17% of takers with scores over 640. See the following table for concrete numbers of GMAT takers by each possible test score fit to a normal distribution with a mean of 540 and SD of 100. For instance, there are 6707 people who scored a 640 on the GMAT, worldwide, based on the number of people taking the test and the mean/SD information.
High-profile business schools (think Harvard, Stanford, MIT-Sloan, Wharton) typically admit between 7-15% of their applicants and have GMAT means of around 720-730. There is an average class size among the top 10 schools of 500 students, leading to a total of ~5000 top school slots available every year. The table above shows that if schools admitted students solely on GMAT score, by order of school rank, we’d see something like Harvard snapping up ALL of the 800 and 790 scores, Stanford getting half of the 780s, Booth getting the 780s and some 770s, etc, down the line. But that’s not exactly how it plays out, due to score distributions.
Those schools provide some helpful data on their websites about their GMAT score distributions. Harvard, for instance, has an admit profile with a median GMAT score of 730 and overall scores between 550 and 790.
Given the total number of GMAT test-takers and after doing a little statistics work in MathCad, we see that the overlaid normal distributions of the general GMAT population (of 264000) and top 10 B-schools indicate that a higher GMAT score correlates with a much higher percentage of admissions. We assume here that the mean score for the top 10 is 730 and the SD is 40 points–not unreasonable, but the actual mean is probably around 710-ish. The following graph shows what the overlaid distributions are. It’s immediately apparent that odds of admissions any of the 5000 available top-10 B-school slots (red line divided by blue line at a X-value) go very much higher at higher GMATs. News flash, right?
For the following calculations, we’re going to look at probability of admissions based SOLELY on GMAT scores, and ONLY to Harvard Business School with a class size of 924, a mean GMAT of 730, and a SD of 40 points. Additionally, we’re going to assume that EVERY GMAT TAKER in the WORLD is applying to Harvard, because it’s a damn fine school.
For real world applications, you could take these calcs and adjust for the ~5000 class slots in the top 10 business schools in the US (or worldwide), and figure out the odds of admissions accordingly by rank order.
Here are the findings of probability of admissions to HBS by test score:
I normalized test scores to a curve with a mean of 730 and SD of 40, and then broke the distribution down to find out how many admits per score range there would be for a class size of 924. The cumulative probability rank column on the far right is mean to account for rank-ordering scores–so that a score of 750 has all the likelihood of a score of 720 of getting in, plus the marginal improvement afforded by those 30 extra points on the test.
A few very important notes for any prospective MBA candidate: These numbers include all GMAT takers in the world for a single year. You would need to scale these figures to 1) the number of likely applicants to your school(s) and the mean/SD of your school’s score distribution. Running these trials gave a much higher percentage chance of admissions to a prestigious school. For instance, adjusting the class size to 5000 (to model the top 10 business schools) gave a much higher probability of admissions–on order of 50% for a 700 GMAT applicant to a class of 5000 with a mean of 710 and SD of 50.
If you have scores on the lower end of the spectrum (e.g. more than 1 SD below your school average), then you’d better be very truly exceptional to get into the school. Otherwise, I’d recommend saving yourself the time, money, and trouble of applying just to boost the school’s US News and World Report exclusivity rankings.
For an even better estimate, schools could provide the score distributions of their applicant pools. However, I suspect we won’t ever see those–“trade secrets”, I’m sure.
Additionally, these numbers of course do not take into account any qualitative application factors, and are based on the less-than-perfect GMAT info that is publicly available (or that I found.)
But, that said: For applying to HBS, knowing that you have a 30% chance of admissions based on GMAT alone at a score of 750 is encouraging–especially because you’re applying against the world in this case. And your odds get better as you refine your applicant pool sample for size and score distribution.
Given that testing strongly correlates to school performance, a reasonable assumption is that the undergrad performance of these test-takers corresponds roughly to their undergrad performance, adjusted for degree difficulty.
The moral of the story is this: If you want to go to Business School, assess yourself. Assess the costs and benefits of going. Then figure out what your actual chances of getting in are by running some numbers. Then– do well on the standardized test.
And those 10-15% admit rates don’t have to be as scary as they look, because most of that scary percentage is coming from people lower on the score curve.
Falling Outside the Normal Moral Constraints 