A 2015 Bloomberg survey throws up surprising data on HBS-Stanford rivalry on MBA admissions. Of 63 dual admits (a good sample size considering that only about 150-odd applicants get accepted to both the schools) they surveyed, 56% opted for Stanford, 22% for HBS, and a *whopping* 22% for a school other than the two.

In this post, I’ll analyze the aforesaid data, using independent data on yield, number of dual admits, and number of accepted applicants, and show why it is *not representative* of the choices made by HBS-Stanford dual admits in the class of 2014.

(Warning: the analysis involves some calculation.)

## Why 22% of HBS-Stanford dual admits can’t join other schools?

(Since Bloomberg survey was done for the class of 2014, data for calculations in this article has also been taken for the same class.)

Let’s analyze from the perspective of HBS:

Applying MCME principle to the entire *accepted* HBS class, accepted students can be divided into following two mutually exclusive and collectively exhaustive subsets:

First subset (or dual admits): Admits to HBS and Stanford, both, and any other schools and

Second subset: Admits to HBS and any other schools excluding Stanford.

Here, ‘other’ and ‘non-Stanford schools’ could be zero or more.

Now, I’ll calculate the yield of second subset and show that it leads to an incredulous result.

Number of dual admits = 150

Number of accepted applicants = 1,029

Yield = 89%

## Yield for the first subset of accepted applicants

As per Bloomberg data, HBS enrolls only 22% of dual admits, which means its yield for dual admits (or the first subset) is 22%.

## Yield for the second subset of accepted applicants

Let’s say it’s ‘x’.

The weighted average yield of the two subsets should be equal to the overall yield (89%) of HBS, which implies:

0.89 = (0.22*150 + x*879)/ (150 + 879)

Solving for x, we get:

x = 100.4%

A yield of 100% for the second subset means that almost no accepted applicant to HBS and other schools (remember, this subset excludes Stanford admits) joined any other school. Or the entire second subset of 879 joined HBS. Now, here is the big question.

As per Bloomberg survey, a sizable chunk (22%) of admits to HBS + Stanford + other school (subset I) opted for other schools. But, almost no one joined other schools from those admitted to HBS + other school (subset II).

Inexplicable!

Historically, there have been few reasons why accepted applicants choose less popular schools despite admission to more prestigious schools, main being attractive fellowship. (In fact, many admits to HBS and Stanford land lucrative fellowships from other schools on the basis of their admission to these two schools, with some applicants even proactively negotiating better deal.)

If this is the main reason (the reason is irrelevant here, though) – and, from anecdotal evidence, most likely it is – why 22% of HBS-Stanford dual admits opt for other schools, how can that bargaining chip reduce *drastically* to 0% for applicants in second subset? Remember, they still have an HBS admission, if not both.

Note: you can change variables such as number of dual admits in the above calculation, but the value of x would be a low single digit percentage.

## Conclusion

The proportion HBS: Stanford: Others = 22: 56: 22 is not representative of the choice of dual admits to HBS and Stanford GSB in the class of 2014.

The biggest suspect is 22% opting for other schools.