Saturday, July 31, 2010

Can Stanford Be #1 in the US News Rankings? The Data

[posted by Bill Henderson]

In a recent story in the San Jose Mercury News, the dean of Stanford Law School, Larry Kramer, announced his intention to make Stanford the #1 law school in the country.  As noted by Brian Leiter, the story did not quote Kramer as saying that he wanted Stanford to be #1 in the U.S. News rankings.  The reporter, nonetheless, inevitably gravitated to this dominant measure. As noted by Dan Filler, most students, alumni, employers, and bystanders, cannot get their heads around the meaning or usefulness of alternative measures. 

Fortunately, Larry Kramer's comments have served up an opportunity to grasp some of the limitations and folly of the current dominant method of ranking law schools. (And by the way, I am certain that Larry Kramer knows most of what I am about to write--he definitely understands the math.  He was making comments for public consumption.  Like Kramer, I am trying to make Indiana Law #1 in the nation, albeit not in US News sense. Every faculty member at every law school ought to share this aspiration.)

The Research Question: What will it take for Stanford Law School to be ranked #1 in the U.S. News Law School rankings?

Andy Morriss and I annually construct a simulation model of the US News rankings.  It routinely explains 99.5% of the variance in the actual rankings, and it enables us to test endless "what if" scenarios.  So let's load the dice and make some really extravagant assumptions:

  • Academic Reputation (25% of the input formula).  Increase Stanford's Academic Reputation from 4.7 to a perfect 5.0 (surpassing Harvard and Yale, who languish at 4.8). 
  • Lawyer/Judge Reputation (15%). Increase the Lawyer/Judge Reputation from 4.8 to a perfect 5.0 (breaking their current 4.8 tie with Harvard and Yale).
  • UGPA (10%).  Increase median UGPA from 3.88 to 4.0 (Harvard and Yale are at 3.89 and 3.9 respectively).
  • LSAT (12.5%).  Increase the median LSAT from 170 to 180 (blowing past the 173 medians at Harvard and Yale).  This assumption is somewhat absurd because there are not enough perfect 180 scores to produce this median at any law school.

Surely, giving Stanford a perfect score on 62.5% of the US News weighting formula will make Stanford #1, right?  It turns out, the answer is no.  Yale still beats out Stanford by a hair.  Stanford would, however, finally muscle ahead of Harvard for #2.

It is fair to ask, what is it about the US News ranking formula that produces these peculiar outcomes?  The answer is standardization of the underlying inputs. In order to make things like library books, LSAT scores, and employment figures commensurable, US News converts the underlying arrays into standard deviation units where the mean is roughly equal to zero and approximately 66% of the input scores fall within one standard deviation above or below the mean.  The US News weighting formula is then applied to each USN input and the weighted inputs are summed to produce the final US News score.

Many of the underlying input distributions, however, do not reflect a typical normal distribution (i.e., bell curve).  They are skewed.  The reputation variables are roughly normal, and therefore they are unimportant--or, more accurately, unlikely to strongly influence school movement.  Likewise, UGPA and LSAT have a natural cap (4.0 and 180) that limits outlier scores.  And outliers are what skew distributions.

The biggest "uncapped" input variable is direct per student expenses at 9.75% of the input formula.  In theory, there is no limit to how expensive legal education can be.  Yale, it turns out, spends over $100,000 per student, not counting financial aid, which is a separate variable accounting for 1.5% of the input formula.  In contrast, Harvard and Stanford spend only $80K+ per year per student.  In standard deviation units, that translates into 5.8 for Yale versus 4.2 for Harvard and 4.5 for Stanford.  So Stanford has a 1.3 standard deviation gap to close.  Reputation, LSAT, and UGPA are not enough to overcome this deficit.

Implications

My back of the envelope calculations suggest that a check for $350 million ought to be enough to produce enough endowment income to eclipse Yale in the US News rankings.  This assumes that the money is used for things like books, more faculty, and higher salaries for everyone.  If the money is spent on student scholarships, however, Stanford would need a check for roughly $1.8 billion to be #1.  Again, these are the idiosyncrasies of the dominant method of law school rankings.

Stanford alumni are well heeled.  And, like all of us, they want to be #1. But here is my my advice: Before you write your check to give Stanford faculty a big pay raise and a lower teaching load, or give some rich kid with a 180 LSAT a free legal education, including living expenses, consider other investment opportunities. $350 million would go a long way to solving the AIDS epidemic an Africa.  $1.8 billion could provide life-altering educational opportunities for children mired in poverty.

The legal profession, especially our students, have some big problems at the moment.  And society's are even larger.  The best law school is one that prepares its students to solve these problems.  This requires a careful balance of innovative teaching and scholarship.  The U.S. News rankings don't capture these metrics.  In fact, they obscure them and create incentives for truly destructive behavior.  By and large the deans are trapped.  From my own perspective, I don't think even one law school in the US News Tier 1 has reached even 10% of its potential to educate and solve problems.  Too many one-professor silos.  Too much ego.

I am sorry to moralize.  But someone needed to say it.  Let's focus on some problems worth solving.  At the end of the day, it will be worth it.

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