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timothy-hagle@uiowa.edu

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Dept of Political Science

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The University of Iowa

Iowa City, Iowa 52242

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**My books**

There are two basic sections to these comments. The first is an exchange of emails I had with a student and the second is a letter from LSAC and my reply.

About a year after posting the 1997 list I received an email from a student about to start law school at a Big Ten university. Some of my students had made similar comments, so I sent him a
lengthy reply and we had one additional exchange. The messages are reproduced below. I've done only minor editing to the messages to remove identifying information. Any typos and
such were in the originals, but are not marked with [sic]. I've added some final comments at the end (in *italics*).

**Student:**

I'm writing because participants in a pre-law discussion group that I sometimes follow were recently directed to your website by one of the participants. I think you've made a couple of mistakes in
your discussion of the admissions index formulas used by law schools.

First, I'm not sure how helpful your calculation of the percent of the maximum index score determined by the GPA part of the formula is. Your formula doesn't take into account the fact that the LSAT is scored from 120 to 180 (and not from 0 to 180), and that the variation in GPA among law school applicants is not so extensive as 0.0 to 4.0; so the percentages calculated with your formula are misleading. I wonder how helpful any such percentages are given the differences in scale? I find it much more helpful (and perhaps your students would find it more helpful) to think, instead, about what sort of increase in GPA is large enough, at each school, to compensate for a one point decrease in LSAT. I think this, since it is a measure entirely independent of the structure of the applicant pool, gives a better sense of the relative importance each school places on LSAT in those formulas (I'd also note, though, that the data I've seen has suggested that those formulas are not the last word in weighting -- that a school with an LSAT heavy formula is not necessarily LSAT heavy in admissions and a school with a GPA heavy formula is not necessarily GPA heavy in admissions).

But I write, mainly, to address your discussion of the constant and to suggest a reason the maximum index scores are not round numbers. What you haven't recognized is that most of those index formulas were generated by regressing LSAT and undergraduate GPA against actual first year law school GPA of previous admitted classes. So the index number represents a predicted GPA and it is not a round number because there is no combination of scores for which the predicted GPA is 4.0. The constant, of course, is included so the estimated plane will not be forced to pass through the origin. It is irrelevant for comparisions between students, but interesting, perhaps, to students who would like to know their predicted first year GPA.

Finally, it may be helpful to you and the students you advise to know that some schools take pains to disguise the fact that their admissions index formulas give predicted first year GPAs. [My school's] current index, for example gives index numbers in the neighborhood of 230. I asked ... the Dean of Admissions ... about this when I talked to him at an admitted students information session (I will be a 1L at [a Big Ten law school] next year). He told me that the index formula is, in fact, derived from a regression of the sort I've described, but that they deliberately changed the scale so the significance of the index number wouldn't be so obvious to the members of the admissions committee. He thought that, psychologically, faculty and student members of the admissions committees would be more likely to exclude or accept candidates solely on the basis of the index number if they could easily interpret the number as a predicted GPA.

**My reply:**

Thank you for your interest in my prelaw materials. My goal is to give my students (and any others who see the materials) more information so they can make better decisions regarding law school. I
certainly don't know everything about law school admissions and am interested in learning more. As such, I found your comments interesting and have some comments in reply.

Let me begin with a "lawyerly" point regarding your suggestion that there are mistakes in my discussion. That you might disagree with some interpretation, or not find it overly helpful, does not make it a mistake. Of course, calling such a difference a mistake is often used in argumentation to put one side on the defensive. It's a relatively minor point, but as the need for precision is inherent in the law I thought I would mention it.

Your first point concerns the helpfulness of the LSAT-GPA comparison, particularly given that the scales for each do not go to zero. The LSAT scale is only 120-180. In most cases GPA is capped at 4.00 (though at Iowa it's 4.33) and for practical purposes it shouldn't be below 2.00, which is the minimum requirement for graduation at most colleges. These limitations, however, do not matter within the context of the formula. (Just as they do not, with one exception I'll mention later, in the regressions.) If the scales were changed to 0-60 and 0-2.00 then the law schools' formulas would change to reflect the smaller scales, but the relative weights between them would not vary. More specifically, because of the linear nature of regression, as long as the scales do not change in terms of range and distance between points, then the coefficients would only vary to maintain the relative weight between the two variables. For example, halving GPA to be on a 0-2.00 scale would result in a doubling of the coefficient for GPA in the regression results.

Your next suggestion is that a comparison between LSAT and GPA is not helpful. This is really a matter of your personal preference. Many law schools give the impression that LSAT and GPA are given nearly equal weight with, perhaps, as much as a 60-40 split in favor of the LSAT. When I obtained the list of formulas I was very surprised to see how much more weight was given to the LSAT. For the law schools that use regression analysis to predict the first year law school GPA based on the results of previous classes the greater weight given to the LSAT simply means that the LSAT is a much better predictor than GPA. This is not surprising. Where a particular GPA may not mean the same thing from one college to the next, or even from one major to the next within a particular college, the LSAT, in contrast, is the great equalizer. Given that the LSAT is a much better predictor of first year grades, it should come as no surprise that more weight is placed on it as admissions committees sort through piles of applications looking for the best students who will succeed in law school and go on to make piles of money, some of which, they hope, will be sent back to the former students' alma mater. Given all this, it may be important for an applicant to know where he or she stands based on a given school's index. A student with a very good LSAT and a weaker GPA may nevertheless be willing to apply to law schools that put much greater weight on the LSAT. Conversely, if the applicant's GPA is stronger, he or she may be more likely to consider law schools that place a bit more weight on the GPA relative to the LSAT. In addition, the applicant may be more likely to consider retaking the LSAT if it is given a much greater weight.

You suggest that it would be more helpful to know how much of a change in GPA is necessary to compensate for a one point decrease in the LSAT. There is nothing particularly wrong with looking at it this way. In fact, one of my students made the same suggestion this last year and I plan to do some additional analysis along those lines. This information can be easily calculated from the formulas, but I'm not sure how valuable it really is. By the time applicants take the LSAT they have had three years of undergrad courses. Some admissions decisions are made during fall of the applicants' senior year, which means no additional grades will be available. Even decisions that are delayed until the spring will only have one additional semester of grades available. Thus, there is little or no ability to improve one's GPA based on this information. As for the LSAT, applicants will, or should, always do their best, so this isn't something that one can change either. At best, one can do a bit more to prepare to take the LSAT, but I have my doubts about how much prep courses actually improve scores. On this point you also suggest that the tradeoff info is better because it is independent of the applicant pool. Technically that is correct because, just as with my formulation, the numbers are not based on the current set of applicants. Both formulations are, however, based on past applicant pools (or more specifically, that subset of applicants who were admitted and completed the first year so that there is a first year GPA to use as the dependent variable).

You next suggest that the index for a school is not determinative. I certainly make no claim that it is. (I suppose I should note that some of my points here are ones I mention in my Prelaw FAQ. You missed them if you only looked at my Admission Index page.) As I tell my students, the index may very well be determinative as a first cut: some will be immediately accepted, others immediately rejected. For the large group in the middle, other items such as strength of undergrad program, quality of resume, letters of recommendation, and race/ethnicity/gender will become more important.

Your next point concerns the constant. It's not a matter, by the way, that I didn't recognize that the constants for many schools are the result of regression analysis, I was simply not aware of it. Even so, about 30 schools on the list do not use a constant, including [your school], and another half dozen have one that is clearly artificial (i.e., an even number such as 100) indicating that the schools do not use regression analysis to calculate their formula. As you are aware that the use of the constant prevents the equation for the plane from being forced through the origin (though it may go there of its own accord), you may also be aware that one problem in using regression in a situation such as this is that its linear nature can create problems given that the predictions can take on values that are not possible when the actual values are bounded in some way. This may also help to explain why the Totals are not always even numbers.

Finally, you mention that law schools don't want folks to know the index values are related to predicted first year GPAs. I am, of course, well aware of this. Frankly, I'm surprised so large a number of schools release their formulas. When applicants have such information they tend to get cranky when they aren't admitted and someone with a lower index score is (i.e., affirmative action). (Along these lines, you will likely read both Bakke (438 US 265) and Hopwood (78 F3d 932). If you see these in a casebook you probably won't get the data presented in the notes, so do look up the cases in the reporters.) I can also understand why the predicted GPA is disguised from the law school's admission committee. Aside from the explanation given to you by your dean, instructors who teach the first year courses might be influenced by a student's index score when doing their own grading if such scores were easily translated to a 4.0 scale.

**Student:**

Thank you for your reply -- I'd hoped you'd take the time to read my note (which is why I wrote it, of course!) but I'm genuinely flattered that you took the time to reply. I do a lot of e-mail
correspondence and it always astonishes me how much more time it takes to reply to someone than it does to read what they've said. But I want to take a little more of your time, because some things
in your reply suggest that I didn't convey very clearly what I wanted to in my first note. For example, you wrote:

Let me begin with a "lawyerly" point regarding your suggestion that there are mistakes in my discussion. That you might disagree with some interpretation, or not find it overly helpful, does not make it a mistake

But I do think there is a mistake in the formula -- I don't think it measures precisely what you are using it to measure. You are, of course, correct that the ratio of one constant to another takes into account scale problems. The real difficulty, though, is not that the LSAT and GPA are measured on different scales, it is that neither begins at zero. That is, there is a certain minimum index number which every student has. Assuming that no one applied to, say, American University with a GPA of less than 1.5 then there, for example, every applicant begins with at least 75.99 points (assuming an LSAT of 120 and excluding the constant). Admissions decisions, though, are made on the basis of the next 46.01 points (122 - 75.99). Of those 46.01 points, 11.45 come from the GPA (just under 25% of the points, not just over 15% as calculated on the basis of the total points possible) while 34.56 come from the LSAT. The LSAT, of course, is still weighted very heavily in the index -- three times as heavily as the GPA -- but not quite so heavily as your calcuations suggest. If, on the other hand, the lowest GPA in the applicant pool at American is 2.0, then every applicant begins with 78.28 points and all variation is in the last 43.72 points. Of those, 34.56 again come from the LSAT while 9.16 (now only 20.95%) come from the GPA. Take another, very silly, example. Assume a very, very bad law school (sort of like the University of District Columbia) where the best applicants had an LSAT of 123, while grade point averages ran from 1.0 to 4.0 (the university has an undergraduate program of similar quality and some of its students applied to the law school). For simplicity's sake, assume its formula is:

LSAT + GPA = INDEX

Calculating the GPA's contribution to total points we find that it constitutes 3.25% of the Index. But, of course, of the points which are contested, half come from the GPA.

The percents tell us something about the relative magnitudes of two numbers in terms of their distance from the origin. But the distance from the origin depends on minimums so to interpret the percents we need to know something about the minimums. Someone with a 130 on the LSAT has 72% of the top score, but only 16 percent of the points he could have earned. So, we're really interested in a bounded planar surface which is parallel to the plane described by the index equation, but which lies below it, touching, at its bottom corner, the origin of the LSAT and GPA axes. In the transposing, the surface might be moved closer to the LSAT or the GPA axis depending on the structure of the applicant pool.

Your next suggestion is that a comparison between LSAT and GPA is not helpful. This is really a matter of your personal preference.

Right. And I understand that many students do want to know how much "weight" each item has in the application, but there is an idea behind my preference and it is this:

Consider two students, Rosencrantz, who got a 180 on the LSAT but only had a GPA of 1.0 (let's say he attempted college several times, flunking out several times and transferring, but eventually he was able to graduate with a 2.0 at his final school which, unfortunately for him, became a 1.0 when the LSAC calculated his GPA using grades from every school he attended although he took far more classes, altogether, than was necessary for graduation at his final school). Then there's Guildenstern, for whom, the utter lack of ability indicated by his 120 on the LSAT, seems to have been no impediment to him as he graduated from a college with a 4.0. At American University, Rosencrantz's admissions index is 108.26; while Guildenstern's is 87.44. Now assume that American University decides to accept all students with index numbers above 108. The weights American puts on LSAT and GPA are really of no help to Guildenstern and would continue to be of no help even if they were substantially different, so long as they're not enough different to push him above 108.

On the other hand, you write:

Given all this, it may be important for an applicant to know where he or she stands based on a given school's index. A student with a very good LSAT and a weaker GPA may nevertheless be willing to apply to law schools that put much greater weight on the LSAT. Conversely, if the applicant's GPA is stronger, he or she may be more likely to consider law schools that place a bit more weight on the GPA relative to the LSAT. In addition, the applicant may be more likely to consider retaking the LSAT if it is given a much greater weight.

And this I see with limpid clarity, as my career has been more Rosencrantzian than typical With my LSAT score (174) and GPA (2.76) I was in precisely the situation you describe first. Unlike my Rosencrantz, I never flunked out of any college, but I did take many classes that I was, perhaps, temprementally and intellecutally unsuited for. Mainly math classes. You will probably meet very few people in your life who have taken differential equations, optimization theory, a full year of abstract algebra &c., as *electives*, but I am one (over a third of my total units were in math classes required neither by the school nor my major). I did very poorly; passing, but sometimes only barely. Which does, of course, say that I have no talent for math and raise the possibility, even the likelihood that I've made some ghastly mistake in my analysis above. If you see it, I'd be happy to have you correct it. But getting back to the point, I did very much want to know which schools were "LSAT heavy" and which "GPA heavy." But I do think a potential applicant can make this sort of comparision if he knows what sort of a GPA deficiency a one point LSAT increase will compensate for at each school he is considering. At least, this was a factor in my decisions about where to apply.

**My reply:**

You are correct about replies taking time. As I mentioned before, my students have raised similar questions, so my reply was a bit longer than it otherwise might have been. That being the case, let
me get a bit more detailed to explain why there isn't a mistake in my formula for %GPA in the table.

As I mentioned before, the point of %GPA is to show how much weight is given to the GPA relative to the LSAT (excluding a constant, if any). My understanding was that the two scores were given fairly even weight, but this was not the case based on the formula. To the extent the law schools were fostering such an impression they were either mistaken or being a bit deceptive. This is not to say that the formula used by any particular school would be incorrect. The questions are whether the formula used is really measuring what the school thinks it is and whether the school is being honest about it.

That said, let me start with the formulas used in Hopwood (78 F3d 932). In footnote 1 the Court of Appeals provides the two formulas then in use at the U of Texas. One is based on the old 10-48 LSAT scale and the other on the current 120-180 scale. The court notes that UT intended to put approximately 60% of the weight on the LSAT because it was a better predictor of success. On the old scale the formula was

(1.25)xLSAT + (10)xGPA

The maximum scale value is generated using the maximum scores: (1.25)x(48) + (10)x(4.0) = 60 + 40 = 100. That the maximum value for this index is an even 100 makes it easy to see the relative weight given to each component. As UT intended, the LSAT accounts for 60% of the total and GPA 40%.

The key to determining the relative weight is to use the maximum values for each component to determine how much each contributes to the total. You suggest starting from some minimum value and working in the other direction, but there are two problems with this. First, in your example you arbitrarily select a minimum GPA, which is not necessarily equivalent to the minimum LSAT. Second, by doing so you changed the scale.

Let me use an example from my courses to illustrate these points. In one of my courses I give two tests and a paper. The first test is worth 30 points, the paper is worth 30 points, and the second test is worth 40 points. As they total to 100 points, each constitutes the same percentage in the total as the number of points. Now suppose that no one has ever gotten less than 10 on the tests or less than 15 on the paper. That effectively makes the minimum score 35. Of the remaining 65 points, 20 come from the first test, 15 from the paper, and 30 from the second test. By your calculations, that would make the weights 31%, 23%, and 46%, which is clearly incorrect.

I have two additional points before moving on to the second UT formula. First, it does not matter whether the scores for any component go all the way to zero. What matters is the amount that component contributes to the total possible value. Second, as opposed to the total, any particular index value may be made up of a different ratio of GPA and LSAT values depending on the person's score. Using my course example, a person could have gotten 50 points my scoring 30 on the first test, 20 on the paper, and 0 on the second test. A second student could have gotten 0, 30, and 20. Each student's score is made up of a different percentage of the three assignments, but the overall weight of the assignments stays the same (30, 30, 40). Put another way, the weight the school puts on the components is not necessarily the same as how much each contributes to any given applicant's index score.

When the new scale was introduced for the LSAT, UT began using LSAT + (10)xGPA as its new formula. Given that UT was comparing applicants for the same first year class who had taken the LSAT under both scales, the formulas should have given the same weight to each component. Unfortunately, they did not. Specifically,

180 + (10)x(4.0) = 220

Thus, GPA contributes only 40 out of a possible 220 index points for a relative weight of only 18.2%. Footnote 5 of the opinion indicates that UT calculated equivalency tables to compare students who took different versions of the LSAT. Even so, those with new LSAT scores had much greater weight put on the LSAT than those who took the old version. That may have been good or bad depending on where the student was strong, but the point is that the difference should not have existed.

The rest of your comments either flow from those addressed by the above or from a personal preference for knowing the more specific tradeoff, so I'll leave it at that with one final comment. Having been a math major as an undergrad, I see great value in students having at least some exposure to mathematical training. The law is increasingly involved with statistical, mathematical, and scientific issues. Unfortunately, many lawyers and judges have very little training in such matters. Even those who do have some training can make mistakes in interpreting data and such.

**Student:**

I'm sorry, but I still fail to see your point. Consider your example:

Let me use an example from my courses to illustrate these points. In one of my courses I give two tests and a paper. The first test is worth 30 points, the paper is worth 30 points, and the second test is worth 40 points. As they total to 100 points, each constitutes the same percentage in the total as the number of points. Now suppose that no one has ever gotten less than 10 on the tests or less than 15 on the paper. That effectively makes the minimum score 35. Of the remaining 65 points, 20 come from the first test, 15 from the paper, and 30 from the second test. By your calculations, that would make the weights 31%, 23%, and 46%, which is clearly incorrect.

Instead of assuming that no one has gotten less than 10 on the tests or 15 on the paper, assume that another professor offers a similar battery of exams and papers, but no one can get less than 5 on the first test, 10 on the paper or 25 on the third test -- that even a paper or test left undone will give the student the minimum number of points. One student in the class is obliged to miss one of the assignments because of an unavoidable, necessity to be out of town for three weeks during the semester, but the particular two weeks are left to his chosing. He has discussed the problem with his professor, but the professor is unwiling to offer him any concession. He cannot do the paper early, because the professor will not assing a topic for it until two weeks before it is due. He respects your opinion so he comes to you for advice. Do you tell him that he should, by no means, miss the last test as it is weighted the most heavily? If he does the rest of his work perfectly, he will, if he skips the first test, have earned 75 points -- five for the first test, thirty for the paper and forty for the third test. If he skips the paper he will have earned 80 points, if he skips the second test he will have earned 85 points. Clearly, the weights on these assignments depend on the minimal as well as the maximal scores.

Now assume that a professor offered two exams and a paper, the first exam and the paper each worth 30 points and the last test worth 40 points, but had minimums as you propose -- no one scores less than 10 points on a test and 15 on a paper and a second professor offered two exams and a paper and gave 20 points for the first test, 15 for the paper and 30 for the second test but gives each student thirty five points to begin with; and the student came to you and explained that he was compelled to leave undone the paper in one of his classes. He has spoken to both professors, but they are willing to make no accomodation, and he asks your advice because, again, he respects your opinion. Do you tell him to skip the paper in the first class or the second? Does your answer change if the second professor gives fifty points for the paper, but all students are given a score of 35 on the paper whether it is done or not?

Looking, again, at my silly example. Let's say that law services adopts a new scoring scheme for the LSAT. Scores now run from 120 to 124 (reported, perhaps, to one decimal place). A school adopts an admissions index:

LSAT + GPA = INDEX

The maximum possible number of points from the LSAT score under this scale is 124. The maximum possible number of points from the GPA remains four. The maximum index is 128. Would you really argue that the weight on the GPA is 3% and the weight on the LSAT is 97%? Where you say, on your website, " This means that law schools place four times as much importance on the LSAT as compared to the GPA!" would you, instead, say "This means that law schools place 32 times as much importance on the LSAT as compared to the GPA!"? If so, why do you think anything of interest to anyone is said when you say the LSAT is weighted 32 times as heavily as the GPA when a student who misses every question on the LSAT but has a perfect GPA is in precisely the same position as a student who has a perfect LSAT score who never took a class but to fail it? If not, why does your method not imply that that is the proper description of the weights? How is my calcuation of the 3% weight on the LSAT in this formula different from your calculation of a 15.02% weight in the American University formula?

While it is undeniable that your method gives the percentage of the total number of points available (ignoring the constant) accounted for by the GPA; I do not see how that can meaningfully be said to be the *weight* given to the GPA by the formula if "weight" is understood to have some meaning like "the importance of the GPA to the committee for the purposes of determining whether to admit students, deny admission to them or hold them for further consideration.

**Final Comments:**

*Given his opening statement, I chose not to reply to this last message. In a previous message he takes pride in having taken many math courses despite not having done very well in
them. Although I am in favor of potential law students taking math and science courses, I have to wonder why his advisor didn't tell him to take something else (or to put more effort into the
math courses). I don't know whether he really doesn't understand my points or is just set in his own view. Aside from some flaws in his analysis, and some rather contrived examples, his
basic preference for knowing the precise tradeoff between LSAT and GPA for his case is certainly acceptable. Although, as I point out in one of my messages, I'm not sure how helpful it is at a
practical level. In any case, there it is and you can make of it what you will. *

In late 2004 (or maybe early 2005), I was asked to meet with the then-new Dean of the UI law school and the Associate Director of Admissions. I was happy about this as it was the first time anyone at the law school seemed interested in talking to me about prelaw students. Although it proved to be a good conversation, it became apparent that their prime motivation was to discuss their concern about the information I have posted on the LSAT index scores and weighting. Prior to our meeting they had asked the folks at LSAC about the matter and received a reply that described some of the procedures and statistics that went into the index formula (as applied to the UI). They gave me a copy of this letter and I said I would look it over and send them a reply, which I finally did in July of 2005.

The letter gets a bit technical, which, I think, is part of the problem. Nothing in the LSAC letter really detracts from what I have to say about the subject, but because the law school folks don't really understand the statistics behind it all they have difficulty evaluating LSAC's explanation versus mine. I try to keep it simple in my reply, but I don't know if I was successful as I didn't hear more about it from the law school folks.

Nothing in the LSAC letter seems confidential, so I am posting it as I received it, with the exception that the version scanned has some notes I made on it as I was preparing my reply. Similarly, I am posting my reply as I originally sent it. As with my prior exchange with the student, you can make of it what you will.