Over the next few days, I'm going to be summarizing key findings from my article on law school racial preferences, and discussing the findings with readers. Today is:

Entry One: The General Operation of Racial Preferences

When law schools talk about race-based admissions preferences - something they generally discuss as little as possible -- they make three claims: (a) the preferences are small and not automatic, (b) race is one of a myriad of factors taken into account to create a diverse class, and (c) everyone admitted is fully qualified to do well at the school. These were the central messages advanced by the University of Michigan Law School in their defense of affirmative action before the Supreme Court. I found in my research that all three claims were substantially untrue, both for Michigan and for law schools generally. More interestingly, I found that each law school follows such a similar pattern that a powerful "cascade" effect sets in, creating interesting collective action problems for the system as a whole and for any school that wants to approach admissions less mechanically.

The problem every university faces is the gap in test scores and grades between whites and Asians on the one hand, and blacks and Hispanics on the other. On a 1000-point academic scale I use throughout my paper, the median black/white gap among law school applicants was about 170 points in the early 1990s and is about 135 points today. As you may recall, the Supreme Court issued two opinions in last year's affirmative action case. In Gratz, the Court found that undergraduate college at the University of Michigan violated the constitution by awarding a fixed number of points to black applications. The Law School's admissions passed muster, according to Justice O'Connor's decisive opinion, because race there was part of a complex individualized assessment of each applicant - the opposite of a mechanical award of points.

Many of O'Connor's colleagues hinted that she was elevating form over substance. With good reason. Using logistic regression and other techniques, I estimated the weight given to race and to academic numbers by the College and the Law School. The Law School's admissions were more dominated by numbers, and the implicit "boost" given black applicants was larger (and as mechanical) as the College's system. The only substantive difference between the two schools is that the College took more account of factors like socioeconomic background, writing samples, and extracurricular activities - differences that should have made it more constitutional in O'Connor's eyes, not less. What apparently saved the law school was the way they talked about their admissions system, and perhaps the plaintiff's failure to adequately demonstrate its actual workings.

The Michigan law school admissions cycles litigated in Grutter (mostly the 1995 through 1999 cycles) are highly representative of practices at law schools nationally. I gathered data from seven other public law schools through FOIA requests, and analyzed another database that has data on 27,000 law students from the Class of 1994. At every law school, at least 80% of admissions decisions (and usually more like 90%) could be predicted by knowing the LSAT, undergraduate GPA, and race of the applicant. Nearly every law school used the same metric for white and black students, but either added points to eliminate the black-white gap in credentials or simply segregated admissions files by race. Nearly every school admitted black and white applicants at rates that were statistically indistinguishable. And in the 1990s, a virtually identical 170-point gap could be found between the credentials of the median white matriculant and the median black - a gap that reached from the most elite schools to the smallest regional schools (ironically, only the historically black law schools were exempt from this pattern).

Herein lies the collective action problem. The preferences awarded by the top tier law schools absorb all the black applicants that would be admitted, in a race-blind system, to second-tier schools. These schools must therefore choose between having essentially no black students or duplicating the types of preferences pursued in the top-tier. Nearly all the second-tier schools choose the latter course, thus putting third-tier schools into the same bind, and so on. The net effect of this system is to move nearly all blacks up a tier (or two) in the law school hierarchy, thus placing nearly all blacks at an enormous academic disadvantage in the schools they attend. The only net addition of blacks to the system comes in the lowest-tier schools, and the black students they admit have such marginal academic credentials that they face long odds against every becoming attorneys.

Tomorrow: The effects of preferences on grades, graduation and the bar

Entry Two: The Effects of Preferences on Grades, Graduation, and the Bar

As I discussed yesterday, a very large majority of American law schools essentially race-norm black and white academic credentials when they admit their classes. Since the black/white credentials gap in the applicant pool is quite large, this means a typical law school has very little overlap between the highest credentials of its black students and the lowest credentials of its white students. This wouldn't matter very much if, as critics have long argued, the LSAT and UGPA were poor predictors of law school performance. And it's true that, individual by individual, these credentials are only rough indicators of performance. But applied to groups they are extremely accurate.

Consequently, blacks as a group have academic trouble in law school in very consistent and predictable patterns. At American law schools that use large racial preferences, half of all black students end up in the bottom tenth of their first-year class. Put a little differently, the median black student performs in the first-year at about the 7th percentile of the median white student. The gap is statistically no different in legal writing classes than in classes with timed exams. And, when we adjust for dropouts, the black-white gap gets slightly wider over the second and third year of law school.

It's important to note that this performance gap has nothing to do with race per se; whites who attend law schools where their credentials are far below most of their peers have pretty much the same types of troubles. The performance gap is a function of preferences. (Now, it's true that the preferences come about in the first place because of the black/white credentials gap - but that is another story, which I'm happy to address later if readers are interested.) There is no credible evidence I've seen that, if schools used race-blind admissions, blacks would underperform whites at all. (I will discuss this issue further, and respond to some reader commentary, this Friday.)

The most obvious consequence of the grade gap in law school is that blacks are expelled, or drop out, at much higher rates than whites (19% of blacks don't complete law school compared to 8% of whites). Almost all of the attrition is among students with very low grades. The more serious consequence is that students at the bottom of the class apparently learn less than the same student would learn at a lower-tier school where the student was closer to the middle of the class. This is what's known as the "mismatch effect".

A number of studies of college students have found various types of mismatch effects. Black law students who go to schools where their credentials are far below most of their classmates are less likely to graduate, more likely to switch out of science majors, and more likely to abandon aspirations for an academic career than blacks who attend college where their credentials place them closer to the middle. These studies have been hampered, however, by the absence of any general test that college students take after graduation; no one could demonstrate that blacks actually learned less at more elite schools.

For my research, I was able to capitalize on a massive database compiled by the Law School Admissions Council in the 1990s, which tracked law graduates through up to five attempts to pass the bar. Bar exams vary state by state, but they have much in common and there are ways to control for the variations. I found that law school grades predicted bar passage rates far more powerfully than school eliteness did -- it was more important to be near or above the middle of the class than at a higher-ranked school -- and, again, this was equally true for blacks and whites. However, since the preferences system pushes most blacks to attend more elite schools, the tradeoff has devastating effects on black bar passage. Blacks are 50% to 100% more likely to fail the bar on their first attempt than are whites who started law school with identical credentials. Combined with the admission, at the bottom of the law school hierarchy, of blacks with very weak academic backgrounds, and one finds that nationally, blacks fail the bar at four times the white rate.

Taking the graduation effect and the bar effect together, and one finds that only 45% of blacks who started law school in 1991 graduated and passed the bar on their first attempt (compared to 80% of whites). Again, this is not a "racial" effect, but a preferences effect. I find in my analysies that the graduate-and-pass rate for blacks would rise to 74% in a preference-free system -- still a little lower than the white rate, but only because the distribution of black credentials is lower than the white distribution.

Tomorrow: Black law graduates in the job market

Entry Four: What Would the Black Bar Look Like With a Reduction or Elimination of Law School Racial Preferences?

Perhaps one of the reasons that few legal academics have delved very far into the issue of law school racial preferences is the widespread assumption that, whatever the other costs and benefits of the system, admissions preferences are the only way to racially integrate the bar. The claim that has been repeated many times - and which figured prominently in the Grutter briefs -- is that black enrollment in law school would drop 50-90% if preferences were abolished. Since a decline of that magnitude seems unimaginable, so does a serious questioning of admissions preferences.

In my research, I found that the usual method academics use to project admissions in a race-neutral world is seriously flawed. Most such projections assume that minority students will continue to apply to the same schools - and only those schools - if preferences disappear. But if preferences are large, and minorities (blacks in particular) take preferential policies into account in deciding where to apply, then it is necessarily the case that minority applications will overwhelmingly be rejected in a race-neutral world.

If one instead asks what proportion of the black applicant pool would be admitted to some law school under a race-blind system, one gets a much rosier result. A 2003 study by Dr. Linda Wightman (who headed LSAC's research operations for many years) found that 86% of blacks admitted to law school in 2001 would have qualified for some law school under a race-blind system. That number has risen sharply over the past decade, because of a steady rise in the number of black applicants and a gradual but steady narrowing of the black-white credentials gap.

Now, recall that in my research I found racial preferences tend to systematically lower black performance in law school, black graduation rates, and black rates of success on the bar exam. Only 45% of entering blacks under the current system graduate and pass the bar exam on their first attempt; another 12% pass the bar on some later attempt. I estimate that the 45% figure would rise to 74% under a race-blind regime. If the pool of entering black law students shrinks a little, but their survival rate rises sharply, it's not hard to see why we might well end up producing more, not fewer, black lawyers in a race-blind system. My best guess is that the total number of blacks passing the bar on their first attempt would rise about 22% in a race-blind system; the number passing after multiple attempts would rise 9%.

The emphasis here should be on the word "guess". Obviously, no one knows what would happen to black interest in attending law school in a world without preferences. There might be a surge of interest in a law school world where blacks perform much better, have much higher chances of success on the bar, and dispense with any stigma from affirmative action. There could be an erosion of interest if blacks are faced with attending less elite schools or if many blacks view the end of preferences as a signal that they are unwelcome. I would hope that my findings, and those of other researchers, would reassure black applicants that going to less elite schools is an excellent career move for them, but of course no one knows. My simulations make the neutral assumption that the total volume of black applications won't increase or decrease.

The stories I've read about my article almost invariably cite the "9% increase in black lawyers" projection and infuse it with an air of artificial precision. That's unfortunate, though perhaps inevitable given the exciting aura such a claim carries with it. I'm really trying to make two other points. First, the end of preferences clearly no longer implies a massive hit to the production of black lawyers. The claims of a 50-90% decline were misleading nonsense. (My most vocal critics are now suggesting a 25-35% decline.) I will defend my 9% increase as a much better guess, but the important point is that the range of debate has shifted.

Second, there can be no question that in a race-blind system, the black bar would be healthier in a number of ways. The proportion of practicing black attorneys who have failed the bar at least once would fall from 22% to less than 10%, and black scores on bar exams (even for those who pass the first time) would be dramatically higher. The median earnings of black attorneys (at least for the early career years I have measured) would be significantly higher, and blacks would be distributed across job sectors in a way much more similar to white patterns. And of course, many, many fewer black law students would spend years earning a degree that failed to gain them admission to the profession. With all this said, I am not at all convinced that a total elimination of preferences is the best way to go. It's certainly the cleanest solution, and perhaps the only one that policy-makers could legislate. But I think there are a variety of alternatives worth exploring. Consider, for example, what I call the "4% solution." Suppose that all law schools agreed that, if they use racial preferences for blacks, they would not apply those preferences to more than 4% of the class. Schools would of course continue to admit all blacks who qualified without preferences, so the 4% would be a floor, not a ceiling.

The beauty of the 4% approach is that it breaks the cascade effect. The top ten law schools would presumably fully use the 4%, and would thereby preserve more racial diversity at the top than we would have (at least initially) in a race-blind system. But the next tier of schools would now have many black applicants who formerly went to top-ten schools; they would be significantly less reliant on preferences. In the third tier and below, preferences would be nearly irrelevant. Enough blacks would have shifted down-market so that schools would have very substantial black enrollments (often larger than current black enrollments) with minimal or no preferences.

This approach has several advantages. It effectively confines the aggressive use of preferences to the top tier of schools, where the academic mismatch is most benign in its effects. It blunts the fear of those who believe that the most talented blacks will shift to other fields if they are unlikely to attend top-ten schools. It mitigates the diversity impact on the most elite classrooms, and provides some reassurance that pipelines of talented blacks into prestigious clerkships and legal academia remain open.

My hope is that, by developing some rough consensus on how to model the systemic effects of affirmative action, we can have a much richer dialog and can identify and test possible compromises, like the 4% solution, that break the ideological logjam.

***Thanks to readers who have sent me comments and questions. On Monday, I'll respond to a number of these.***

Although my article on affirmative action appeared in the Stanford Law Review less than five months ago, a legion of critics has sprung into print, publishing rebuttals with very non-ivory-tower speed. By my (probably incomplete) count, eleven articles entirely devoted to "debunking" Systemic Analysis have been published or accepted for publication in legal or education journals, and dozens of more informal critiques have appeared in the media and a variety of websites.

Through most of this period, I've tried to focus on taking the criticisms to heart -- understanding the arguments, looking closely at the evidence, and trying to separate the wheat from the chaff. I am publishing a lengthy response to critics in the May issue of the Stanford Law Review (which probably won't be out for another four weeks) and a shorter response in the June issue of the Yale Law Journal (which should be out in two or three weeks). These responses tend to be pretty technical and very detailed. What I would like to do in this space, for the next couple of weeks, is something more informal and, I hope, more interactive.

So starting Friday, June 10th in this space, I will examine seriatim the fallout and controversies that followed in the wake of Systemic Analysis. I will leave an open comments section at the end of each post, and on the following workday I'll both cover a new topic and address significant questions raised in the last day's comments. If any of the major critics or commentators on the article is willing, I'd love to arrange an on-line debate on this or any other site. My goal is to have a substantive, issue-driven discussion that goes into some depth while avoiding arcane terminology.

In the first column this Friday, I will discuss a new data source which no one, including myself, had looked at before Systemic Analysis was published, and which provides the most definitive test yet devised for the arguments I've advanced about racial preferences.

The basic argument of Systemic Analysis is simple: if there is a very large disparity at a school between the entering credentials of the "median" student and the credentials of students receiving large preferences, then the credentials gap will hurt those the preferences are intended to help. A large number of those receiving large preferences will struggle academically, receive low grades, and actually learn less in some important sense than they would have at another school where their credentials were closer to the school median. The low grades will hurt their graduation rates, bar passage rates, and prospects in the job market. This is what I call the "mismatch effect."

My paper tested this idea by comparing the outcomes of whites (who generally receive small or no admissions preferences from law schools) with blacks (who generally receive large, race-based preferences) to compare the outcomes of students who start with similar credentials. My results are robust and, as I'll discuss in coming days, have withstood criticism pretty well. But I and everyone else agree that it would be preferable to compare blacks with other blacks. In other words, the ideal control group for examining blacks who receive large racial preferences would be a group of blacks who received smaller preferences, or no preferences at all.

As I discuss in my Stanford "Reply to Critics", such a comparison group not only exists -- we now even have data on their outcomes. After Systemic Analysis had gone to press, Ian Ayres and Richard Brooks at Yale pointed out that the Law School Admissions Council, in one of the surveys administered to students in its Bar Passage Study (a major source for my paper), had asked the students in detail about how they applied to, and selected, the law school they attended. About ten percent of the 1800-odd blacks in their study reported that they had chosen to pass up their "first-choice" school even though they had been admitted to that school. Most of these students apparently went to a lower-choice school because of financial aid offers or for geographic reasons. The data suggests that these black "second-choice" students had credentials substantially closer to those of their classmates. Compared to other blacks, these blacks closed nearly half the credentials gap.

These "second-choice" students are not a perfect control group, of course -- no one was randomly assigned to attend schools offering different levels of racial preference -- but it is about as good a chance to test the mismatch theory as we are likely to have for some time. If the theory is right, then the second-choice students should have better outcomes: higher graduation rates and more success on the bar. In the table below, I make predictions about how the blacks going to their second-choice schools should perform, based on simple linear assumptions (if blacks going to second-choice schools close one-third of the credentials gap with their classmates, they should close a proportionate amount of the outcomes gap, once one controls for index differences).

If the theory is wrong, in contrast, then of course the blacks going to second-choice schools should have about the same outcomes as blacks who took full advantage of the preferences they were offered. In the data presented below, we'd expect the blacks going to second-choice schools to do slightly better, since they somewhat better index scores than the average black law student (but this difference alone would only close about one-eighth of the gap in outcomes).

The actual outcomes look like this:

These are pretty remarkable results. The "mismatch" predictions are either right on target or, in some cases, too low. The differences in success rates between black law students generally and those going to their second-choice schools are huge. As with everyone else, the black second-choice students' outcomes depend heavily on their grades. But these blacks are substantially less mismatched than other blacks, and they get substantially higher grades (they average about ten percentile points higher in their classes -- another outcome exactly in line with predictions).

Many critics of Systemic Analysis, when they come to the question of why black law students have such low graduation and bar passage rates, either offer no explanation or rather wearily suggest a "something about race" problem. These data offer a very clear example of how well blacks can perform.

There are two sorts of objections one might raise about this data. First, are the samples involved large enough to produce statistically significant, reliable results, or could these results somehow be a fluke? And second, is there some way that the blacks going to second-choice schools are systematically different (other than their slightly higher credentials) from other black law students? I think the answers are (a) the results are very reliable and (b) there are no alternative explanations for these results. But these require slightly longer explanations, and I'll elaborate in my next post.

This is the second in a series of postings further explaining my work on the use and effects of racial preferences in law schools, and responding to critics of my work. One of the central claims in my research is that black law students are often "mismatched" by large racial preferences, placing them at schools where they do poorly and actually learn less than they would at a school with a smaller preference or no preference at all.

On Friday, I posted a new analysis that strongly corroborates the "mismatch" story: for a large sample of blacks admitted to law schools, those who passed up their "first choice" law school and went to a lower-ranked school -- in other words, going to a school where they would have been admitted with a smaller preference -- had dramatically better outcomes (grades, graduation, and bar passage) than blacks who made no such choice. Today I want to address some questions raised by this analysis.

First, are the results significant and reliable? The database for this analysis includes 1,757 black students entering law school in 1991. Just under one-tenth of these students (171) were admitted to their first-choice law school but chose to go to another school. This is a pretty large sample, and it means that any outcome where the success rate of the two groups of blacks is more than six or seven points apart (e.g., 80% vs. 87%) will be statistically significant. Pretty much all of the outcomes for black second-choice students are, in fact, better than the outcomes for other black students, by at least that margin (and sometimes by as much as 20 percentage points). So the answer to the first question is a resounding Yes.

Second, are there differences between the black second-choice students, and other black law students, that might account for their different rates of success? There is one important difference -- the blacks who chose their second-choice school have, as a group, slightly higher average credentials than other black students. That difference accounts for about one-seventh of their higher performance. Otherwise, the black second-choice students are largely indistinguishable from other blacks at the outset of their law school careers. They are about equally likely to have a parent who attended law school (6% for the second-choicers vs. 7% for other blacks), to have a "burning desire" to become a lawyer (30% vs. 30%), to be "very concerned" about getting good grades (89% vs. 88%), and to believe they experienced discrimination during college (68% vs. 64%).

The factor that makes second-choice blacks truly different is simply that they are less mismatched with their classmates than other blacks are. Because they have turned down their "first-choice" school, they are at a school where, on average, their "academic index" is only 93 points below the class mean, compared with a 140-point deficit for other blacks. This in turn means that they get significantly higher grades, on average -- and that, in all likelihood, makes all the difference for their future outcomes.

Going back to the technical discussion, controlling for differences in entering credentials makes one of the six interesting outcomes for these two groups statistically insignificant (ultimate bar passage). But the other five (first-year grades, third-year grades, graduation rate, first-time bar passage, and rate at which matriculants become lawyers) are significant, and all six outcomes are much higher for the second-choice blacks. One can debate what the proper controls should be -- which factors and comparison groups provide the fairest comparison -- but I have seen no analysis in which the second-choice blacks do not substantially outperform the comparison black group, and in which at least some of the differences are highly statistically significant.

Moreover, since the findings of the mismatch theory came from an entirely different analysis (comparing blacks and whites), but predict with great precision the actual improvements in outcomes for the black second-choice students, it would be hard to imagine a more compelling confirmation of its basic theses.

Responding to comments:

"Mahan Atma" says the results are "nonsense" because the blacks going to second-choice schools are not randomly selected; without randomization, there can be no true statistical significance. Not so. It is of course possible to determine the signficance of a difference between two groups that have not been randomly selected—all that significance in this context means is that the difference almost certainly is not due to randomness, but to some real distinction between the two samples. The crucial issue then is what variable accounts for this difference. The point of all regression analysis in the social sciences is to control for plausible differences that might explain why two groups have different outcomes. I find that when one uses these controls, the performance gap between the black second-choice students and others is largely intact -- and statistically significant.

"Michael" contends that the BPS dataset is too noisy to be useful; some respondents do not understand the questions properly and miscategorize themselves. But I counted as "second-choice" students only those who said that they had been admitted to more than one law school, and who did not attend their first-choice school for an identified reason (usually geographic or financial constraints). Moreover, we can accurately estimate the size of the mismatch these students faced at their schools. Certainly it's possible that some of the students I've identified as black "second-choice" students had their hearts set on going to UCLA, but went to their second-choice, Harvard, because Harvard offered them more money. But there can't be many such students (or the average size of the mismatch these students face wouldn't show up as being as small as it does), and to the extent such noise exists in the data, it simply implies that the results were strong enough to show through that noise.

"Donald" and several others wondered how the "second-choice" effects would play out for whites. I discuss this issue in some detail in my "Reply to Critics". Here's a short answer. The substantial number of whites who indicated they turned down their first-choice school (largely for the same reasons as blacks) tended to end up with a "positive mismatch" -- that is, they had higher credentials than most of their classmates. This led, predictably, to higher grades in law school -- well above the class median. In the top half of the class at most law schools, however, there isn't much difference in graduation and bar outcomes -- the vast majority of students graduate and pass the bar. Consequently, the benefits from a "positive mismatch" are a lot smaller than the harms of a large "negative mismatch". So "theory" predicts that whites going to second-choice schools will see little if any improvement in graduation and bar passage rates, and that's borne out by the data. (The white "second-choice" students may see significant job market benefits, but I haven't tested that idea yet.)

More coming up….

I've posted in this space data that shows blacks who pass up the best law school that admits them, and go to their "second-choice" school, are closer in credentials to their classmates and have much better outcomes during and after law school. The postings have generated much discussion. Professor Dirk Jenter, while defending me from the social science nihilism of "Mahan Atma", offers a pointed critique of the "second-choice" analysis: isn't the analysis contaminated by self-selection? The students going to their second-choice schools are, of course, doing so consciously; maybe that means they're a group that believes they will optimize performance at a less elite school, which makes their subsequent, superior performance at those schools and on the bar exam less surprising.

Selection-bias problems are an ever-present danger in this type of observational data, creating pitfalls which more than one of my critics have fallen into. It is probably not possible to eliminate entirely all danger of selection-bias in this comparison of first- and second-choice students, but I am pretty confident that there's little or no such bias here, for several different reasons. (See my "Reply to Critics" for a fuller discussion)

First, these students chose responses indicating that financial or geographic factors led them to turn down their first choice school and go somewhere else. And their other answers to the detailed surveys they completed were consistent with those answers -- although they cared about school "eliteness" almost as much as other students, they cared about "cost" and "financial aid" a lot, too. So, the motivations of these students didn't seem related to some kind of strategy of seeking out a less competitive environment.

Second, we have a wealth of data about the strategies of these students as they started law school; in every way I've been able to measure, they seem to be approaching law school with strategies and expectations that are indistinguishable from all the other black students. For example, both the second-choice and other students are equally likely to respond that they are "very concerned" about getting good grades in law school (89% vs. 88%), and both groups are equally likely to think they are going to end up in the top tenth of their law school classes (37% vs. 38%). Blacks in general express more concern in the survey data about passing the bar -- but, ironically enough, both black going to second-choice schools and all the other blacks tend to think that going to a more elite school will improve their chances on the bar. All of this data points against selection bias.

Third, it is important to keep in mind that this entire exploration of the "second-choice" phenomenon is a way of confirming the hypotheses I developed and tested with entirely different data in my original article. I didn't observe this high performance among blacks going to second-choice schools, and then construct a theory around it; this data was brought to light by others after Systemic Analysis had gone to press. In Systemic Analysis, I'm comparing blacks (as a group that generally is boosted into more elite schools by racial preferences) against whites (who sometimes receive preferences, but generally don't), while controlling for entering credentials. Certainly there's no self-selection process there (or only a little, accounting for students with mixed-race backgrounds). What's nice about the first-choice/second-choice analysis is that it avoids arguable pitfalls of the white/black analysis, and vice versa. But both methods produce essentially identical results.

"Michael" raises another interesting issue. In estimating the average "credentials gap" facing blacks at their second-choice schools (and comparing that with the credentials gap facing other blacks), I use the six loosely-defined "tiers" in the LSAC-BPS database. The creators of this database grouped schools into "clusters" by using some indicators of prestige (e.g., student scores) and some indicators unrelated to prestige (e.g., public sector vs. private sector). The six tiers certainly correlate substantially with school prestige, but they also undoubtedly overlap. So the most elite Tier 2 schools are almost certainly higher-ranked than the least elite Tier 1 schools, even though Tier 1 as a whole is clearly more elite than Tier 2 as a whole.

Consequently, one needs to be careful about using the tiers in sensible ways. In the second-choice analysis, I know each student's grades (standardized by school) and individual outcomes (e.g., graduation), but in terms of school identity I only know what tier they are in. I compared each student's index score to the median index score of students in the same tier to estimate the typical credentials gap between students and their classmates. This is, of course, a rough measure -- but the key concern is whether there's some reason to think it's biased in a way that helps my analysis. The answer is: I don't think so. Blacks other than the second-choice students should be distributed more or less randomly across the six tiers. The blacks going to second-choice schools should also be pretty randomly distributed -- with one exception. In Tier 1, they are more likely to be in schools near the bottom of that elite tier rather than at the top (since they have generally rejected a more elite school, they are unlikely to be going to Harvard or Yale). But that distortion would mean I was overstating their actual mismatch with their fellow students, which cuts against my analysis, not in favor of it. And, in any case, for the whole group of students this is likely to be a small distortion indeed.

Consider, by way of contrast, an analysis done by Dan Ho (a recent Yale graduate and Harvard Ph.D. whose critique, and my reply, are in the June issue of the Yale Law Journal). Ho compared blacks who had the same index scores but attended schools in adjacent tiers. Ho's argument went like this: if two blacks with the same entering credentials went to adjacent tiers, and passed the bar at the same rate, then there's no penalty to blacks from going to higher tier schools, and Sander is wrong. But of course, if the BPS tiers overlap, then for any analysis which selects blacks from, say, Tier 1 and Tier 2 schools who have matching index scores, it's quite likely that these students are actually going to schools of equivalent eliteness. Here the bias is likely to be quite significant, and it all is in the direction of the results Ho wants. Ho's analysis is invalid for other demonstrable reasons, but I offer it here as an example of an improper use of tiers.

A final point: "Michael" also asks whether we know the blacks going to their second-choice schools actually got into their first-choice school. The answer is yes, we do -- the questionnaire asks that question, and we used it as a filter.

Tomorrow I'll address some critiques of Systemic Analysis itself.