Concentrated Influence™

As a data analytics company focused on educational rankings, develops a variety of institutional and people-based rankings, both for internal use and for licensing to other educational technology companies. Concentrated Influence™ is’s key ranking metric for gauging academic excellence at the undergraduate level. Besides providing deep insights into higher education, Concentrated Influence™ constitutes a data analytics service to businesses focused on educational rankings.

This page provides a detailed account of our concentrated influence metric. Concentrated influence is a derivative metric that depends on our more basic influence metric, which is computed through our InfluenceRanking™ engine. Readers who want to understand the technology underlying our approach to influence as such are urged to consult our page on the InfluenceRanking™ engine.

The Underlying Idea

Concentrated influence measures how densely influence is distributed within a group or organization. Specifically, concentrated influence adjusts overall influence (as calculated with our InfluenceRanking engine) by a factor that is inversely proportional to the size of the group or organization. Thus, for two groups with the same overall influence, but where one group is smaller than the other, the smaller group will have the greater concentrated influence. At its simplest, concentrated influence is an influence score for a group divided by size of the group. Given the same overall influence, the smaller group has the greater concentrated influence.

Concentrated influence, as a way of understanding and clarifying influence, makes good sense and is implicit in many contexts. Value distributed among individuals in a group can be dense or diluted. Take a small college with 3,000 students versus a large college with 20,000 students. What if the smaller school is able to field a football team that is as good as the large one (let’s say they play to a tie)? It then seems fair to say that the concentration of football talent at the small school is greater than at the large school, and if talent is interpreted as influence, the small school has greater concentrated influence than the large one.

A Metric for Excellence

At, we regard concentrated influence as a valuable indicator of academic excellence. Colleges and universities have influential faculty and alumni. The influence of these individuals is measurable, and their influence scores can be summed to give a measure of influence for schools and their disciplinary programs. Such measures of influence and the rankings they induce lie at the heart of our InfluenceRanking engine. Accordingly, for overall influence, large schools, by employing more faculty and having more alumni, will tend to have larger influence scores than small schools, and thus rank more highly for influence.

But such an approach to influence puts smaller schools at a disadvantage simply because of a size difference. Take a large school four times the size of a smaller school, but with only twice as many comparably influential faculty and alumni. The large school has more influential people of the same caliber, in absolute numbers, than the small school. But think of a student at the small school versus one at the large school. Leaving aside alumni, a student at the small school has the benefit of a higher “influential faculty to student ratio.” Concentrated influence thus becomes a measure of how accessible influential faculty are to their students.

Such a ratio, comparing influential faculty to number of students, refines the usual faculty-to-student ratio and and is captured by concentrated influence. Our measure of concentrated influence looks specifically at the ratio of combined influence scores for faculty and alumni to size of the undergraduate student body. So defined, concentrated influence is relevant to undergraduates, with higher concentrated influence indicating greater accessibility of undergraduates to influential faculty. But it is also relevant to graduate students who, along with faculty, face fewer demands from undergraduate teaching and guidance when concentrated influence is high (though an additional adjustment to concentrated influence for graduate studies is needed, as we’ll see below).

What We Mean by “Best”

At, we regard concentrated influence as the single most important factor in guiding prospective undergraduate students (though less so graduate students) to select a school where they will have the best opportunities to interact with outstandingly influential faculty and fellow students.

Concentrated influence even applies to departments and fields of study. This is because we are able to drill down with concentrated influence into disciplines and subdisciplines, so that, for example, we can compute at a given school the concentration of influential anthropologists among faculty and alumni.

The roles of faculty and alumni in concentrated influence may seem asymmetrical, but in fact they are complementary. Think of a school that has many influential faculty but few alumni that go on to be influential. Or think of a school that has many influential alumni but few influential faculty. Having one or the other is good as far as it goes. But having both is clearly better. Yet concentrated influence goes even further, rewarding schools that achieve such joint influence of faculty and alumni, albeit with smaller numbers. Concentrated influence is about doing more with less.

Schools with high concentrated influence provide an exceptionally rich and intense educational experience, especially for undergraduates. We therefore want to commend and publicize these schools. Indeed, we see concentrated influence as the critical factor in determining what makes an undergraduate experience great and what justifies ranking one undergraduate program as better than another. Thus, at, what we mean by “the best schools” and “the best disciplinary programs” at the undergraduate level are those with the highest concentrated influence.

Where does that leave graduate programs in relation to concentrated influence? Concentrated influence is still relevant at the graduate level, but less so than at the undergraduate level. In part that’s because by the time one is a graduate student, one is focused on a particular discipline and so what’s crucial is a school’s influence in that discipline. Also, at the graduate level, having more graduate students and disciplinary programs is a plus rather than a minus, enriching the graduate student experience. Thus the emphasis of concentrated influence on small numbers at the undergraduate level needs some adjustment at the graduate level.

Calculating Concentrated Influence

As a ranking method, concentrated influence requires precise formulae to calculate it. Only by laying out such calculations can we use concentrated influence to rank colleges, universities, and disciplinary programs. In fact, we identify four variants of concentrated influence. These variants arise because the form of concentrated influence needs to differ at the undergraduate versus the graduate level, and for overall influence versus influence by discipline.

For a given school, the following key terms are required to calculate its concentrated influence: I = overall influence score, d = discipline, Id = influence by discipline score (d = “anthropology” or “biology” or ...), U = undergraduate student body size, G = graduate student body size. The following four variants of concentrated influence thus gauge academic excellence at the undergraduate versus graduate level, whether overall or by discipline:

  • Concentrated Influence Undergraduate Overall = I/U (used to determine best overall undergraduate schools);
  • Concentrated Influence Undergraduate by Discipline = (I/U) x Id (used to determine best undergraduate schools by discipline);
  • Concentrated Influence Graduate Overall = (I/U) x G (used to determine outstanding overall graduate schools);
  • Concentrated Influence Graduate by Discipline = (I/U) x Id x G (used to determine outstanding graduate schools by discipline);

The four ranking metrics defined in these calculations are variants of concentrated influence and capture combinations of influence and school size that can set one school or disciplinary program above another. At the undergraduate level, it is how we at make sense of the comparative “better” and the superlative “best.” At the graduate level, it provides a useful complement to how we make sense of “better” and “best,” which we gauge in terms of pure influence. In the next section, we motivate and explain these concentrated influence variants.

Why Four Concentrated Influence Variants?

As is immediately clear from inspecting the four variants of concentrated influence, all of them contain the factor I/U. I/U is the most basic form of concentrated influence and coincides with overall concentrated influence at the undergraduate level (without reference to any particular discipline). For undergraduates, this metric seems exactly right for capturing academic excellence overall, without specifying any particular discipline. Why is that?

Many undergraduates, in embarking on their college education, are uncertain about the discipline or department in which they want to major. And even those who think they know what they’re going to major in often change majors. That’s as it should be. Undergraduates are often finding their way, getting exposed in the course of their studies to new and interesting ideas that channel their efforts in unexpected directions. Concentrated Influence Undergraduate Overall (CIUO) thus seems like the right metric for gauging what are the best undergraduate schools when no particular discipline is specified.

Once a particular discipline d is specified, however, then an adjustment to the CIUO metric is required to determine the best undergraduate schools for that discipline. This metric, Concentrated Influence Undergraduate by Discipline or CIUD, takes the CIUO metric, or I/U, and multiplies it with the influence by discipline of the school, namely, Id. The “d” here is any of the disciplines or subdisciplines for which our InfluenceRanking engine is able to calculate influence scores.

In the definition of CIUD, the product (I/U) x Id makes good sense: on the one hand, this metric needs to reward schools that score high in disciplinary influence (i.e., Id); on the other hand, a school that is best is not one that is just best in a single discipline but that is uniformly excellent, which is captured by I/U. The product rewards both high concentrated influence overall and high disciplinary influence. Moreover, because I (i.e., overall influence of a school) is the sum of the various Id’s (i.e., the influence scores of a school across disciplines), I and Id are commensurable, and the product (I/U) x Id gives I and Id the right balance in this metric.

The two graduate metrics, Concentrated Influence Graduate Overall (CIGO) and Concentrated Influence Graduate by Discipline (CIGD), are just the corresponding undergraduate metrics (CIUO and CIUD respectively) multiplied by G, the size of the graduate student body. Alternatively, one can think of concentrated influence at the graduate level as multiplying influence I not by the factor 1/U (the reciprocal of U) but by the factor G/U.

At, we regard the two concentrated influence metrics at the graduate level as offering valuable insights into a graduate school’s or graduate program’s academic excellence. Yet we also think that what’s best at the graduate level is, at the end of the day, captured by our pure influence scores (i.e., the influence scores that result from the default setting of our Custom College Rankings tool and that is the first score our InfluenceRanking engine outputs). That’s because, by the time students reach graduate school, we think they will not only know what they want to study but also have a clear sense of the key influential faculty with whom they should want to study.

Graduate students can be expected to be resourceful so that, once situated at an institution, they will be able to find key influential faculty to guide and mentor them. Influence as such thus seems to suffice to determine what’s best at the graduate level. Also, influence as such, whether overall or by discipline, is readily commensurable, allowing for ready comparisons of institutions and disciplinary programs worldwide. For all these reasons, we use influence as such to gauge what is best for graduate schools/programs and for schools/programs where the level of study is left unspecified. Notwithstanding, we still find concentrated influence at the graduate level a useful ranking metric for highlighting outstanding schools and departments.

The rationale for concentrated influence at the graduate level parallels concentrated influence at the undergraduate level (i.e., CIGO corresponds to CIUO and CIGD corresponds to CIUD), the difference being multiplication by the factor G. It turns out that even though the concentration of influence at the undergraduate level is enhanced by lowering the size of the undergraduate body, at the graduate level it helps to have a large and vibrant community of graduate students (who promise to become the new generation of academic influencers). Much exciting research these days is cross-disciplinary, and a larger graduate student body allows for such work to flourish.

If it seems counterintuitive to reward larger graduate student bodies in a measure of concentrated influence, consider that some schools that call themselves “universities” offer only one or a handful of graduate programs. Factoring in G into concentrated influence (whether overall or by discipline) effectively and rightly removes such schools. The bottom line is that the variety, depth, and size of the various graduate programs at a school counts in favor of a school’s excellence for graduate education and needs to be factored into its concentrated influence metric at the graduate level.

The Difference That Concentrated Influence Makes

The philosopher Charles Sanders Peirce used to quip that for a difference to be a difference it has to make a difference. In this last section we want to pick up on Peirce’s point as it relates to concentrated influence. Specifically, we want to address the difference concentrated influence makes to the rankings of colleges, universities, and disciplinary programs.

The difference is most notable at the undergraduate level. Suddenly, large schools that, in virtue of their size, dominate influence-based rankings find their advantage diminished. Top notch liberal arts colleges now rank up there with the big schools, and some big schools, precisely because their bigness dilutes their influence, find their rankings go down.

Perhaps the most surprising finding was to see Caltech, which in terms of overall influence ranks #17, go up the #1 spot at the undergraduate level for overall concentrated influence as well as for several disciplines. Caltech’s undergraduate student body is just under 1,000 but its ratio of influential faculty to students is extraordinarily high, causing it to punch well above its weight class.

At the graduate level, the surprises are fewer. Harvard, with its dominating influence scores, both overall and by discipline, and its large graduate student population (ca. 15,000) tends also to occupy the #1 spot in many concentrated influence graduate rankings. This is consistent with many other rankings that give pride of place to Harvard. Other renowned schools tend to follow suit.

Yet there are also a few surprises with concentrated influence at the graduate level. Princeton, with its comparatively larger undergraduate versus graduate student body, tends not to fare as well with concentrated influence as it does in terms of pure influence. For example, while Princeton occupies the top spot for influence in mathematics, its CIGD metric for mathematics puts it only within the top ten. This may seem counterintuitive, but it makes sense if we think of math graduate studies as enhanced by a vibrant community of fellow graduate students spanning many fields related to mathematics. Princeton tends to be thinner on the ground in such related fields.

A final question now arises: If you get into a top ranked school as measured by concentrated influence, whether at the undergraduate or graduate level and whether overall or by discipline, should you attend it? Our advice at is that you should seriously consider attending it. At the undergraduate level, no question. With concentrated influence at the undergraduate level (CIUO and CIUD), prospective undergraduate students are getting an objective measure for ranking the best colleges, universities, and disciplinary programs, underscoring influence but at the same time controlling for its dilution by size.

At the graduate level, or with no reference to study level, concentrated influence is less convincing. Pure influence seems clearer and cleaner at capturing academic excellence and thus determining what are the best institutions and disciplinary programs. Even so, concentrated influence metrics at the graduate level (CIGO and CIGD) provide a useful counterbalance to pure influence and are worth considering. For that reason, when we do rankings of the best graduate institutions and degree programs, we use pure influence to determine the ranking but we also offer concentrated influence as a complementary ranking.

At the end of the day, prospective students are in their rights to want to attend the most influential school overall or in their chosen discipline. And they are in their rights to drill down further and attempt to study with the most influential person in a given discipline, whatever the school. All such information is available on this website through its various tools (notably the Schools, People, and Custom College Rankings tools).

Perhaps focusing on influence exclusively is best for you. But coming to that determination should not be made without at least considering concentrated influence. If you want to know what’s truly best in higher education, you’ll want to consider both pure influence and concentrated influence. Both ranking metrics are available through the Custom College Ranking tool.