At a glance: 2008 JEE results

IIT-Roorkee has released a lot of data on JEE-2008. As we have seen earlier, the IITs use two filters before students are given a rank. The first filter gets rid of students who fall in the bottom quintile in *any* of the three subjects (math, physics, chemistry). The subject-wise cut-off marks are, respectively, 5, 0 and 3. Yes, you read it right: in physics, this cut-off is indeed zero.

The IITs have used a reduced cut-off for reserved categories. This concession is 10 percent for OBC candidates, and 40 percent for SC and ST candidates. Thus, for SC and ST candidates, the subject-wise cut-offs were at 3, 0, 1.8 marks in math, physics and chemistry, respectively.

The second filter simply picks the top N students using just one measure (this year, N=7903): the aggregate (or, the raw total of the marks in the three subjects). When multiple people end up with the same total, some procedure is used for breaking the tie. The details of this procedure does not interest me, so I won't go into it.

The cut-off in the aggregate score is 172. The reserved category students enjoyed a concession in the aggregate score as well; thus, the effective cut-offs for the OBC, SC and ST candidates were, respectively, 172, 104 and 104. The reason for the OBC cut-off being the same as the overall cut-off must be because of technicality, which I am yet to figure out. We will re-visit it later, if needed.

In another disclosure, IIT-R has revealed the aggregate scores for a bunch of uniformly spaced ranks. It has given this data for not only the common pool (for which the cut-off is 172), but also the OBC, SC and ST candidates. Let's see what these data look like; in the following plot, the aggregate score is on the horizontal axis, and the rank (in the respective lists) is on the vertical axis. Here's the plot:

Figure 1

The first thing that strikes you is the steep drop-off in the aggregate as you go up in ranks at the higher end. For example, the first five hundred ranks span a range of 146 (287 to 433), the remaining 7403 ranks span a range of just 107! The latter range works out to almost 70 students for each aggregate score between 172 and 287; In other words, there's a whole lot of tie-breaking the IITs would have indulged in from the 500th rank onwards!

Figure 1 is not particularly useful, because our reservation formula ensures that the x percent of the seats in each class (Institution-Department combination) is reserved for the beneficiaries. This means that the top 10 percent of the OBC students (for example) will be studying in the same classes as the top 10 percent of the common pool (and the next 10 percent in OBC will study with the next 10 percent in the common pool). It makes sense, therefore, to use a scaled rank on the vertical axis; thus, the rank in each category is divided by the total number of ranks in that category, so that each curve will end up at 1 at the top/left. Here's the scaled plot:

Figure 2

The striking thing in this figure is the closeness of the OBC curve with that of the common pool. I have to warn you, however, that the common pool includes the OBC candidates. Thus, the curves for the non-OBC general pool and the OBC pool are likely to be separated a little; I am confident that this difference is small, because both the curves end at an aggregate score of 172 (by definition), a cut-off that was used for both the groups.

Here's a second warning: The OBC students form about 14 percent of the common pool (1134 out of 7903). In the next couple of years, this fraction will have to be ramped up (theoretically, to at least 27 percent). If the full OBC reservation had been implemented this year, the additional OBC students would all have come with an aggregate of less than 172. I don't know what kind of cut-off the IITs would have employed for OBCs, but let's assume that they used a cut-off that selected 2000 OBC students. We can now re-plot the above figure and see what effect of a higher OBC reservation would looks like. Here it is:

Figure 3

[Caution: I need to warn you again that this figure is based on speculations about where the IITs might have drawn the line for the OBCs.]

Now, you can see the effect of reservation, which was absent in the second figure. You have the common pool, followed (to its left) by the OBCs, SCs and STs at a difference of about 30 marks, 80 marks and 80 marks, respecitively.

[Aside: One can perform this sort of an analysis for each subject, but that kind of disaggregated data has not been made public.]

Let's go back to the second figure. If we assume (and this is a BIG assumption) that JEE marks are a good predictor of a student's performance in IIT, some conclusions follow. Since the OBC and general pool curves are so close, an OBC student is not particularly at a disadvantage in choosing one of the 'highest' branches available to him / her. This is because the difference between his / her marks and those of his / her classmates are not likely to be terribly large (at least, this year).

Alas, the same cannot be said about SC and ST students. In particular, life would be extremely difficult for someone with a rank of SC 100 (whose aggregate of 167 is already below the common pool's cut-off) to compete against his / her classmates whose ranks are likely to be near 500 (for which the aggregate is 287). Such a student is better off by choosing a "lower" discipline where the students will have scores closer to his / her own.