IIM Ahmedabad selection criterion and the idea of conditional probability

IIM Ahmedabad's selection criteria also opened a can of worms and had people talking about how cruel it was to be born as an Engineer. Let us face it, if you are born in India into some type of families, you have only two choices, be an Engineer or be a loser.

Having said that, a great many students have taken this as an open season to crib when they have no reason to. Let us see why.

To cut a long story short, an engineer cannot get called for an IIMA interview if he did not score an average of 80 in 10th and 12th and a minimum of 78% in Engineering. It does not matter if you have scored 99.99th percentile in CAT, you cannot get into IIMA if your BE percentage is 76%.

Now, let us look at this within the framework of conditional probability. P(A / B) is defined as the Probability of event A happening given that event B has already happened.

Here the big crib is that Prob (IIM A interview / BE score of 77.5%) = 0. However, this is not necessarily the correct metric to look at to see how cruel the rule is. Scoring 77.5% is a necessary condition to have a shot at this, but how close is it to being a sufficient condition is key.

To give an extreme example - Prob (IIMA admit / student does not take CAT) is also zero. This does not mean that merely taking the CAT will ensure an admit. In this case, the condition taking CAT is necessary but not even close to being sufficient.

What we need to think of is this wonderful Probability(BE score being the reason for missing out  / student did not make it to IIMA). If a particular engineer did not make it to IIMA, what are the odds that it was the BE score that prevented him/her from doing so? Now, if that number is high, this is indeed an unfair criterion.

Now, let us put a framework on to it.

If there are three possible reasons, A, B and C for not getting into IIMA. Then we can represent them with a diagram like this -

Now, if we have to attribute reason A as the key determinant for missing out then that should be the region where A alone is the reason. In other words, the region where an 'x' is marked. Any other region would include other factors also playing a part.

Now, for our specific scenario, let us include only two factors - CAT percentile and Score being less 78%. The diagram would look like this.

Now, Venn diagrams do not have a notion of scale. But I have drawn this diagram deliberately like this to convey that the big circle incorporates 99.67% of the candidates. The least percentile for an engineer to get a call from IIMA is 99.67. So, x can at the maximum be 0.33% of the candidates.

So, in the worst case scenario 0.33% of the candidates appearing for CAT miss out because their engineering percentage is too low.

Hold on, that's not it. Let us add some more facts and assumptions (All you aspiring MBAs, also keep this as an important lesson. If you are peddling some hypothesis, you should always talk about facts and assumptions as if they can be used interchangeably. As long as you can incorporate your assumptions in along with the facts, you can peddle any theory).

IIM Ahmedabad gives admits to probably ~180 engineers from general category, and they probably call around ~500 engineers from the general category for the interviews. Now, under the scenario that 1.65 lakh people take the exam, 0.33% of this is roughly 550. Among the top 550 candidates based on CAT score, CAT calls ~500 engineers. Assuming that around 20-30 students securing above 99.67 percentile are likely to be non-engineers, only around 20-30 engineers who score above 99.67 percentile miss out. So, probably only around 20 students miss out because of their UG mark.

So, the number of students who miss out purely because of their BE percentages is possibly only around 10. Not 0.33% of test-takers, but around 0.01% of test-takers.

Now, probably half the engineers (or more) will have a score of less than 78%. How come only 20 engineers miss out? This is because there is a very high correlation between academic records. So, the folks who score very high in CAT are likely to have scored high in 10th, 12th and UG and vice versa. So, what the 99.67 percentile cut off number tells us is that the students who have missed out due to other criteria are very unlikely to have scored 99.67 as well. A point that is completely lost on many students. The game is not rigged against you. The game is rigged against candidates who do not deserve to get in. In other words, it is a meritocracy. One of the best B-schools in India wants to make sure that they select only the best candidates available in India. Who woulda thunk?

To speak without all this probability mumbo-jumbo - An overwhelming number of engineers who have scored less than 78% in BE and missed out on IIMA call would have missed out on the IIMA call even if they had a 98% in their engineering. 

To put it differently, the only Engineers who have a right to crib about IIMA's high BE cut-off criterion are the ones who can and do score 99.67+. If you score 99.6 and do get a call from IIMA, it is not because of your percentages, it is because of your percentile.

So, every time you feel like IIMA is conning you out of an interview call, tell yourself you have to get 99.67 to deserve the right to voice that crib. 

In case you are among the 20 unlucky souls who score above 99.67 and still do not have a call, my commiserations are with you. Chances are you have secured an admit into IIM B or IIM C and you have told yourself that you will never again miss out on anything because of some silly criterion. Probably a great lesson learnt, and one for which missing out on IIMA might be not such a big price.

Ten Golden rules while Taking CAT or Mock CATs

Ten rules to follow while taking CAT (or Mock CATs)

Video by Rajesh Balasubramanian on frequently made mistakes, things to look out for, and ideas to keep in mind while taking CAT.

Some key ideas: Never Compromise on accuracy,  Do not chase attempts, Take careful chances, See ball hit ball.

Visit mockcat.2iim.com to take a free mock. Try before you buy!

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How to review mock CATs

Everyone tells you that the value in taking mock CATs lies in analyzing them, and not just in mechanically taking them. How exactly does one analyze a mock CAT? Here is a simple guide

Check your percentile.
The starting point for any mock analysis is the percentile. Not because it is very relevant, but because it is impossible to ignore. So, go ahead, knock yourself out. Check the section-wise percentiles, stare long and hard at the numbers, extrapolate the percentiles from the last 3 mocks and see where they are going, imagine how high your overall percentile would be if only you could produce your best section performances in the same mock, give in to curiosity, triumphalism and envy by figuring out others' percentiles.

Do all this to get the damn thing out of the system. Now, ignore it and focus on something that can actually be useful. There are three parts to this -

1. Mocks have the best questions, learn how to solve all of these
Mocks are often seen merely as a tool for assessment and bench-marking rather than as a tool for learning. Mock CATs usually have the best questions, the ones that have an elaborate 6-minute solution while also having the elegant 1-minute solution. So, make it a habit to review the questions that have gone wrong, questions that you have skipped and then the ones that you got right as well. Very often, students ignore the ones they have gotten correct. If all your attempts were through the best approaches, chances are you would have attempted 5 more in each section. There is a learning angle to every mock CAT. Do not ignore this. As this article says, the mock CATs have quite a few Now-you-know questions.

This is why it is very important to pick a mock CAT provider who focuses on providing detailed solutions and helps with the thought process. In other words, have a look at the 2IIM mocks before you go looking elsewhere. :-)

2. Which 3 get kicked out, which ones get in?
After every mock, do a simple exercise to improve decision-making. Select at least three attempts from each section that you should have skipped, and replace these with three you should have attempted. In your first few mocks, you might even be able to select 5-6 questions in each section. The big gains in mocks come from improved decision-making; and you have to take a conscious effort to improve this. If you can reach your point where you cannot find more than 1 question in each section that you had incorrectly chosen to attempt, you can count yourself ready for the exam.

3. Topic-wise and timing-wise analysis
You should ask yourself a few questions similar to the ones given below -
How good is the hit-rate in Sentence Rearrangament? Was it worth doing the DI even after taking 15 minutes, did I at least get all 4 correct? Should I completely skip Sentence Elimination questions from now on? Did I get a Permutation Combination question wrong again? Should I completely dump this topic?

On the timing front, figure out when the fatigue errors creep in. All of us find that there are 2-3 questions where we cannot really fathom why we marked that stupid wrong choice in the first place. This is essentially down to fatigue. There is a spell of 15-20 minutes where not much gets done and errors creep in. Locate this spell, see when it usually happens and reduce it methodically.

On the timing front, it is important to know which type of question gets you the best marks/minute. You might easily attempt 3 RC passages accounting for 12 questions within 30 minutes. But if you get 6 of these wrong, that is effectively same as attempting only one RC and getting all questions correctly. Four correct answers in 30 minutes is a very poor return.