# Luck, Skill or Both: Department Change at IITs

A friend recently asked me to provide some advice on department change to some freshers. The usual _fundaebaazi_ is something I didn’t want to do; it’s not impressionable, and won’t motivate any fresher to study for a department change. Instead, I chose to show and not tell

## So is it luck or skill?

Short answer: Both.

Let’s look at how first year courses are graded. For most theory courses (3 lecture hours + 1 tutorial hour / 2 lab hours), there’s a normal distribution of marks, and the top 7% of people on this distribution get an A.

(Well, the actual grade distribution is discrete, but the marks are approximately normally distributed).

If we assume that everyone is equally skilled, then the probability of a person obtaining an A grade in one course is $0.07$. The probability of the same person obtaining an A grade across all the seven theory courses then is $0.07^{7}$. This seems theoretically okay, but there are only around 1300 people in a batch, give or take a few hundred. If this is true, the number of people who get a 10 in every theory course should come out to be $1300 \times 0.07^{7} \approx 10^{-5}$. Which is practically zero. However, we know for a fact that there are people who obtain tens across all the seven theory courses, and across the labs as well. There are people who graduate with a perfect ten, so the above calculation is wrong somewhere. This brings us to the first fallacy:

> Not everyone is equally skilled.

There is talent, and there is genius. Talent hits a target no one else can hit. Genius hits a target no one else can see.

## How much skill?

Let’s condition on the students instead rather than on the gradecard. I would give a candidate DepC student a probability of $0.8$ to obtain an $A$ in a theory course, and a probability of $0.5$ to obtain an A in a lab course. Because lab courses are super random and everyone gets either a 10, 9 or an 8 (CMP and PYP, I’m looking at you).

With these probabilities, let’s reasonably assume that $7$ students get a straight ten in all seven theory courses. The number of people with these odds would then be $7 / (0.8)^{7} = 33.37 \approx 30$.

## What about luck?

This is super hard to quantify in words, but I’ll give it a shot. Given our 30 geniuses and taking all permutations and combinations of grades into account, the set of possible CGPAs one could obtain after their first year is finite. So what happens if two people obtain the same CGPA and they are in line for a Department Change into a higher branch?

> In case more than one student applying for programme change have the same CGPA, the tie shall be resolved on the basis of JEE ranks of such applicants.

So how likely is it that two people obtain the same CGPA and are required to tiebreak on the basis of their JEE rank? Let’s run a simulation and find out! I’ll simulate grades across 5 lab courses, 4 of which are worth 2 credits each and the last one is worth one credit. I’ll also simulate the seven four-credit theory courses. Also assume that if the genius doesn’t get a 10, they get a 9.

We see that nobody gets a 10, and five people get a CG of 9.82. Five! And multiple people have the same CG. Even though we assume CGPAs lie on a continuous scale, the spectrum doesn’t become as dense as one would expect at the end of first year.

However, all this shows us is that there are chances of a tiebreak. It still doesn’t put things into perspective. Let’s make a fake DepC list, so that the point really hits home. I’ll allocate 7 seats in the 4-year CSE programme, 2 in 5-year CSE Dual, 6 in Mathematics and Computing, 2 in MathComp Dual and assume a similar distribution across others. The final list looks like this:

name| cg| from| to  
---|---|---|---  
0| Anay Shanker| 9.97| ME1| CS1  
1| Nirvaan Choudhury| 9.94| ES1| CS1  
2| Sara Behl| 9.94| ME2| CS1  
3| Kiara Kakar| 9.88| MT1| CS1  
4| Aniruddh Batra| 9.88| MS1| CS1  
5| Mehul Krishnan| 9.85| MT6| CS1  
6| Jhanvi Chaudhary| 9.85| CH1| CS1  
7| Madhup Kapur| 9.82| MT6| CS5  
8| Zoya Virk| 9.82| MT6| CS5  
9| Tara Swaminathan| 9.82| AM1| MT1  
10| Rasha Kakar| 9.82| MS1| MT1  
11| Ranbir Brahmbhatt| 9.82| MS1| MT1  
12| Tarini Ganguly| 9.79| ME2| MT1  
13| Divij Gupta| 9.79| EE3| MT1  
14| Taimur Vaidya| 9.76| EE1| MT1  
15| Lavanya Deo| 9.76| EE3| MT6  
16| Samiha Karpe| 9.76| CE1| MT6  
17| Uthkarsh Baral| 9.73| CH1| EE1  
18| Mishti Ranganathan| 9.73| CE1| EE1  
19| Kashvi Char| 9.7| ME1| EE1  
20| Azad Sahota| 9.7| AM1| EE1  
21| Trisha Dhillon| 9.67| MS1| EE1  
22| Mehul Verma| 9.64| BB1| EE1  
23| Vaibhav Dewan| 9.61| MS1| EE1  
24| Myra Tiwari| 9.58| ME2| EE1  
25| Ishaan Goyal| 9.58| CH7| EE3  
26| Lakshay Sampath| 9.55| CE1| EE3  
27| Rati Sanghvi| 9.48| ME2| EE3  
28| Mahika Ravi| 9.48| CH1| EE3  
29| Hazel Sethi| 9.39| BB1| AM1  
  
My heart goes out to Tara, Rasha, Ranbir, Lavanya, Samiha and Ishaan. The boys and girls played well, but in the end it came down to luck. And having a better JEE rank.

## What next?

Making this minigame taught me two things: one, just how incredibly lucky I got with my own department change, and two, how huge of a factor luck plays. All the _fundae_ my seniors gave me about luck and randomness are sort of true.

My advice to any juniors reading this would be to not worry about the outcome. The driving force behind most people seeking a DepC is better job prospects and possibly the associated social status and prestige that comes with it (which is a very freshie thing; nobody cares about which department you’re from once you’re a bit more senior). If this is your primary driving goal behind the DepC, you’ll neither gain the skill, nor have the luck. The best course of action is to truly enjoy (or atleast make an effort to enjoy) what you’re studying, becaues most of it is an extension of the JEE syllabus anyway, and keep your CGPA as high as possible. Expect nothing else from the system, and you won’t be disappointed.

**UPDATE** : I gave a talk regarding this at Pathfinder, BSW’s session on department change for freshers. You can find the slides here

## Appendix: Code for the luck simulation