Why Nobita Always Gets Zero Scores: An Analysis Using Probability Theory

There are various conspiracy theories around this anime. One of the most cruel suggests that the character Nobita was inspired by a real story of a schizophrenia patient and Doraemon is just Nobita's imagination. But what I want to highlight here is the conspiracy theory stating that Nobita isn't actually stupid. I will analyze this conspiracy theory using Probability Theory, one of the statistics courses I studied worth 3 credits.

As we know, in his stories Nobita is characterized by Fujiko Fujio as an elementary school student who is lazy and stupid. He's so stupid that in almost every test he always gets zero. Yes, a complete zero, not a result of rounding down. This always gets him scolded by his mother or, if he's lucky, just scolded by Doraemon. Due to his stupidity, he always becomes the target of Gian and Suneo's bullying.

Nobita's zero scores concern me. Is it really that easy to get zero scores at school? This analysis stems from the Instagram account @ngobrolmatematika which recently released a brief and conspiratorial analysis claiming that Nobita is actually smart. I will complement the analysis with various assumptions about why Nobita gets zero scores.

Why Nobita always gets zero scores, assumption #1: Nobita's tests are in essay and/or short answer format

In this type of question, all possible scores are open from zero to 100 or perfect score. Generally, essay questions are used in exams that test memorization or opinion abilities, such as religion or civics. Additionally, this model is also used to test students' writing abilities in language exams.

In essay questions, grading is subjective. The scores can even differ between teachers. Good teachers usually appreciate essay writing by giving writing points, of course if students write something. In this possibility, we can assume Nobita's teacher is good, but Nobita intentionally leaves his answers blank. He's not stupid, he's just being humble.

Another possibility is that Nobita's teacher is truly a cruel teacher who doesn't give writing points even if there's writing on the answer sheet. No matter how hard and how long Nobita writes on his essay sheet, it still won't yield any points. I think this assumption is the most appropriate. Although Nobita is lazy, he wouldn't do something as stupid as leaving his essay sheet blank.

Why Nobita always gets zero scores, assumption #2: Multiple choice questions but Nobita leaves the answer sheet blank

With any form of questions, if Nobita keeps being humble by leaving his answer sheet blank, his score will remain a complete zero. Of course, with various other assumptions like a 1-0-0 or 4-0-1 scoring system, no bonus questions, or no additional points. Although I think this assumption doesn't make sense, Nobita wouldn't intentionally not try at all.

Why Nobita always gets zero scores, assumption #3: Multiple choice questions, 4-0-1 scoring system, and Nobita answers randomly

In this system, students who answer—choose an option—correctly will be given a score of 4, if the answer is blank (no choice) then given a score of 0, and if they choose the wrong option, they will get a point deduction of 1 point. Therefore, in systems like this, students tend not to answer if they don't know.

Multiple choice questions with a 4-0-1 scoring system are indeed rarely used in regular exam questions at elementary level or even high school. Usually, the 4-0-1 scoring system is applied to olympiad questions—OSN, OSK, and similar—or university entrance selection questions—such as SBMPTN score calculation from 2017 and earlier. However, we will still use the 4-0-1 scoring system assumption with the reason that the education system in Japan is more advanced than Indonesia.

This assumption can be explained with probability theory and a bit of statistics. Generally, in multiple choice questions there are 5 answer options: A, B, C, D, and E. There will be 1 correct answer and 4 wrong answers. So the probability of answering correctly is $\frac{1}{5} = 0.2$ while the probability of answering incorrectly is $\frac{4}{5} = 0.8$.

Now we use the concept of expected value. Assume Nobita answers randomly because he spent the night adventuring to Cloud Country. If we use the concept of expected frequency, from 50 questions answered by Nobita with a 4-0-1 scoring system, we get Nobita's expected value as follows:

$\text{Score} = P(\text{correct}) \times n \times \text{correct score} + P(\text{wrong}) \times n \times \text{wrong score}$

$\text{Score} = (0.2 \times 50 \times 4) + (0.8 \times 50 \times (-1)) = 40 + (-40) = 0$

I somewhat believe this assumption because Nobita has tried even though he answered randomly. However, there's still a big concern in my mind whether it's possible for elementary students in Japan to be so advanced that they're already given a scoring system like university students in Indonesia. It seems not too common. So what if the scoring system is actually 1-0-0?

Why Nobita always gets zero scores, assumption #4: Multiple choice questions, 1-0-0 scoring system, and Nobita knows the correct answers

The multiple choice scoring system widely used today is 1-0-0, where students only get points when answering correctly and get no points and no point deduction if they choose the wrong option or leave the answer option blank. This system is used at all levels of formal exams that measure ability, such as daily tests, midterm and final exams, School Exams (US), to National Exams a.k.a. UN which has now been eliminated.

Same as before, we assume first that Nobita doesn't study and answers randomly. The questions consist of 5 answer options with 1 correct answer and 4 wrong answers. So the probability of answering correctly for one question is $0.2$ while the probability of answering incorrectly for one question is $0.8$.

First, we try using the expected value approach. Suppose the number of questions worked on is 50 questions and Nobita works on all of them randomly. Then his expected score is as follows:

$\text{Score} = P(\text{correct}) \times n \times \text{correct score} + P(\text{wrong}) \times n \times \text{wrong score}$

$\text{Score} = (0.2 \times 50 \times 1) + (0.8 \times 50 \times 0) = 10 + 0 = 10 \text{ out of } 50 \text{ points} = 20 \text{ out of } 100 \text{ points}$

With this assumption, it's statistically very difficult for Nobita to consistently get zero scores if he's answering randomly. The probability of getting all questions wrong in a 50-question multiple choice test with 5 options each is:

$P(\text{all wrong}) = (0.8)^{50} \approx 6.81 \times 10^{-6}$

This probability is incredibly small - about 1 in 146,000. Getting this result consistently across multiple tests would be virtually impossible by chance alone.

The Statistical Impossibility

If Nobita truly answered randomly on multiple tests, the probability of consistently getting zero scores becomes astronomically small. For example, getting zero on just 3 consecutive tests would have a probability of:

$P(\text{3 zeros}) = (6.81 \times 10^{-6})^3 \approx 3.16 \times 10^{-16}$

This is less than 1 in a quadrillion chance!

From a probability standpoint, the most logical explanation is that Nobita's consistent zero scores are intentional rather than accidental. This mathematical analysis gives credence to the theory that Nobita might be smarter than he appears, choosing to underperform for reasons known only to him.

The real lesson here isn't about Nobita's intelligence, but about how probability theory can be used to analyze seemingly simple situations and uncover surprising insights. Sometimes the most obvious explanation isn't the most mathematically sound one.