You are a Statistical Anomaly

“What are the chances that you’re the next Mark Zuckerberg or Elon Musk?”

The answer to this question is ‘small’. Very very small. So small that it almost becomes insignificant, or as everyone tells you — impossible. In a world of 7.4 billion people, there is only one Elon Musk and one Mark Zuckerberg (I use Zuck and Musk as benchmarks for ultra-super-extraordinarily high performers). However, for the sake of quantifying someone’s level of performance, I’ll use their net worth.

As of 2016, the proportion of billionaires in this world is a meager 0.000024%, or one in 4 million. On the other hand, the chances of us becoming mediocre earners is significantly higher. To illustrate this more simply, our population can be graphed out to look something like this:


As of all large data, our population follows a normal distribution, where the probability of each of us ending up smack in the middle of the performance index is the highest. What does this mean for our individual ambitions? Does it mean that it is illogical and irrational to think that we can somehow defy this statistic and become a statistical anomaly like Musk? Should we then reduce the size of our ambitions, and rationalize this reduction using probabilities and statistics?

This common phenomenon is also known as “being realistic”.

The Paradox of Small Data

The rationalization of “being realistic” is based on one significant premise — we envision ourselves as a data point on this curve with respect to the other 7.39999 billion data points. Using this premise, if a single data point (you) is chosen from the 7.4 billion, the data point would be expected to fall within the yellow region.


However, what happens when you take that same data point (you) and look at it as a standalone data point? Without the population data, there is no way to tell whether the single data point will be a low performer, an average performer, or a high performer. In fact, the chances of the data point falling anywhere along the x-axis is equal.

This is the paradox of small data – once you look at data points on a small scale, the central limit theorem falls apart. There is no way to predict the outcome of the data point without comparing it to the rest of the population.

Implications of this Paradox

As we had illustrated earlier, the logic behind “being realistic” only works when you compare singular data points to the entire population. On a small enough scale, it is impossible for anyone to predict where the data point falls — whether it falls on the extreme right of the x-axis (like Elon) or the extreme left.

With this new perspective, one important question which we naturally need to ask is: Why do we observe ourselves as data points within a population instead of a standalone data point?

The answer is because humans are fundamentally creatures of imitation. We learn by mimicking others — from a baby learning how to walk to a teenager learning how to fit in. We look outwards to gain insights about ourselves. We seek validation by comparing ourselves to others, instead of deriving confidence from within. We set our ambitions not based on our own strengths but instead based on what seems realistic with respect to the people around us.

From young, it is drilled into our thinking that following by example is paramount in getting ahead in life. We are told that “when in Rome do as the Romans do” and we should behave the way people around us expect us to. The people who don’t behave this way are labelled misfits — they are shunned, bullied, and outcast from society. We are told to look outwardly when we make decisions; our brains are conditioned to compare ourselves to the people around us to see how we measure up. Our internal voice gets drowned among the noise of crowds — many of us can’t even hear ourselves anymore.

We simply don’t know better.

Maybe its time to look inwards for once. Maybe its time to look at ourselves as standalone data points instead of comparing ourselves with the population data set. Maybe its time to disregard the notion of averages and instead set our ambitions as large — and as ludicrously — as we can.