Saturday Serendipity
Quote, Mental Model, Interesting find.
Hi.
Reading time: About 5 minutes
Quote
“We learn more from people who challenge our thought process than those who affirm our conclusions. Strong leaders engage their critics and make themselves stronger. Weak leaders silence their critics and make themselves weaker. This reaction isn’t limited to people in power. Although we might be on board with the principle, in practice we often miss out on the value of a challenge network.”
― Adam M. Grant, Think Again: The Power of Knowing What You Don't Know
Mental Model
Law of Large Numbers
The law of large numbers is a very important but complicated concept taught in statistics and probability. I am not that smart, which is why I have written it for all of us to understand the basic concept instead of getting into the intricate details.
The law is very simple.
As the sample size keeps increasing the mean gets closer to the average population.
“The law of large numbers was first proved by the Swiss mathematician Jakob Bernoulli in 1713. He and his contemporaries were developing a formal probability theory with a view toward analyzing games of chance.” - Brittanica
There is a very simple example to explain this.
Consider a coin. There is a 50/50 probability that the coin will land heads or tails.
Let’s focus on heads for now.
The probability of landing a coin on heads is 50% or 0.5.
Let’s say you flip a coin 10 times. The result is you get heads 4 times and tails 6 times. Hence your result shows that the outcome is 40% heads or 0.4.
Now we’ll flip it 50 times. The result is we get heads 24 times and tails 26 times. Now your result is 0.48 or 48%.
Now if we flip it 100 times, the result is heads 51 times and tails 49 times. Now your result is 0.51 or 51%.
Suppose we continue and flip it 1000 times. The result is heads 497 times and tails 503 times. Your result is 0.497 or 49.7%.
This example shows us how as we keep tossing the coin more the probability of getting 50% increases. This is because the result is random. So random that there is a very minute possibility of it landing heads 1000 times.
This is very similar to the idea of mean reversion where everything reverts to the mean over the course of time. In this case basically the larger the sample size the higher the probability of achieving mean.
Here is the main difference between mean reversion and the law of large numbers. Mean reversion: If we saw a player like Virat Kohli perform poorly for one match then we would expect him to return to his mean of average performance instantly in a few games.
Law of large numbers: We would analyze Virat Kohli's mean of average by actually looking at every single match he has played. The more matches you look at the more the performance converges to the mean.
In Business
If we look at the insurance companies they need to analyse the data of which people are more likely to claim insurance. For instance, if a car insurer wants to give high premiums to people who are more likely to crash their car than he/she needs more and more data to prove which ones are actually the most likely. You need a large data set to tell you the actual picture not a small one which tells you something which might be an anomaly.
“As the insurance agency collects more data, it experiences the law of large numbers, they may soon find that young, male drivers are most likely to cause an accident. This larger sample becomes more representative of driving incidents, and the insurance company can arrive at more accurate conclusions about the appropriate insurance premiums to charge.” - Investopedia
This can apply to every single company which is looking for data. Banks can use larger data sets to get a little bit of an extra edge as to which type of people don’t repay their loans.
In Investing
As investors we want to look for 100 baggers. We want to compound our money so much that we can achieve financial freedom. Now if we want to achieve good returns we have to invest in companies which have room to grow a lot. For instance, all the investors who have bought HDFC bank right now during the dip should realise that it is the 7th largest bank in the world. It is the biggest bank in India. How much room is there to grow? Can the previous growth rates be achieved again? These are the questions I ask and to be honest the answer is uncertain.
We know that a company cannot grow at high rates forever. So to expect growth rates of the past make no sense. As you get bigger as a company the returns of the company go to the mean. This is the law of large numbers.
It should also be applied in economics. Economies work in cycles. The growth rates which are high will go down at some point in time. So just remember the longer the amount the more chances you have of not experiencing only one type of an economy. There will be a boom and a bust. The longer you last the more chance you have to not get eaten up. Thus the importance of being anti fragile.
Interesting find
That’s it. Enjoy your weekend.
Thank you for reading,
Samvit.