4 mathematical principles that every entrepreneur should use to make smart decisions

We share four and a half mathematical principles that will help you become smarter in business.

Humans evolved to do calculations. We have specific brain regions dedicated to numbers and calculations. The latter was used by our ancestors to distribute the apples with their cave companions and calculate if they could cross the jungle before nightfall.

As the centuries passed and our science improved, we began to use mathematics for more sophisticated purposes. Below are three and a half mathematical principles that will help you become smarter in business.

Probability is a branch of mathematics designed to calculate the probability of an event. For example, in a coin toss, heads and tails have a uniform probability of 50% each.

Smart entrepreneurs rely on probability to estimate the chances of success of their businesses, which keeps them rational and grounded. For example, Elon Musk gave SpaceX and Tesla a 10% chance of success when he started them. It seems like a pessimistic prediction, but on average 90% of startups fail.

Those realistic numbers motivated Elon Musk and his teams to keep going because they knew the odds were against them. And in case of failure, it's comforting to know that you won't be the only ones.

By the way, the 90% failure rate among startups is called the baseline.

In general, a baseline is the average probability of a specific event or the reference point that can be used to calculate an estimate. Most of the time, baselines produce realistic predictions.

The Elon Musk story was a good illustration of how baselines are in the context of a prediction. Here is an example of how to use baselines in an estimate.

In the United States, 12% of people use bicycles regularly. That's our baseline.

Let's say you have a business where you sell tires in a city of 10,000 inhabitants. The numbers say you probably have 1,200 potential customers. If each customer changes their tires once a year, they can make up to 2,400 sales.

Just like that, you can estimate your annual income.

Probabilities and baselines are great decision-making tools because they are based on objective data. Unfortunately, most entrepreneurs fall short on objectivity. They pride themselves on irrational gut decisions and end up closing their businesses.

Don't be those businessmen. Bet instead on rationality. Use baselines.

John Kelly was a scientist who worked in an innovation lab that was later acquired by Nokia (the best phone company before Apple decided to join the party). Kelly's job was to analyze telephone signals.

He devised a formula that allowed him to determine the optimal magnitude of long-distance calls. Little did he know that legendary investors like Warren Buffet and Bill Gross would later use his discovery to maximize their chances of winning in the investment game.

There are many versions of the Kelly Criterion, but they all serve the same central purpose: telling you what percentage of your money you should allocate to a given investment.

This is the basic formula of the Kelly criterion:


Let's say you have an investment opportunity with an 80% chance of success (probability of winning), and you are promised a 20% profit (profit). However, if the investment fails, you will lose 10% of your money (deficit).

In this case, the Kelly criterion (K%) suggests that you invest 70% of your money. I've chosen these ridiculous numbers to show you that, even with ultra-amazing odds, math advises against going all-in.

In more realistic situations, the formula returns a number that rarely exceeds 26%. By the way, these results do not only apply to monetary investments. You can also use the Kelly Criterion to manage your time, your sales, and your content.

In all cases, never bet 100% of your resources on the same bet.

Vilfredo Pareto was an Italian engineer interested in philosophy and economics. One fateful day in the late 1880s, Pareto decided to study how wealth was distributed in Italy.

He quickly discovered that 80% of Italian wealth belonged to 20% of the population. Decades later, another smart guy named Joseph Juran realized that Pareto's finding applied to other distributions like productivity, fundraising, and even the population of big cities.

This is how Pareto's first observation was generalized into the following principle

80% of the consequences come from 20% of the causes.

In business, the Pareto distribution means that 80% of your income will come from 20% of your work. If you want to optimize your time and energy, you must identify your 20% (which can be products, tasks or clients) and pay more attention to them.

This was the first reason I mentioned the Pareto Principle.

The second reason has to do with an analogous observation that can change the rules of the game for many entrepreneurs. Is called…

When I worked at Charles De Gaulle Airport in Paris, I had a Muslim colleague who I hung out with quite a bit. Once, we decided to escape the company canteen and go to a nearby shopping center to eat something tasty.

Muslims only eat Halal meat and that's why I had sushi on my mind while we were looking for restaurants. But my friend stopped in front of a French franchise specializing in roast chicken.

“The food is great here.”said. “It is also 100% Halal.”

It seemed unlikely to me, since most Halal restaurants had Arabic or Asian names. Why was this purely French restaurant, supposedly of Christian origin, serving Halal food?

If you analyze the situation from a commercial point of view, the answer is very clear. Those who don't eat Halal don't care about eating Halal. But Halal eaters would never eat non-Halal food.

Therefore, a group of, say, 12 people among whom one individual is a Halal diner is almost guaranteed to dine at a sushi restaurant rather than go to a non-Halal chicken franchise. That's minority rule in a nutshell.

Here is how Nassim Nicholas Taleb formulated it:

“It is enough for an intransigent minority – a certain type of intransigent minorities – to reach a minuscule level, say three or four percent of the total population, for the entire population to have to submit to its preferences.”

Smart entrepreneurs anticipate minority rule by catering to the preferences of inflexible minorities. They know that the flexible majority will simply follow them. Thus, they expand their clientele and maximize their profits.

Here are four quick examples that span different sectors:

  • When you open a restaurant, you want to have vegan options. Vegetarians, flexitarians, and everyone else can eat vegan food, but vegans never eat non-vegan food.
  • When creating video content, add subtitles. People whose ears are not accustomed to English will still be able to consume its content. The same goes for those who cannot turn on the sound because they are in a public place.
  • When developing an app, make a web version for people who use computers more than phones.
  • When developing a product, make sure you adhere to the safety measures of the strictest countries. This will make it easier to ship your products across the sea.

Mathematics enhances logical reasoning and logical reasoning enhances intelligent decisions. In the game of business, those who make the smartest decisions win.

Give yourself a tactical advantage by remembering these four principles:

  • Probability and baseline: Make your estimates based on general trends, such as 90% of startups fail. You will be much more realistic.
  • Kelly criterion: Never bet more than 25% of your resources on a single bet. Diversify your investments, including how you spend your time.
  • Pareto Distribution: 80% of the consequences come from 20% of the causes. Focus on what matters.
  • Minority rule: Vegans never eat non-vegan food, but non-vegans eat vegan food. Meet specific needs to expand your clientele.

I leave you with a precious memory of me.

My high school math teacher was the kind of elderly genius you see in comics. He had a long white beard, oversized glasses perched on his pointy nose, and a mad scientist's laugh.

“It's all math”he told me once. “But math isn't everything… MUHAHA!”.

Never forget that you have the power to be the exception to any equation.