As technology developed, we began to use mathematics for more complex purposes. Below, we’ll introduce you to three and a half mathematical principles that can make you smarter in business.

Probability, Baselines, and Estimation

Probability is the branch of mathematics that we use to calculate the likelihood of an event occurring. Smart entrepreneurs rely on probability to estimate their business’ chances of success, which keeps them rational and grounded in reality.

For example, when Elon Musk started SpaceX and Tesla, he said they had a 10% chance of success. This may seem like a pessimistic prediction, but it is true that on average 90% of startups fail. These realistic numbers gave Musk and his team the impetus to move forward, because they knew that they had no advantage in terms of probability. And knowing that they are not the only ones facing failure is indeed a comforting thing.

It is worth mentioning that the 90% failure rate of startups is generally referred to as the baseline. Typically, a baseline is the average likelihood of a particular event, or a reference point from which estimates can be calculated. It tends to produce realistic forecasts.

For example, in the United States, 12% of people ride bicycles regularly. This is the baseline for the example we’ll be referring to.

Suppose you run a bicycle tire company in a city of 10,000 inhabitants. A baseline would tell you that there might be 1,200 potential customers. If each customer changes their tires once a year, you can sell tires for up to 2,400 vehicles. This way you can estimate your annual income.

Probability and baselines are great decision-making tools because they rely on objective data. Unfortunately, most entrepreneurs lack objectivity. They conceitedly choose to use irrational instincts to make decisions and end up closing their doors.

So don’t be those entrepreneurs. Be rational and use the baseline. The Kelly

Criterion There are many versions of the Kelly Criterion, but their core purpose is to tell you what percentage of your capital should be allocated to an investment.

The formula of the basic Kelly criterion looks like this: K%=W-(1-W)/R

K%=The proportion you should invest (expressed as a percentage)

W=Probability of winning

R=Profit/loss

A small example: Suppose You have an investment opportunity with an 80% probability of success (probability of winning), and if successful, you will receive a 20% profit (yield). However, if the investment fails, you will lose 10% of your capital (loss). In this case, the Kelly criterion (K%) recommends that you invest 70% of your capital.

The 80% probability of success here is something I made up at random, and I want to tell you that even if the odds of winning are surprisingly high, mathematics advises you not to play stud.

In more realistic scenarios, the formula rarely yields a figure above 26%. By the way, these results don’t just apply to monetary investments, you can also use the Kelly Criteria to manage time, sales strategy, and content placement.

Under no circumstances should you ever put all your eggs in one basket.

Pareto Distribution

In the late 1880s, Wilfredo Pareto found that 80 percent of Italy’s wealth belonged to 20 percent of the population. Decades later, another man named Joseph Juran realized that Pareto’s findings applied to other distributions, such as productivity, fundraising activity, and even the population of large cities.

Pareto’s first observation was later summarized as the following principle: 20 percent of the cause is 80 percent of the effect.

In business, the Pareto distribution means that 80% of income will come from 20% of jobs. If you want to optimize your time and energy, you should identify your 20% (could be products, tasks or customers) and give them more attention.

This is the first reason I came up with the Pareto principle.

The second reason involves a similar observation that can be a game-changer for many business owners. It’s called –

the rule of the minority

Once, a colleague and I decided to go to a shopping mall for lunch. My colleague is a vegetarian and we stopped in front of a store.

”The food here is great,” he said, “and everything is vegetarian.”

Looking at the situation from a business point of view, although I have no food restrictions myself, because of his eating habits, our consumption choices are limited to vegetarian restaurants. . That way, a group of 12 people (one of whom is vegetarian) is almost guaranteed to eat at a vegetarian place rather than a regular restaurant. In short, this is the rule of the minority.

Nassim Nicholas Taleb puts it this way: “A minority that sticks to a rule needs to be a very small percentage of the population, say 3 or 4 percent, for the population to adopt their preferences. ”

Smart entrepreneurs anticipate the Law of the Minority in advance, allowing them to craft business strategies that take into account minority preferences. They know that flexible majorities are often receptive to minority preferences. As a result, they expand their customer base and maximize revenue.

Here are a few simple examples covering different industries:

When creating video content, add subtitles. People whose ears are not accustomed to English can still read your content. The same applies to those who are in public places and therefore cannot turn on the sound.

When developing an app, make a web version for those who use computers more than phones.

When developing products, the strictest national security measures must be observed. This will make it easier to transport your product by sea.

Finally, never forget to learn to use these mathematical things alive, don’t let it bind you.