In the Win for Life game, the top prize is an annuity of 3,000 euros monthly for 20 years. Too bad that only one case out of about 3.7 million gets the annuity. Whereupon someone tosses out a sports metaphor with which one can do very badly: you don’t score goals in 100 percent of the games you don’t play.
The average entrepreneur in Italy earns, at a minimum, about 2100 euros per month. Clearly it depends on the industry.
However, the average lifespan of a company turns out to be less than the years of income from the game above: 12.3 years, which also depends on the sector.
The probability of having a salary as an entrepreneur depends on entrepreneurial risk, which is notoriously high for startups. Let’s exclude them. Then the probability of success of having an income, as an SME owner, can be modeled using the negative exponential distribution that uses the life expectancy above. Surely you have bought a light bulb and I would have read the expected life hours. This statistical quality control comes right from that distribution.
Knowing the average life expectancy of companies, we arrive at 92.22% probability of having an income in one year. About 8% chance of not having it.
This probability of success obviously turns out to be extremely greater than Win for Life, partly because it requires work, responsibility, worry. There are no free meals in the universe, but more profitable meals.
However, the use of that distribution has a rigidity that is why a lot of people get hurt by playing, for example in the lotto, numbers that have not come up in a while, the so-called laggards. This strategy comes from ignoring the absence of memory for some distributions. In this case, rigidity has to do with the probability of having a gain that does not depend on the time that has already passed (years). But we know very well that reality violates this theoretical assumption: younger firms are more at risk of failure, thus more at risk of not giving the owner an income. It is no coincidence that start-ups turn out to be an emblematic case of this.
By relaxing this assumption we arrive at another distribution used in statistical quality control, but not only: the Weibull distribution. This relaxation makes us pay a price: the need for another assumption that is used to do the math. So in addition to the average life expectancy of firms, we will need a shape parameter of the distribution of their life years, which I am NOT able to retrieve since only already processed data can be found. Another thesis idea for some reading students.
At this point the strong hypothesis, in numerical terms, not conceptual, becomes: since life expectancy increases as a function of firm age, then the distribution will have shape parameter >1, in the previous case it was equal to 1. We give the value 2 as the strong hypothesis.
Then the probability of earnings in year one becomes about 99.31%. A pleasant difference with, however, a theoretical pippone preceding it.
However, while Win for Life has a negative average net profit (about -43%) , resulting from mathematical expectation, a company has a positive average gross margin. For example, in the Euronext market, so a value not really representative of SMEs, we are talking about 19.3%. Obviously higher than the stock return: 9.7 percent over the last 20 years for the SP500, 4.5 percent over the last 20 years for the FTSE MIB.
I would say that this last comparison alone justifies having a lower return, compared to the winning return, despite the work, responsibilities and concerns that come with entrepreneurial activity. Clearly the probability of above calculated over 20 years is lowered: 3.83 percent. But it can be raised by refining the starting assumption
If you are interested in winning more easily, with your business, we can hear from you in a free call to begin to see, specifically, how to increase your gross margin through statistical advice.