Right skewed distributions

Some of the things we do, produce right skewed distributions. In certain cases we want to be on the left side of the right skewed distribution, and in different ones we want to be on its right side. Left side Examples here are the time needed in sports like running a marathon, or the time needed to solve a math test. In all these cases we quickly experience diminishing returns after a certain point. In appreciation of the effort required to achieve the corresponding nevertheless impressive results, we have built mechanisms to reward the people who manage the rare by definition feat to be at the leftmost side. We give gold medals or scholarships to the first, and we sponsor the people at the top. We may even use a projected scale that tries to make apparent even smaller differences. Nevertheless, the difference between the top 0.1% and 1% is not that huge in absolute terms of outcomes compared what happens on the right side. That is, the top athletes may finish a marathon with…