Lucky versus skill

I’ve added the result of a quick random generation of possible outcomes of two types of individuals. This is not Monte Carlo simulation as has been discussed below, but rather a very simple illustrative example. This will further illustrate the points about in my previous post (and do also read the comments for some more discussion, and add your own thoughts and questions).

For this example, we have two types of people

  1. Traders who pursue a risk strategy by not managing risk and operating in an environment where randomness affects the outcomes in a large way.
  2. Dentistswho operate in areas where luck has little to do with the outcome. Hard work and studying pays off, but randomness has less to do with ultimate success.

For trader (in this example) feel free to use “entrepreneur” or “writer” with similar effect.

The outcome is on the y-axis (the vertical axes) so that more successful outcomes are higher up on the graph.

Dentists and traders
Four things can be seen quite clearly:

  1. The dentists have on average better outcomes than the traders
  2. The range of outcomes is much greater for the traders
  3. Overall, you’re probably better off being a typical dentist than a typical trader, and certainly better off being a unsuccessful dentist compared with a successful trader.
  4. The successful traders are on average very much more successful than the successful dentists.

That last point is the important one. If were to imagine that traders with a “success score” of less than 0 were to leave, and then sampled the remaining populations to estimate the relative success or failure of the individuals, the diagram would look slightly different.

Diagram of success of dentists and traders with unsuccessful traders removed from the sample
Now if we consider the results, we observe the following:

  1. The traders now have on average better outcomes than the dentists. The mean, median and maximum outcome are all better for traders, and sometimes to a great extent.
  2. The range of outcomes is slightly greater for the traders
  3. Trading now seems clearly to be the better occupation.

So what is the conclusion? That we should all become dentists? No. That we should all give up our dreams and settle for tedium and mediocrity? Definitely not. The conclusion is that one needs to be exceptionally careful when considering the track record of a sample of individuals, when the sample suffers from some form on intrinsic selection. In this case, the population of traders that we see (in movies and in real life) are usually the successful traders. Furthermore, in this example, the successful traders owe their success to luck alone. In fact, their luck overcame their lack of skill. This holds to a certain extent in the real world as well.

Published by David Kirk

The opinions expressed on this site are those of the author and other commenters and are not necessarily those of his employer or any other organisation. David Kirk runs Milliman’s actuarial consulting practice in Africa. He is an actuary and is the creator of New Business Margin on Revenue. He specialises in risk and capital management, regulatory change and insurance strategy . He also has extensive experience in embedded value reporting, insurance-related IFRS and share option valuation.

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