Well there are several things that are incoherent about the article's application of this model.
1. Coin flipping is not a fit analogy, despite the fact that it's parroted in financial discussions ad nauseum. Take this quote from the article, for example:
Maybe the string of investment and managerial decisions that made one person’s company successful, and that seem so very wise in retrospect, were actually just the entrepreneurial equivalent of flipping a coin 20 times and getting all heads. The chances of that happening are about 1 in 1 million, so if enough people try it, someone is bound to get lucky and look like a coin-flipping genius—purely by chance.
What? How do you map the theoretical probabilities of individual entrepreneurial decisions to the chance of a heads or tails on a coin flip? Is the chance of getting into YC 50%? Is the chance of securing venture capital in a Series A round 50%? How about? This is before we even consider that the theoretical chance for each decision will obviously not be the same for everyone, whereas a coin flip is. This is important because it's not falsifiable if we can't map decisions to probabilities. It's also important because the numbers could be wildly different. If each entrepreneurial decision has a 50% chance of success, that might result in a 1 in 1 million chance of getting rich. But what if the actual chances of success for each entrepreneurial decision in lieu of the coin-flip mapping result in a 1 in 4 quadrillion chance of success? One result indicates that essentially all successes could be due to chance, the other suggests the opposite.
2. The author uses very fuzzy measurements with no empirical basis in reality to support the model. For example:
To make the game more realistic, assume that if investors’ wealth declines below some level they have to drop out of the game, and are replaced by newly rich players emerging from the middle class. Eventually, the game will reach a kind of equilibrium—one in which the number of players going up is always balanced by the number going down, so that the overall distribution of wealth reaches a steady state and doesn’t change anymore.
Wait a second, why are we assuming that this game reaches an equilibrium? We can't just use textbook economics here - there is no reason to assume the "game" won't be weighted towards more players dropping out than moving up or vice versa.
3. The author tries to repair the issues with chance being theoretically equal in my first point with the following:
Still, it is possible to get a crude sense of the effect of talent by modifying the investment game to include two types of players. Normal investors are just like those in the first game: They flip a coin with heads yielding a return of 30 percent, and tails producing a loss of 10 percent. But the talented investors are more skilled at playing the market: They earn slightly more than 30 percent when the coin comes up heads, and lose slightly less than 10 percent when the coin comes up tails. Now we set the players loose and ask an empirical question: How big can this “talent differential” be and still stay statistically consistent with the power law wealth distribution we see in the real world?
Where are these numbers coming from? How are these a rigorous, empirical model of talent and the subsequent chance differential? By this point in the article the entire game is becoming so "in the clouds" that it doesn't have any basis in reality anymore. It's like I came up with a "law" based on one extremely convoluted thought experiment and attempted to extrapolate it to the entire market in real-world conditions.
Basically, the author's model is narrow in some places, vague in others and overall does not empirically prove the premises it attempts to build upon. He hand waves the (extremely common) power law distribution as a sort of magic wand that smooths away all the lack of rigor. There's just not much evidence that the model reflects the real world.