The title of this post is an allusion to an earlier one: “Modeling Is Not Science“. This post addresses a model that is the antithesis of science. Tt seems to have been extracted from the ether. It doesn’t prove what its authors claim for it. It proves nothing, in fact, but the ability of some people to dazzle other people with mathematics.

In this case, a writer for MIT Technology Review waxes enthusiastic about

the work of Alessandro Pluchino at the University of Catania in Italy and a couple of colleagues. These guys [sic] have created a computer model of human talent and the way people use it to exploit opportunities in life. The model allows the team to study the role of chance in this process.

The results are something of an eye-opener. Their simulations accurately reproduce the wealth distribution in the real world. But the wealthiest individuals are not the most talented (although they must have a certain level of talent). They are the luckiest. And this has significant implications for the way societies can optimize the returns they get for investments in everything from business to science.

Pluchino and co’s [sic] model is straightforward. It consists of N people, each with a certain level of talent (skill, intelligence, ability, and so on). This talent is distributed normally around some average level, with some standard deviation. So some people are more talented than average and some are less so, but nobody is orders of magnitude more talented than anybody else….

The computer model charts each individual through a working life of 40 years. During this time, the individuals experience lucky events that they can exploit to increase their wealth if they are talented enough.

However, they also experience unlucky events that reduce their wealth. These events occur at random.

At the end of the 40 years, Pluchino and co rank the individuals by wealth and study the characteristics of the most successful. They also calculate the wealth distribution. They then repeat the simulation many times to check the robustness of the outcome.

When the team rank individuals by wealth, the distribution is exactly like that seen in real-world societies. “The ‘80-20’ rule is respected, since 80 percent of the population owns only 20 percent of the total capital, while the remaining 20 percent owns 80 percent of the same capital,” report Pluchino and co.

That may not be surprising or unfair if the wealthiest 20 percent turn out to be the most talented. But that isn’t what happens. The wealthiest individuals are typically not the most talented or anywhere near it. “The maximum success never coincides with the maximum talent, and vice-versa,” say the researchers.

So if not talent, what other factor causes this skewed wealth distribution? “Our simulation clearly shows that such a factor is just pure luck,” say Pluchino and co.

The team shows this by ranking individuals according to the number of lucky and unlucky events they experience throughout their 40-year careers. “It is evident that the most successful individuals are also the luckiest ones,” they say. “And the less successful individuals are also the unluckiest ones.”

The writer, who is dazzled by pseudo-science, gives away his Obamanomic bias (“you didn’t build that“) by invoking fairness. Luck and fairness have nothing to do with each other. Luck is luck, and it doesn’t make the beneficiary any less deserving of the talent, or legally obtained income or wealth, that comes his way.

In any event, the model in question is junk. To call it junk science would be to imply that it’s just bad science. But it isn’t science; it’s a model pulled out of thin air. The modelers admit this in the article cited by the Technology Review writer, “Talent vs. Luck, the Role of Randomness in Success and Failure“:

In what follows we propose an agent-based model, called “Talent vs Luck” (TvL) model, which builds on a small set of very simple assumptions, aiming to describe the evolution of careers of a group of people influenced by lucky or unlucky random events.

We consider N individuals, with talent Ti (intelligence, skills, ability, etc.) normally distributed in the interval [0; 1] around a given mean mT with a standard deviation T , randomly placed in xed positions within a square world (see Figure 1) with periodic boundary conditions (i.e. with a toroidal topology) and surrounded by a certain number NE of “moving” events (indicated by dots), someone lucky, someone else unlucky (neutral events are not considered in the model, since they have not relevant effects on the individual life). In Figure 1 we report these events as colored points: lucky ones, in green and with relative percentage pL, and unlucky ones, in red and with percentage (100􀀀pL). The total number of event-points NE are uniformly distributed, but of course such a distribution would be perfectly uniform only for NE ! 1. In our simulations, typically will be NE N=2: thus, at the beginning of each simulation, there will be a greater random concentration of lucky or unlucky event-points in different areas of the world, while other areas will be more neutral. The further random movement of the points inside the square lattice, the world, does not change this fundamental features of the model, which exposes dierent individuals to dierent amount of lucky or unlucky events during their life, regardless of their own talent.

In other words, this is a simplistic, completely abstract model set in a simplistic, completely abstract world, using only the authors’ assumptions about the values of a small number of abstract variables and the effects of their interactions. Those variables are “talent” and two kinds of event: “lucky” and “unlucky”.

What could be further from science — actual knowledge — than that? The authors effectively admit the model’s complete lack of realism when they describe “talent”:

[B]y the term “talent” we broadly mean intelligence, skill, smartness, stubbornness, determination, hard work, risk taking and so on.

Think of all of the ways that those various — and critical — attributes vary from person to person. “Talent”, in other words, subsumes an array of mostly unmeasured and unmeasurable attributes, without distinguishing among them or attempting to weight them. The authors might as well have called the variable “sex appeal” or “body odor”. For that matter, given the complete abstractness of the model, they might as well have called its three variables “body mass index”, “elevation”, and “race”.

It’s obvious that the model doesn’t account for the actual means by which wealth is acquired. In the model, wealth is just the mathematical result of simulated interactions among an arbitrarily named set of variables. It’s not even a multiple regression model based on statistics. (Although no set of statistics could capture the authors’ broad conception of “talent”.)

The modelers seem surprised that wealth isn’t normally distributed. But that wouldn’t be a surprise if they were to consider that wealth represents a compounding effect, which naturally favors those with higher incomes over those with lower incomes. But they don’t even try to model income.

So when wealth (as modeled) doesn’t align with “talent”, the discrepancy — according to the modelers — must be assigned to “luck”. But a model that lacks any nuance in its definition of variables, any empirical estimates of their values, and any explanation of the relationship between income and wealth cannot possibly tell us anything about the role of luck in the determination of wealth.

At any rate, it is meaningless to say that the model is valid because its results mimic the distribution of wealth in the real world. The model itself is meaningless, so any resemblance between its results and the real world is coincidental (“lucky”) or, more likely, contrived to resemble something like the distribution of wealth in the real world. On that score, the authors are suitably vague about the actual distribution, pointing instead to various estimates.

(See also “Modeling, Science, and Physics Envy” and “Modeling Revisited“.)