Luck is very important, but just how insignificant is talent? A comment on Pluchino et al. (2018)

A tweet recently came across my feed about an article by Pluchino et al.  that generated some media interest last year, and that looks at the relative roles of luck and talent in people’s success. The paper gives some interesting empirical support to a contention that many, including me, intuitively feel is true: “The most successful people in the world aren’t necessarily the most talented. They are the luckiest”.

In this season of early career researchers going on the job market, and academics preparing for the fall grant submission deadlines, with their wildly uncertain outcomes, this seems an important subject to tackle. Specifically, Pluchino et al. explore the seeming contradiction between the normal distribution of talent in the population for any given activity, and the fact that success (or wealth, at least) follows what is sometimes called a Paretto distribution: Very few people are very wealthy, and very many people are not.

Anyone who has heard a Bernie Sanders speech about the top one percent of the top one percent will be familiar with the idea. If most people are of average talent, and only very few have very low or very high talent, and if success is primarily tied to talent, then most people should have average success, very few people should have very low or very high success. In reality, however, we find that very few people have very high success, and very many people have relatively low success. I believe this is true in academia, but also in sports, the arts, or any field of human endeavour. It bears looking into.

I’ve written about the role of luck in my own academic journey, and I am quite convinced that luck is a dominant factor in most important outcomes in our lives. Pluchino et al. agree, and they even claim to demonstrate, using an agent-based simulation, that luck is the only really significant driver of success. “An important result of the simulations is that the most successful agents are almost never the most talented ones, but those around the average of the Gaussian talent distribution”.

They do a good job of demonstrating that luck can be very important, but I think their work needs a bit of expansion to assess the extent to which talent is unimportant. First I analyze the reasons why luck is so dominant in their model, and then I modify it slightly to look at the potential for talent to make a difference.

Pluchino et al.’s model

Pluchino et al. build a model in which a population of individuals with various degrees of talent (normally distributed) are exposed to events throughout their lives. Some of the events are lucky breaks and can increase the success of individuals, and some events are unlucky and decrease success.

When they encounter a lucky event, individuals have a certain probability, proportional to their talent, of benefiting by doubling their current level of success. The more talented individuals have a higher chance of benefitting from lucky events. When individuals encounter unlucky events, their success is cut in half, regardless of talent.

The model is very good at producing a Paretto distribution of success out of a normal distribution of talent. Within a very short time, a very few individuals have achieved very high levels of success, while most individuals have moderate or low success. The very successful individuals are consistently from the middle of the talent distribution, and highly talented individuals often have relatively low success.

This effect is increased by a two main factors. First, lucky and unlucky events work asymmetrically. Individuals have a limited probability of encountering events during any given time step. If the event is a lucky one, there is a further limited probability that they will benefit. When they encounter an unlucky event, however, individuals are automatically punished, regardless of talent. This means that talented individuals suffer a form of double jeopardy. They don’t always benefit from lucky events, but they always suffer from unlucky ones.

Second, the relative scarcity of events means that individuals actually encounter quite few of them during a whole run of the simulation. There are also very few time steps (80). Each event encounter is extremely important in determining the final outcome for any individual.  Since event encounters are random, and since most individuals are in the middle of the talent distribution, most event encounters involve moderately talented individuals, and very few encounters involve individuals with high or low talent. This means that more individuals with moderate talent have opportunities to grow their success than those with low or high talent.

The extended model

But what happens if we give talent a bit more of a chance? What happens if 1) we make lucky and unlucky events symmetrical in their impact, 2) give talented individuals a way to mitigate the impact of unlucky events and benefit from lucky ones in proportion to their talent, and 3) give more opportunities to all individuals to encounter events, so that talent has more of chance of expressing itself?

I modified Pluchino et al.’s model so that lucky events add to the success of an individual in proportion to their talent, so that talented individuals benefit slightly more from lucky events than untalented ones. Unlucky events work the same way by reducing success in reverse proportion to talent. In other words, talented individuals can mitigate the impact of unlucky events relative to less talented ones.

I ran the model with various event densities (number of events per times-step) over longer simulations, to provide more opportunities for talent to express itself, to see whether that would make a difference.

Finally, I changed the model so that it could track, in any given time-step, the number of individuals who have above average talent but who also have below average success. That gives a rough measure of the alignment between the talent distribution and the success distribution. Under various conditions of event density and run duration, does the success of individuals roughly reflect their level of talent?

For technical reasons, I also capped the amount of success any individual could accumulate. Because of the multiplicative nature of the success measure in the original model, longer runs resulted in individuals accumulating success numbers that NetLogo couldn’t handle. The cap is high enough that it doesn’t affect the ability of the model to produce a Paretto distribution out of a normal distribution of success and therefore doesn’t affect the basic dynamics of the simulation.

Results

 

Figure 1

Figure 1 shows the percentage of individuals in the population (500) who are above median talent and below median success, that is, the individuals who are relatively talented yet relatively unsuccessful. Solid lines show the results for the Pluchino et al. default model, and the dashed lines show the results for the modified model in which talent mitigates the impact of unlucky events.

The different sets of lines show the results for different event densities (Events / Population). All lines represent the average of 25 simulation runs for each set of values.

Regardless of mitigation, increasing event density (ED) decreases the proportion of high talent individuals who have low success (HTLS), but it doesn’t eliminate it. As event density increases, HTLS grows faster, but then peaks and also falls faster as time passes. It peaks first at the highest ED, and falls the fastest afterwards. Mitigation decreases HTLS only very slightly, but doesn’t change its fundamental behaviour.

Figure 2

Figure 2 shows that the model behaves the same way using Puchino et al.’s original values of 2000 for the population, and 80 time steps in duration. Increasing event density with those values also results in a decrease in HTLS.

Figure 3

Figure 3 shows a very long simulation (10 000 steps) and very high event density (10.0). HTLS continues to decrease over time, but the level of mitigation used here seems to no longer make a difference.

Discussion

It is clear that event density mainly drives whether individuals have a level of success which is proportional to their talent, and that even an event density 20 times higher than that used by Pluchino et al. fails to drive HTLS below 10% of the population. It is equally clear that giving talented individuals the ability to mitigate the impact of unlucky events, at least at the level used here, makes very little difference in long-term outcomes.

Under a very broad range of conditions, between ten and twenty percent of individuals who have more than median talent will have less than median success. I have to increase ED to 10 and give individuals 10 000 time step in order to drive HTLS down to about 2.5%. The key question, then, is whether we are exposed in our lives to relatively few, or relatively many events, lucky or unlucky, that could be significant to us.

Pluchino et al. take the approach that we face relatively few significant events in our lives. They give their individuals only 80 time steps in which to encounter events, and set ED at 0.5. Events in their simulations are few and far between. A sequence of two or three lucky or unlucky events will make the whole difference for individuals.

My view, which emerges from complexity theory, is that we are exposed every day to events which affect us significantly, and that we are not aware of most of them. Some of them don’t even involve us except for the impact they have on us.

That’s why I tested what would happen if I gave Pluchino et al.’s individuals more opportunities to encounter events. I also thought that perhaps, talent could make a difference by allowing some people to mitigate the effect of bad luck.

It turns out that more potential events in our lives does help success reflect talent, but there still remains significant misalignment, at the population level, between talent and success. I am not surprised.

What did surprise me was the relative insignificance of mitigation. It hardly seems to matter. In my next post I will explore different values for the advantage that mitigation gives, and see how far we have to push it to make a difference.

Perhaps in a third post, I will explore the policy implications of these results, as Pluchino et al. do. Eventually, I would like to see what happens if we separate talent from ability, and let individuals learn and gain ability in proportion to their talent as they encounter events, over time.

Data: NoMitVsMitClean

Link to Code