Back in the fall, I commented on a simulation paper by Pluchino et al that argued that luck is much more important than talent in determining life outcomes. The authors focus on the mismatch between the distribution of talent, which is thought to be a normal curve, and the distribution of success, such as accumulated wealth, which is often observed to be a pareto distribution.

There are few people who have very low or very high talent, and most people have moderate or average talent. On the other hand, there are very few people who have high success, and very many who have relatively low success. If talent was an important driver of outcomes, the success distribution would tend to look like the talent distribution. It usually doesn’t.

Many of us feel intuitively that talent does not guarantee success. Talent is a necessary but insufficient condition for success. You also have to be at the right place and the right time. You need the right breaks and you need to avoid the wrong dangers, such as illness at a critical time, for example. The missing link between the talent distribution and the success distribution, is dumb luck.

Of course, this entire discussion supposes that talent is something that can be defined and measured in some meaningful sense. That idea is easier to defend in narrow fields, such as the execution of specific tasks, but it becomes more difficult to imagine when speaking of general life outcomes. Still, for the purposes of this little study, let’s suspend disbelief, and let’s imagine that there is some attribute called talent, that is normally distributed in a population, and that should be reflected in a person’s overall success in life, however measured.

Pluchino et al.’s result

Pluchino et al. represent luck through events which individuals encounter and that can be either lucky (beneficial) or unlucky (detrimental) to their success. Individuals with higher talent are more likely than those with low talent to benefit from the lucky events they encounter. The authors clearly show that under their model, using the parameter values they test, the most talented individuals are almost never the most successful. They show that individuals with close to average talent are most likely to be highly successful.

Last September, I extended their model and I was able to show that the number of events available in the environment, relative to the number of individuals, which I called event density (ED), was important in helping talented individuals climb the success curve. When individuals encounter lots of events, success tends to be more closely aligned with talent. However, even with ED values of up to 20 times higher than those in the original simulation, between 10% and 20% of individuals with more than average talent had less than average success at the end of runs that were up to 60 times longer than Pluchino et al’s, and in which talent, in theory, therefore had more time to express itself.

The most talented individuals were still not likely to be the most successful. Even given substantially more opportunities to capitalize on their talent over much longer periods of time, talent was still struggling to overcome luck as a driver of individual outcomes in the system.

I modified the model some more and did some additional experiments to explore what happens 1) if individuals can mitigate the impact of unlucky events in proportion to their talent, and 2) if we make the environment more or less challenging by varying the proportion of lucky to unlucky events.

In brief, as I did in the fall, I find that mitigation does not help talented individuals to be more successful relative to less talented ones. In fact, to the contrary, mitigation of bad luck tends to help less talented individuals keep up with more talented ones. However, I did find that talent does have a big impact on success when the environment is highly challenging. I am not yet sure what to make of the result on mitigation, but the hostile environment result is very compelling.

The (extended) extended model

I further revised the model by making good luck and bad luck more symmetrical, and by giving agents more ability to mitigate luck in proportion to their talent. When encountering a lucky event, individuals now have their success multiplied by (1 + talent) * mitigation, where talent is a value between 0 and 1, and mitigation is a global value.

An individual with a current success value of 1 and a talent value of 0.5, in an environment in which mitigation is set to the neutral value of 1 (no mitigation), after encountering a lucky event, would have a success value of 1.5.

The same individual, after encountering an unlucky event, would have a success value of 1 – (1 – talent) / mitigation, or in this case, 0.5. Under the same conditions, an individual with 0.9 talent would have a success value of 1.9 after a lucky event, while an individual with 0.1 talent would have a success of 1.1. The same individuals would have success values respectively of 0.99 and 0.91 after an unlucky event.

If there is a mitigation value, the talented individual would be even less affected by an unlucky event, and could capitalize more on a lucky one. With a mitigation value of 2, the highly talented individual would have a success value of 2.8, while the less talented individual would have a success value of 1.2. After an unlucky event, the talented individual would still have a success value of 0.95, while the less talented individual would have a value of 0.55.

In this set of experiments, mitigation varies between 1 and 2, and event density between 0.5 and 2. The proportion of lucky events, which is a parameter in the original simulation, but not explored by Pluchino et al. varied between very challenging environments (10% lucky events, 90% unlucky), neutral environments (50 % lucky events), and favourable environments (90% lucky events). I did an exploratory run in which event density is 10 and only 1% of events are lucky, just to see what would happen under those more extreme conditions.

The simulation tracks the proportion of individuals with above average talent who also have below median success (high talent, low success, or HTLS). It records the success of each individual at the end of a run, along with their talent, which doesn’t change).

I did 5 runs of 5000 time steps for each combination of settings (event density, mitigation, % of lucky events).


The proportion of HTLS individuals, those with high talent and low success, is lowest (14%) after 5000 time steps in the environments with the highest proportion of unlucky events, the highest event density (ED), and when there is no mitigation (Figure 1).


Figure 1: The proportion of individuals that have above average talent and below median success (HTLS) after 5000 time steps under each combination of settings.

The proportion of HTLS is highest (31%) when mitigation is highest and event density lowest. The proportion of lucky events does not seem to make much difference when mitigation is high.

The distribution of talent vs success for single runs (Figure 2), confirms that success is much more closely tied to talent when event density is high and the proportion of lucky events is low. Under the best conditions I found for keep the success distribution flat, when ED is low, mitigation is high, and 90% of events are lucky, the slope for the talent vs success distribution is 0.21 and the R2 is 0.46. When ED is high, there is no mitigation, and only 10% of events are lucky, the slope climbs to 0.34 and the R2 to 0.83.


Figure 2: The distribution of talent vs success under various conditions. ED is event density, M is mitigation, and L is the percentage of lucky events.

The gray squares represent a neutral scenario in which ED is one, mitigation is absent, and 50% of the events are lucky. The black crosses show the extreme scenario in which ED is 10 (20 times higher than in the original Pluchino et al. paper), there is no mitigation, and only 1% of events are lucky. The slope for that run shoots up to 0.89, and the points are very closely clustered around the regression line, with an R2 of 0.97.

The relationship between success and talent forms a steeper, tighter line when ED is high and few events are lucky, indicating that talent plays a bigger role in determining success. The other interesting feature of the graph is that under the first set of conditions (blue circles), the most successful individuals are not the most talented, but under the second set of conditions (orange triangles), they are.


As I found in the fall, event density is very important in aligning success with talent. The more events there are out there, the better. It seems, however, that the proportion of lucky events is even more important. If there are many potentially harmful events and few potentially beneficial ones, talent is rewarded.

Mitigation, the ability to reduce negative consequences and capitalize on good luck, on the other hand, seems to favour a flatter success distribution relative to talent. I need to think about that. Unless, of course, I have a sign error somewhere in the code. I haven’t found it yet. If you do, let me know.

So what sort of a world do we have to imagine for talent to be the main driver of success? Clearly, from the results above, it is a very dark world. It is a world in which untold numbers of events outside our control are lurking, waiting to hurt us, and in which only very few events can have a positive impact on us. It is a world in which only the most supremely talented can avoid being hurt, or wiped out entirely.

It isn’t even the dark and dangerous worlds of Rollerball or Bladerunner, in which the undifferentiated mass can be insulated from disaster, if only they are resigned to their fate. It is the world of Mad Max, in which extinction is the only logical conclusion. It is a world in which you don’t have to seek risk. It will find you.

I suspect that the real world in which we live, as opposed to the Mad Max world of 1% favourable events, has a better balance between potentially lucky and potentially unlucky events. I suspect that event density is fairly high, and that mitigation is low. Mitigation assumes that people can either limit the damage or increase the benefit of events outside their control. That requires very good planning and foresight in a complex system. I am not a big believer in the human ability to do these things.

If I had to assign values from the simulation to the real world, event density would be on the higher end, mitigation would be absent, and the proportion of lucky events would be somewhere near half. That would result in a distribution of success that has a limited correspondence to talent. The most talented agents would almost never be the most successful, but most talented agents would have better success than most untalented ones. Luck would still be a significant factor in producing outcomes, and success would be no guarantee of talent. It follows that lack of success would be no good basis for finding fault.

Code link

Data: TvLmodelACAdvantageRunsSymmetrical

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