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The largely dominant meritocratic paradigm of highly competitive Western cultures is rooted on the belief that success is due mainly, if not exclusively, to personal qualities such as talent, intelligence, skills, efforts or risk taking. Sometimes, we are willing to admit that a certain degree of luck could also play a role in achieving significant material success. But, as a matter of fact, it is rather common to underestimate the importance of external forces in individual successful stories. It is very well known that intelligence or talent exhibit a Gaussian distribution among the population, whereas the distribution of wealth - considered a proxy of success - follows typically a power law (Pareto law). Such a discrepancy between a Normal distribution of inputs, with a typical scale, and the scale invariant distribution of outputs, suggests that some hidden ingredient is at work behind the scenes. In this paper, with the help of a very simple agent-based model, we suggest that such an ingredient is just randomness. In particular, we show that, if it is true that some degree of talent is necessary to be successful in life, almost never the most talented people reach the highest peaks of success, being overtaken by mediocre but sensibly luckier individuals. As to our knowledge, this counterintuitive result - although implicitly suggested between the lines in a vast literature - is quantified here for the first time. It sheds new light on the effectiveness of assessing merit on the basis of the reached level of success and underlines the risks of distributing excessive honors or resources to people who, at the end of the day, could have been simply luckier than others. With the help of this model, several policy hypotheses are also addressed and compared to show the most efficient strategies for public funding of research in order to improve meritocracy, diversity and innovation.
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Talent vs Luck:
the role of randomness in success and failure
A. Pluchino
, A. E. Biondo
, A. Rapisarda
The largely dominant meritocratic paradigm of highly competitive Western cultures is
rooted on the belief that success is due mainly, if not exclusively, to personal qualities such as
talent, intelligence, skills, smartness, efforts, willfulness, hard work or risk taking. Sometimes,
we are willing to admit that a certain degree of luck could also play a role in achieving
significant material success. But, as a matter of fact, it is rather common to underestimate
the importance of external forces in individual successful stories. It is very well known
that intelligence (or, more in general, talent and personal qualities) exhibits a Gaussian
distribution among the population, whereas the distribution of wealth - often considered
a proxy of success - follows typically a power law (Pareto law), with a large majority of
poor people and a very small number of billionaires. Such a discrepancy between a Normal
distribution of inputs, with a typical scale (the average talent or intelligence), and the scale
invariant distribution of outputs, suggests that some hidden ingredient is at work behind
the scenes. In this paper, with the help of a very simple agent-based toy model, we suggest
that such an ingredient is just randomness. In particular, we show that, if it is true that
some degree of talent is necessary to be successful in life, almost never the most talented
people reach the highest peaks of success, being overtaken by mediocre but sensibly luckier
individuals. As to our knowledge, this counterintuitive result - although implicitly suggested
between the lines in a vast literature - is quantified here for the first time. It sheds new
light on the effectiveness of assessing merit on the basis of the reached level of success and
underlines the risks of distributing excessive honors or resources to people who, at the end
of the day, could have been simply luckier than others. With the help of this model, several
policy hypotheses are also addressed and compared to show the most efficient strategies for
public funding of research in order to improve meritocracy, diversity and innovation.
Keywords: Success, Talent, Luck, Randomness, Serendipity, Funding strategies.
1 Introduction
The ubiquity of power-law distributions in many physical, biological or socio-economical complex
systems can be seen as a sort of mathematical signature of their strongly correlated dynamic
behavior and their scale invariant topological structure [1, 2, 3, 4]. In socio-economic context,
Department of Physics and Astronomy, University of Catania and INFN Sezione di Catania, Italy; alessan-
Dept. of Economics and Business, Univ. of Catania, Italy;
Department of Physics and Astronomy, University of Catania and INFN Sezione di Catania, Italy; Complexity
Science Hub Vienna;
arXiv:1802.07068v3 [physics.soc-ph] 9 Jul 2018
Advances in Complex Systems (2018) in press
after Pareto’s work [5, 6, 7, 8, 9], it is well known that the wealth distribution follows a power-
law, whose typical long tailed shape reflects the deep existing gap between the rich and the poor
in our society. A very recent report [10] shows that today this gap is far greater than it had been
feared: eight men own the same wealth as the 3.6 billion people constituting the poorest half
of humanity. In the last 20 years, several theoretical models have been developed to derive the
wealth distribution in the context of statistical physics and probability theory, often adopting a
multi-agent perspective with a simple underlying dynamics [11, 12, 13, 14, 15, 16, 17].
Moving along this line, if one considers the individual wealth as a proxy of success, one could
argue that its deeply asymmetric and unequal distribution among people is either a consequence
of their natural differences in talent, skill, competence, intelligence, ability or a measure of their
willfulness, hard work or determination. Such an assumption is, indirectly, at the basis of the so-
called meritocratic paradigm: it affects not only the way our society grants work opportunities,
fame and honors, but also the strategies adopted by Governments in assigning resources and
funds to those who are considered the most deserving individuals.
However, the previous conclusion appears to be in strict contrast with the accepted evidence
that human features and qualities cited above are normally distributed among the population,
i.e. follow a symmetric Gaussian distribution around a given mean. For example, intelligence,
as measured by IQ tests, follows this pattern: average IQ is 100, but nobody has an IQ of 1,000
or 10,000. The same holds for efforts, as measured by hours worked: someone works more hours
than the average and someone less, but nobody works a billion times more hours than anybody
On the other hand, there is nowadays an ever greater evidence about the fundamental role
of chance, luck or, more in general, random factors, in determining successes or failures in our
personal and professional lives. In particular, it has been shown that scientists have the same
chance along their career of publishing their biggest hit [18]; that those with earlier surname
initials are significantly more likely to receive tenure at top departments [19]; that the distribu-
tions of bibliometric indicators collected by a scholar might be the result of chance and noise
related to multiplicative phenomena connected to a publish or perish inflationary mechanism
[20]; that one’s position in an alphabetically sorted list may be important in determining ac-
cess to over-subscribed public services [21]; that middle name initials enhance evaluations of
intellectual performance [22]; that people with easy-to-pronounce names are judged more pos-
itively than those with difficult-to-pronounce names [23]; that individuals with noble-sounding
surnames are found to work more often as managers than as employees [24]; that females with
masculine monikers are more successful in legal careers [25]; that roughly half of the variance
in incomes across persons worldwide is explained only by their country of residence and by the
income distribution within that country [26]; that the probability of becoming a CEO is strongly
influenced by your name or by your month of birth [27, 28, 29]; that the innovative ideas are the
results of a random walk in our brain network [30]; and that even the probability of developing
a cancer, maybe cutting a brilliant career, is mainly due to simple bad luck [31, 32]. Recent
studies on lifetime reproductive success further corroborate these statements showing that, if
trait variation may influence the fate of populations, luck often governs the lives of individuals
[33, 34].
In recent years many authors, among whom the statistician and risk analyst Nassim N.
Taleb [35, 36], the investment strategist Michael Mauboussin [37] and the economist Robert H.
Frank [38], have explored in several successful books the relationship between luck and skill in
financial trading, business, sports, art, music, literature, science and in many other fields. They
reach the conclusion that chance events play a much larger role in life than many people once
imagined. Actually, they do not suggest that success is independent of talent and efforts, since
in highly competitive arenas or ’winner-takes-all’ markets, like those where we live and work
today, people performing well are almost always extremely talented and hard-working. Simply,
they conclude that talent and efforts are not enough: you have to be also in the right place at
the right time. In short: luck also matters, even if its role is almost always underestimated by
successful people. This happens because randomness often plays out in subtle ways, therefore it
is easy to construct narratives that portray success as having been inevitable. Taleb calls this
tendency ”narrative fallacy” [36], while the sociologist Paul Lazarsfeld adopts the terminology
”hindsight bias”. In his recent book ”Everything Is Obvious: Once You Know the Answer”
[39], the sociologist and network science pioneer Duncan J. Watts, suggests that both narrative
fallacy and hindsight bias operate with particular force when people observe unusually successful
outcomes and consider them as the necessary product of hard work and talent, while they mainly
emerge from a complex and interwoven sequence of steps, each depending on precedent ones:
if any of them had been different, an entire career or life trajectory would almost surely differ
too. This argument is also based on the results of a seminal experimental study, performed
some years before by Watts himself in collaboration with other authors [40], where the success
of previously unknown songs in an artificial music market was shown not to be correlated with
the quality of the song itself. And this clearly makes very difficult any kind of prediction, as
also shown in another more recent study [41].
In this paper, by adopting an agent-based statistical approach, we try to realistically quantify
the role of luck and talent in successful careers. In section 2, building on a minimal number of
assumptions, i.e. a Gaussian distribution of talent [42] and a multiplicative dynamics for both
successes and failures [43], we present a simple model, that we call ”Talent vs Luck” (TvL) model,
which mimics the evolution of careers of a group of people over a working period of 40 years. The
model shows that, actually, randomness plays a fundamental role in selecting the most successful
individuals. It is true that, as one could expect, talented people are more likely to become rich,
famous or important during their life with respect to poorly equipped ones. But - and this is a
less intuitive rationale - ordinary people with an average level of talent are statistically destined
to be successful (i.e. to be placed along the tail of some power law distribution of success) much
more than the most talented ones, provided that they are more blessed by fortune along their
life. This fact is commonly experienced, as pointed in refs.[35, 36, 38], but, to our knowledge, it
is modeled and quantified here for the first time.
The success of the averagely-talented people strongly challenges the ”meritocratic” paradigm
and all those strategies and mechanisms, which give more rewards, opportunities, honors, fame
and resources to people considered the best in their field [44, 45]. The point is that, in the
vast majority of cases, all evaluations of someone’s talent are carried out a posteriori, just by
looking at his/her performances - or at reached results - in some specific area of our society like
sport, business, finance, art, science, etc. This kind of misleading evaluation ends up switching
cause and effect, rating as the most talented people those who are, simply, the luckiest ones
[46, 47]. In line with this perspective, in previous works, it was advanced a warning against
such a kind of ”naive meritocracy” and it was shown the effectiveness of alternative strategies
based on random choices in many different contexts, such as management, politics and finance
[48, 49, 50, 51, 52, 53, 54, 55]. In section 3 we provide an application of our approach and sketch
a comparison of possible public funds attribution schemes in the scientific research context. We
study the effects of several distributive strategies, among which the ”naively” meritocratic one,
Figure 1: An example of initial setup for our simulations. All the simulations presented in this paper
were realized within the NetLogo agent-based model environment [56]. N= 1000 individuals (agents),
with different degrees of talent (intelligence, skills, etc.), are randomly located in their fixed positions
within a square world of 201x201 patches with periodic boundary conditions. During each simulation,
which covers several dozens of years, they are exposed to a certain number NEof lucky (green circles)
and unlucky (red circles) events, which move across the world following random trajectories (random
walks). In this example NE= 500.
with the aim of exploring new ways to increase both the minimum level of success of the most
talented people in a community and the resulting efficiency of the public expenditure. We also
explore, in general, how opportunities offered by the environment, as the education and income
levels (i.e., external factors depending on the country and the social context where individuals
come from), do matter in increasing probability of success. Final conclusive remarks close the
2 The Model
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 Nindividuals, with talent Ti(intelligence, skills, ability, etc.) normally dis-
tributed in the interval [0,1] around a given mean mTwith a standard deviation σT, randomly
placed in fixed positions within a square world (see Figure 1) with periodic boundary conditions
(i.e. with a toroidal topology) and surrounded by a certain number NEof ”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
Figure 2: Normal distribution of talent among the the population (with mean mT= 0.6, indicated
by a dashed vertical line, and standard deviation σT= 0.1 - the values mT±σTare indicated by two
dotted vertical lines). This distribution is truncated in the interval [0,1] and does not change during the
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 NEare uniformly
distributed, but of course such a distribution would be perfectly uniform only for NE→ ∞. In
our simulations, typically will be NEN/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 different individuals to different amount of lucky or unlucky events during their
life, regardless of their own talent.
For a single simulation run, a working life period Pof 40 years (from the age of twenty to
the age of sixty) is considered, with a time step δtequal to six months. At the beginning of the
simulation, all agents are endowed with the same amount Ci=C(0) i= 1, ..., N of capital,
representing their starting level of success/wealth. This choice has the evident purpose of not
offering any initial advantage to anyone. While the agents’ talent is time-independent, agents’
capital changes in time. During the time evolution of the model, i.e. during the considered
agents’ life period, all event-points move randomly around the world and, in doing so, they
possibly intersect the position of some agent. More in detail, at each time each event-point
covers a distance of 2 patches in a random direction. We say that an intersection does occur
for an individual when an event-point is present inside a circle of radius 1 patch centered on
the agent (the event-point does not disappear after the intersection). Depending on such an
occurrence, at a given time step t(i.e. every six months), there are three different possible
actions for a given agent Ak:
1. No event-point intercepts the position of agent Ak: this means that no relevant facts have
happened during the last six months; agent Akdoes not perform any action.
2. A lucky event intercepts the position of agent Ak: this means that a lucky event has
occurred during the last six month (notice that, in line with ref.[30], also the production
of an innovative idea is here considered as a lucky event occurring in the agent’s brain);
as a consequence, agent Akdoubles her capital/success with a probability proportional to
her talent Tk. It will be Ck(t)=2Ck(t1) only if rand[0,1] < Tk, i.e. if the agent is
smart enough to profit from his/her luck.
3. An unlucky event intercepts the position of agent Ak: this means that an unlucky event has
occurred during the last six month; as a consequence, agent Akhalves her capital/success,
i.e. Ck(t) = Ck(t1)/2.
The previous agents’ rules (including the choice of dividing by a factor of 2 the initial capital
in case of unlucky events and doubling it in case of lucky ones, proportionally to the agent’s
talent), are intentionally simple and can be considered widely shareable, since they are based
on the common sense evidence that success, in everyone life, has the property to both grow or
decrease very rapidly. Furthermore, these rules gives a significant advantage to highly talented
people, since they can make much better use of the opportunities offered by luck (including
the ability to exploit a good idea born in their brains). On the other hand, a car accident or
a sudden desease, for example, are always unlucky events where talent plays no role. In this
respect, we could more effectively generalise the definition of ”talent” by identifying it with ”any
personal quality which enhances the chance to grab an opportunity”. In other words, by the
term ”talent” we broadly mean intelligence, skill, smartness, stubbornness, determination, hard
work, risk taking and so on. What we will see in the following is that the advantage of having a
great talent is a necessary, but not a sufficient, condition to reach a very high degree of success.
2.1 Single run results
In this subsection we present the results of a typical single run simulation. Actually, such results
are very robust so, as we will show later, they can be considered largely representative of the
general framework emerging from our model.
Let us consider N= 1000 agents, with a starting equal amount of capital C(0) = 10 (in
dimensionless units) and with a fixed talent Ti[0,1], which follows a normal distribution
with mean mT= 0.6 and standard deviation σT= 0.1 (see Figure 2). As previously written,
the simulation spans a realistic time period of P= 40 years, evolving through time steps of
six months each, for a total of I= 80 iterations. In this simulation we consider NE= 500
event-points, with a percentage pL= 50% of lucky events.
At the end of the simulation, as shown in panel (a) of Figure 3, we find that the simple
dynamical rules of the model are able to produce an unequal distribution of capital/success,
with a large amount of poor (unsuccessful) agents and a small number of very rich (successful)
ones. Plotting the same distribution in log-log scale in panel (b) of the same Figure, a Pareto-
like power-law distribution is observed, whose tail is well fitted by the function y(C)C1.27.
Therefore, despite the normal distribution of talent, the TvL model seems able to capture the
first important feature observed in the comparison with real data: the deep existing gap between
rich and poor and its scale invariant nature. In particular, in our simulation, only 4 individuals
have more than 500 units of capital and the 20 most successful individuals hold the 44% of
the total amount of capital, while almost half of the population stay under 10 units. Globally,
the Pareto’s ”80-20” rule is respected, since the 80% of the population owns only the 20% of
the total capital, while the remaining 20% owns the 80% of the same capital. Although this
disparity surely seems unfair, it would be to some extent acceptable if the most successful people
Figure 3: Final distribution of capital/success among the population, both in log-lin (a) and in log-log
(b) scale. Despite the normal distribution of talent, the tail of distribution of success - as visible in panel
(b) - can be well fitted with a power-law curve with slope 1.27. We also verified that the capital/success
distribution follows the Pareto’s ”80-20” rule, since 20% of the population owns 80% of the total capital,
while the remaining 80% owns the 20% of the capital.
were the most talented one, so deserving to have accumulated more capital/success with respect
to the others. But are things really like that?
In panels (a) and (b) of Figure 4, respectively, talent is plotted as function of the final capi-
tal/success and vice-versa (notice that, in panel (a), the capital/success takes only discontinuous
values: this is due to the choice of having used an integer initial capital equal for all the agents).
Looking at both panels, it is evident that, on one hand, the most successful individuals are not
the most talented ones and, on the other hand, the most talented individuals are not the most
successful ones. In particular, the most successful individual, with Cmax = 2560, has a talent
T= 0.61, only slightly greater than the mean value mT= 0.6, while the most talented one
(Tmax = 0.89) has a capital/success lower than 1 unit (C= 0.625).
As we will see more in detail in the next subsection, such a result is not a special case, but
it is rather the rule for this kind of system: the maximum success never coincides with the
maximum talent, and vice-versa. Moreover, such a misalignment between success and talent
is disproportionate and highly nonlinear. In fact, the average capital of all people with talent
T > T is C20: in other words, the capital/success of the most successful individual, who
is moderately gifted, is 128 times greater than the average capital/success of people who are
more talented than him. We can conclude that, if there is not an exceptional talent behind the
enormous success of some people, another factor is probably at work. Our simulation clearly
Figure 4: In panel (a) talent is plotted as function of capital/success (in logarithmic scale for a better
visualization): it is evident that the most successful individuals are not the most talented ones. In panel
(b), vice-versa, capital/success is plotted as function of talent: here, it can be further appreciated the
fact that the most successful agent, with Cmax = 2560, has a talent only slightly greater than the mean
value mT= 0.6, while the most talented one has a capital/success lower than C= 1 unit, much less of
the initial capital C(0). See text for further details.
shows that such a factor is just pure luck.
In Figure 5 the number of lucky and unlucky events occurred to all people during their
working lives is reported as a function of their final capital/success. Looking at panel (a), it
is evident that the most successful individuals are also the luckiest ones (notice that it in this
panel are reported all the lucky events occurred to the agents and not just those that they took
advantage of, proportionally to their talent). On the contrary, looking at panel (b), it results
that the less successful individuals are also the unluckiest ones. In other words, although there
is an absence of correlation between success and talent coming out of the simulations, there is
also a very strong correlation between success and luck. Analyzing the details of the frequency
distributions of the number of lucky or unlucky events occurred to individuals, we found - as
shown in panels (c) and (d) - that both of them are exponential, with exponents 0.64 and 0.48,
and averages 1.35 and 1.66, respectively, and that the maximum numbers of lucky or unlucky
events occurred were, respectively, 10 and 15. Moreover about 16% of people had a ”neutral” life,
without lucky or unlucky events at all, while about 40% of individuals exclusively experienced
only one type of events (lucky or unlucky).
It is also interesting to look at the time evolution of the success/capital of both the most
successful individual and the less successful one, compared with the corresponding sequence of
Figure 5: Total number of lucky events (a) or unlucky events (b) as function of the capital/success of the
agents. The plot shows the existence of a strong correlation between success and luck: the most successful
individuals are also the luckiest ones, while the less successful are also the unluckiest ones. Again, having
used an initial capital equal for all the agents, it follows that several events are grouped in discontinuous
values of the capital/success. In panels (c) and (d) the frequency distributions of, respectively, the number
of lucky and unlucky events are reported in log-linear scale. As visible, both the distributions can be well
fitted by exponential distributions with similar negative exponents.
lucky or unlucky events occurred during the 40 years (80 time steps, one every 6 months) of
their working life. This can be observed, respectively, in the left and the right part of Figure 6.
Differently from the panel (a) of Figure 5, in the bottom panels of this figure only lucky events
that agents have taken advantage of thanks to their talent, are shown.
In panels (a), concerning the moderately talented but most successful individual, it clearly
appears that, after about a first half of his working life with a low occurrence of lucky events
(bottom panel), and then with a low level of capital (top panel), a sudden concentration of
favorable events between 30 and 40 time steps (i.e. just before the age of 40 of the agent)
produces a rapid increase in capital, which becomes exponential in the last 10 time steps (i.e.
the last 5 years of the agent’s career), going from C= 320 to Cmax = 2560.
On the other hand, looking at (top and bottom) panels (b), concerning the less successful
individual, it is evident that a particularly unlucky second half of his working life, with a dozen
of unfavorable events, progressively reduces the capital/success bringing it at its final value of
C= 0.00061. It is interesting to notice that this poor agent had, however, a talent T= 0.74
which was greater than that of the most successful agent. Clearly, good luck made the difference.
And, if it is true that the most successful agent has had the merit of taking advantage of all the
opportunities presented to him (in spite of his average talent), it is also true that if your life is
as unlucky and poor of opportunities as that of the other agent, even a great talent becomes
useless against the fury of misfortune.
All the results shown in this subsection for a single simulation run1are very robust and, as
1A demo version of the NetLogo code of the TvL model used for the single run simulations can be found on
the Open ABM repository -
Figure 6: (a) Time evolution of success/capital for the most successful individual and (b) for the less
successful one, compared with the corresponding sequences of lucky or unlucky events occurred during
their working lives (80 semesters, i.e. 40 years). The time occurrence of these events is indicated, in the
bottom panels, with upwards or downwards spikes.
we will see in the next subsection, they persist, with small differences, if we repeat many times
the simulations starting with the same talent distribution, but with a different random positions
of the individuals.
2.2 Multiple runs results
In this subsection we present the global results of a simulation averaging over 100 runs, each
starting with different random initial conditions. The values of the control parameters are the
same of those used in the previous subsection: N= 1000 individuals, mT= 0.6 and σT= 0.1 for
the normal talent distribution, I= 80 iteration (each one representing δt= 6 months of working
life), C(0) = 10 units of initial capital, NE= 500 event-points and a percentage pL= 50% of
lucky events.
In panel (a) of Figure 7, the global distribution of the final capital/success for all the agents
collected over the 100 runs is shown in log-log scale and it is well fitted by a power law curve with
slope 1.33. The scale invariant behavior of capital and the consequent strong inequality among
individuals, together with the Pareto’s ”80-20” rule observed in the single run simulation, are
therefore conserved also in the case of multiple runs. Indeed, the gap between rich (successful)
and poor (unsuccessful) agents has even increased, since the capital of the most successful people
surpass now the 40000 units.
This last result can be better appreciated looking at panel (b), where the final capital Cmax
Figure 7: Panel (a): Distribution of the final capital/success calculated over 100 runs for a population
with different random initial conditions. The distribution can be well fitted with a power-law curve with
a slope 1.33. Panel (b): The final capital Cmax of the most successful individual in each of the 100 runs
is reported as function of their talent. People with a medium-high talent result to be, on average, more
successful than people with low or medium-low talent, but very often the most successful individual is a
moderately gifted agent and only rarely the most talented one. The mTvalue, together with the values
mT±σT, are also reported as vertical dashed and dot lines respectively.
Figure 8: (a) Talent distribution of the most successful individuals (best performers) in each of the 100
runs. (b) Probability distribution function of talent of the most successful individuals calculated over
10000 runs: it is well fitted by a normal distribution with mean 0.667 and standard deviation 0.09 (solid
line). The mean mT= 0.6 of the original normal distribution of talent in the population is reported for
comparison as a vertical dashed line in both panels.
of the most successful individuals only, i.e. of the best performers for each one of the 100 runs,
is reported as function of their talent. The best score was realized by an agent with a talent
Tbest = 0.6048, practically coinciding with the mean of the talent distribution (mT= 0.6), who
reached a peak of capital Cbest = 40960. On the other hand, the most talented among the most
successful individuals, with a talent Tmax = 0.91, accumulated a capital Cmax = 2560, equal to
only 6% of Cbest.
To address this point in more detail, in Figure 8 (a) we plot the talent distribution of the
best performers calculated over 100 runs. The distribution seems to be shifted to the right of the
talent axis, with a mean value Tav = 0.66 > mT: this confirms, on one hand, that a medium-high
talent is often necessary to reach a great success; but, on the other hand, it also indicates that
it is almost never sufficient, since agents with the highest talent (e.g. with T > mT+ 2σT, i.e.
with T > 0.8) result to be the best performers only in 3% of cases, and their capital/success
never exceeds the 13% of Cbest.
In Figure 8 (b) the same distribution (normalized to unitary area in order to obtain a PDF)
is calculated over 10000 runs, in order to appreciate its true shape: it appears to be well fitted
by a Gaussian G(T) with average Tav = 0.667 and standard deviation 0.09 (solid line). This
definitely confirms that the talent distribution of the best performers is shifted to the right of
the talent axis with respect to the original distribution of talent. More precisely, this means
that the conditional probability P(Cmax|T) = G(T)dT to find among the best performers an
individual with talent in the interval [T , T +dT ] increases with the talent T, reaches a maximum
around a medium-high talent Tav = 0.66, then rapidly decreases for higher values of talent. In
other words, the probability to find a moderately talented individual at the top of success is
higher than that of finding there a very talented one. Notice that, in a ideal world in which
talent were the main cause of success, one expects P(Cmax|T) to be an increasing function of T.
Therefore, we can conclude that the observed Gaussian shape of P(Cmax|T) is the proof that
Figure 9: Time evolution of success/capital for the most successful (but moderately gifted) individual
over the 100 simulation runs, compared with the corresponding unusual sequence of lucky events occurred
during her working life.
luck matters more than talent in reaching very high levels of success.
It is also interesting to compare the average capital/success Cmt 63, over 100 runs, of
the most talented people and the corresponding average capital/success Cat 33 of people
with talent very close to the mean mT. We found in both cases quite small values (although
greater than the initial capital C(0) = 10), but the fact that Cmt > Cat indicates that, even
if the probability to find a moderately talented individual at the top of success is higher than
that of finding there a very talented one, the most talented individuals of each run have, on
average, more success than moderately gifted people. On the other hand, looking at the average
percentage, over the 100 runs, of individuals with talent T > 0.7 (i.e. greater than one standard
deviation from the average) and with a final success/capital Cend >10, calculated with respect
to all the agents with talent T > 0.7 (who are, on average for each run, 160), we found
that this percentage is equal to 32%: this means that the aggregate performance of the most
talented people in our population remains, on average, relatively small since only one third of
them reaches a final capital greater than the initial one.
In any case, it is a fact that the absolute best performer over the 100 simulation runs is
an agent with talent Tbest = 0.6, perfectly aligned with the average, but with a final success
Cbest = 40960 which is 650 times greater than Cmt and more than 4000 times greater than the
success Cend <10 of 2/3 of the most talented people. This occurs just because, at the end of the
story, she was just luckier than the others. Indeed, very lucky, as it is shown in Figure 9, where
the increase of her capital/success during her working life is shown, together with the impressive
sequence of lucky (and only lucky) events of which, despite the lack of particular talent, she was
able to take advantage of during her career.
Summarizing, what has been found up to now is that, in spite of its simplicity, the TvL model
seems able to account for many of the features characterizing, as discussed in the introduction,
the largely unequal distribution of richness and success in our society, in evident contrast with
the Gaussian distribution of talent among human beings. At the same time, the model shows, in
quantitative terms, that a great talent is not sufficient to guarantee a successful career and that,
instead, less talented people are very often able to reach the top of success - another ”stylised
fact” frequently observed real life [35, 36, 38].
The key point, which intuitively explains how it may happen that moderately gifted indi-
viduals achieve (so often) far greater honors and success than much more talented ones, is the
hidden and often underestimated role of luck, as resulting from our simulations. But to under-
stand the real meaning of our findings it is important to distinguish the macro from the micro
point of view.
In fact, from the micro point of view, following the dynamical rules of the TvL model, a
talented individual has a greater a priori probability to reach a high level of success than a
moderately gifted one, since she has a greater ability to grasp any opportunity will come. Of
course, luck has to help her in yielding those opportunities. Therefore, from the point of view of
a single individual, we should therefore conclude that, being impossible (by definition) to control
the occurrence of lucky events, the best strategy to increase the probability of success (at any
talent level) is to broaden the personal activity, the production of ideas, the communication
with other people, seeking for diversity and mutual enrichment. In other words, to be an open-
minded person, ready to be in contact with others, exposes to the highest probability of lucky
events (to be exploited by means of the personal talent).
On the other hand, from the macro point of view of the entire society, the probability to find
moderately gifted individuals at the top levels of success is greater than that of finding there
very talented ones, because moderately gifted people are much more numerous and, with the
help of luck, have - globally - a statistical advantage to reach a great success, in spite of their
lower individual a priori probability.
In the next section we will address such a macro point of view, by exploring the possibilities
offered by our model to investigate in detail new and more efficient strategies and policies to
improve the average performance of the most talented people in a population, implementing more
efficient ways of distributing prizes and resources. In fact, being the most talented individuals
the engine of progress and innovation in our society, we expect that any policy able to improve
their level of success will have a beneficial effect on the collectivity.
3 Effective strategies to counterbalance luck
The results presented in the previous section are strongly consistent with largely documented
empirical evidences, discussed in the introduction, which firmly question the naively meritocratic
assumption claiming that the natural differences in talent, skill, competence, intelligence, hard
work or determination are the only causes of success. As we have shown, luck also matters and it
can play a very important role. The interpretative point is that, being individual qualities diffi-
cult to be measured (in many cases hardly defined in rigorous terms), the meritocratic strategies
used to assign honors, funds or rewards are often based on individual performances, valued in
terms of personal wealth or success. Eventually, such strategies exert a further reinforcing action
and pump up the wealth/success of the luckiest individuals through a positive feedback mech-
anism, which resembles the famous ”rich get richer” process (also known as ”Matthew effect”
[57, 58, 59]), with an unfair final result.
Let us consider, for instance, a publicly-funded research granting council with a fixed amount
of money at its disposal. In order to increase the average impact of research, is it more effective
to give large grants to a few apparently excellent researchers, or small grants to many more
apparently ordinary researchers? A recent study [44], based on the analysis of four indices
of scientific impact involving publications, found that impact is positively, but only weakly,
related to funding. In particular, impact per dollar was lower for large grant-holders and the
impact of researchers who received increases in funding did not increase in a significant way.
The authors of the study conclude that scientific impact (as reflected by publications) is only
weakly limited by funding and suggest that funding strategies targeting diversification of ideas,
rather than ”excellence”, are likely to be more productive. A more recent contribution [60]
showed that, both in terms of the quantity of papers produced and of their scientific impact, the
concentration of research funding generally produces diminishing marginal returns and also that
the most funded researchers do not stand out in terms of output and scientific impact. Actually,
such conclusions should not be a surprise in the light of the other recent finding [18] that impact,
as measured by influential publications, is randomly distributed within a scientist’s temporal
sequence of publications. In other words, if luck matters, and if it matters more than we are
willing to admit, it is not strange that meritocratic strategies reveal less effective than expected,
in particular if we try to evaluate merit ex-post. In previous studies [48, 49, 50, 51, 52, 53, 54, 55],
there was already a warning against this sort of ”naive meritocracy”, showing the effectiveness of
alternative strategies based on random choices in management, politics and finance. Consistently
with such a perspective, the TvL model shows how the minimum level of success of the most
talented people can be increased, in a world where luck is important and serendipity is often
the cause of important discoveries.
3.1 Serendipity, innovation and efficient funding strategies
The term ”serendipity” is commonly used in the literature to refer to the historical evidence
that very often researchers make unexpected and beneficial discoveries by chance, while they
are looking for something else [61, 62]. There is a long anecdotal list of discoveries made just
by lucky opportunities: from penicillin by Alexander Fleming to radioactivity by Marie Curie,
from cosmic microwave background radiation by radio astronomers Arno Penzias and Robert
Woodrow Wilson to the graphene by Andre Geim and Kostya Novoselov. Just to give a very
recent example, a network of fluid-filled channels in the human body, that may be a previously-
unknown organ and that seems to help transport cancer cells around the body, was discovered
by chance, from routine endoscopies [63].Therefore, many people think that curiosity-driven
research should always be funded, because nobody can really know or predict where it can lead
to [64].
Is it possible to quantify the role of serendipity? Which are the most efficient ways to
stimulate serendipity? Serendipity can take on many forms, and it is difficult to constrain and
quantify. That is why, so far, academic research has focused on serendipity in science mainly as a
philosophical idea. But things are changing. The European Research Council has recently given
to the biochemist Ohid Yaqub a 1.7 million US dollars grant to quantify the role of serendipity
in science [65]. Yaqub found that it is possible to classify serendipity into four basic types [66]
and that there may be important factors affecting its occurrence. His conclusions seem to agree
with ideas developed in earlier works [67, 68, 69, 70, 71, 72] which argues that the commonly
adopted - apparently meritocratic - strategies, which pursuit excellence and drive out variety,
seem destined to be loosing and inefficient. The reason is that they cut out a priori researches
that initially appear less promising but that, thanks also to serendipity, could be extremely
innovative a posteriori.
From this perspective, we want to use the TvL model, which naturally incorporates luck
(and therefore also serendipity) as a quantitative tool for policy, in order to explore, in this
subsection, the effectiveness of different funding scenarios. In particular, in contexts where,
as above discussed, averagely-talented-but-lucky people are often more successful than more-
gifted-but-unlucky individuals, it is important to evaluate the efficiency of funding strategies in
preserving a minimum level of success also for the most talented people, who are expected to
produce the most progressive and innovative ideas.
Starting from the same parameters setup used in subsection 2.2, i.e.N= 1000, mT= 0.6,
σT= 0.1, I= 80, δt= 6, C(0) = 10, NE= 500, pL= 50% and 100 simulation runs, let
us imagine that a given total funding capital FTis periodically distributed among individuals
following different criteria. For example, funds could be assigned:
1. in equal measure to all (egalitarian criterion), in order to foster research diversification;
2. only to a given percentage of the most successful (”best”) individuals (elitarian criterion),
which has been previously referred to ”naively” meritocratic, for it distributes funds to
people according to their past performance;
3. by distributing a ”premium” to a given percentage of the most successful individuals and
the remaining amount in smaller equal parts to all the others (mixed criterion);
4. only to a given percentage individuals, randomly selected (selective random criterion);
We realistically assume that the total capital FTwill be distributed every 5 years, during the
40 years spanned by each simulation run, so that FT/8 units of capital will be allocated from
time to time. Thanks to the periodic injection of these funds, we intend to maintain a minimum
level of resources for the most talented agents. Therefore, a good indicator, for the effectiveness
of the adopted funding strategy, could be the percentage PT, averaged over the 100 simulation
runs, of individuals with talent T > mT+σTwhose final success/capital is greater than the
initial one, i.e. Cend > C(0).
This percentage has already been calculated, in the multiple runs simulation presented in
section 2.2. There, we have shown that, in absence of funding, the best performance was scored
by very lucky agents with a talent close to the mean, while the capital/success of the most
talented people always remained very low. In particular, only a percentage PT032% of the
total number of agents with T > 0.7 reached, at the end of the simulation, a capital/success
greater then the initial one. Hence, in order to compare the efficiency of different funding
strategies, the increment in the average percentage PTof talented people which, during their
career, increase their initial capital/success should be calculated with respect to PT0. Let us
define this increment as P
T=PTPT0. The latter quantity is a very robust indicator: we have
checked that repeating the set of 100 simulations, the variation in the value of P
Tremains under
2%. Finally, if one considers the ratio between P
Tand the total capital FTdistributed among
Figure 10: Funding strategies Table. The outcomes of the normalized efficiency index Enor m are reported
(2nd column) in decreasing order, from top to bottom, for several funding distribution strategies with
different targets (1st column). The corresponding values of both the percentage PTof successful talented
people and its net increase P
Twith respect to the ”no funding” case, averaged over the 100 simulation
runs, are also reported in the third and fourth columns respectively. Finally, the total capital FTinvested
in each run, is visible in the last column.
all the agents during the 40 years, it is possible to obtain an efficiency index E, which quantifies
the increment of sufficiently successful talented people per unit of invested capital, defined as
In the table shown in Figure 10, we report the efficiency index (2nd column) obtained for
several funding distribution strategies, each one with a different funding target (1st column),
together with the corresponding values of PT(3rd column) and P
T(4th column). The total
capital FTinvested in each run is also reported in the last column. The efficiency index E
has been normalized to its maximum value Emax and the various records (rows) have been
ordered for decreasing values of Enorm =E/Emax . For the no funding case, by definition,
Enorm = 0. The same scores for Enorm are also reported in the form of a histogram in Figure
11, as a function of the adopted funding strategies. Thanks to the statistical robustness of PT,
which shows fluctuations smaller than 2%, the results reported for the efficiency index Enorm
are particularly stable.
Looking at the table and at the relative histogram of Figure 11, it is evident that, if the
goal is to reward the most talented persons (thus increasing their final level of success), it is
much more convenient to distribute periodically (even small) equal amounts of capital to all
Figure 11: Normalized Efficiency index for several funding strategies. The values of the normalized
efficiency index Enorm are reported as function of the different funding strategies. The figure shows that
for increasing the success of a larger number of talented people with Cend > C(0), it is much more efficient
to give a small amount of funds to many individuals instead of giving funds in other more selective ways.
individuals rather than to give a greater capital only to a small percentage of them, selected
through their level of success - already reached - at the moment of the distribution.
On one hand, the histogram shows that the ”egalitarian” criterion, which assigns 1 unit of
capital every 5 years to all the individuals is the most efficient way to distribute funds, being
Enorm = 1 (i.e. E=Emax ): with a relatively small investment FTof 8000 units, it is possible
to double the percentage of successful talented people with respect to the ”no funding” case,
bringing it from PT0= 32.05% to PT= 69.48%, with a net increase P
T= 37.43%. Considering
an increase of the total invested capital (for example, setting the egalitarian quotas to 2 or 5
units), this strategy also ensures a further increment in the final percentage of successful talented
people PT(from 69.48% to 84.02% and to 94.40%), even if the normalized efficiency progressively
decreases from Enorm = 1 to Enor m = 0.74 and to Enorm = 0.37.
On the other hand, the ”elitarian” strategies which assign every 5 years more funds (5, 10,
15 or 20 units) only to the best 50%, 25% or even 10% of the already successful individuals, are
all at the bottom of the ranking, with Enorm <0.25: in all of these cases, the net increase P
the final number of successful talented people with respect to the ”no funding” case remains very
small (in almost all the cases smaller than 20%), often against a much larger invested capital if
compared to that of the egalitarian strategy. These results do reinforce the thesis that this kind
of approach is only apparently - i.e. naively - meritocratic.
It is worth noticing that the adoption of a ”mixed” criterion, i.e. assigning a ”meritocratic”
funding share to a certain percentage of the most successful individuals, for instance 25%, and
distributing the remaining funds in equal measure to the rest of people, gives back better scores
for the efficiency index values with respect to the ”naively meritocratic” approach. However,
the performance of this strategy is not able to overtake the ”egalitarian” criterion. As it clearly
Figure 12: Funding strategies Table with fixed funds. The outcomes of the normalized efficiency index
Enorm are reported again in decreasing order, from top to bottom, for several funding distribution
strategies with different targets (1st column). At variance with Fig. 10, now the total capital invested in
each run was fixed to FT= 80000. The egalitarian strategy is, again, at the top of the ranking.
appears - for example - by the comparison between the sixth and the fourth rows of the funding
table, in spite of the same overall investment of 16000 units, the value of PTobtained with
the mixed criterion stays well below the one obtained with the egalitarian approach (70.83%
against 84.02%), as also confirmed by the values of the corresponding efficiency index Enorm
(0.55 against 0.74).
If one considers psychological factors (not modeled in this study), a mixed strategy could
be revalued with respect to the egalitarian one. Indeed, the premium reward - assigned to
the more successful individuals - could induce all agents towards a greater commitment, while
the equally distributed part would play a twofold role: at the individual level, it would act
in fostering variety and providing unlucky talented people with new chances to express their
potential, while feeding serendipity at the aggregate level, thus contributing to the progress of
research and of the whole society.
Looking again at the funding strategy table, it is also worthwhile to stress the surprising high
efficiency of the random strategies, which occupy two out of the three best scores in the general
ranking. It results that, for example, a periodic reward of 5 units for only the 10% of randomly
selected individuals, with a total investment of just 4000 units, gives a net increase P
T= 17,78%,
which is greater than almost all those obtained with the elitarian strategies. Furthermore,
increasing to 25% the percentage of randomly funded people and doubling the overall investment
(bringing it to 10000 units), the net increase P
T= 35.95% becomes comparable to that obtained
with the best egalitarian strategy, first in the efficiency ranking. It is striking to notice that this
latter score for P
Tis approximately four times grater than the value (P
T= 9.03%) obtained with
the elitarian approach (see 12th row in the table), distributing exactly the same capital (10000
units) to exactly the same number of individuals (25% of the total). The latter is a further
confirmation that, in complex social and economical contexts where chance plays a relevant
role, the efficiency of alternative strategies based on random choices can easily overtake that
of standard strategies based on the ”naively meritocratic” approach. Such a counterintuitive
phenomenon, already observed in management, politics and finance ([48, 49, 50, 51, 52, 53, 54,
55]), finds therefore new evidence also in the research funding context.
To further corroborate these findings, in Figure 12, the results of another set of simulations
are presented. At variance with the previous simulations, the total capital invested in each one
of the 100 runs is now fixed to FT= 80000, so that FT/8 = 10000 units are distributed every
5 years among the agents following the main funding strategies already considered. Looking at
the table, the egalitarian strategy results again the most efficient in rewarding the most talented
people, with a percentage PTclose to 100%, immediately followed by the random strategy (with
50% of randomly funded individuals) and by the mixed one, with half of the capital distributed to
the 25% of the most successful individuals and the other half in equal measure to the remaining
people. On the contrary, all the elitarian strategies are placed again at the bottom of the ranking,
thus further confirming the inefficiency of the ”naively meritocratic” approach in rewarding real
The results of the TvL model simulations presented in this subsection, have focused on the
importance of external factors (as, indeed, efficient funding policies) in increasing the opportu-
nities of success for the most talented individuals, too often penalized by unlucky events. In the
next subsection we investigate to what extent new opportunities can be originated by changes
in the environment as for example the level of education or other stimuli received by the social
context where people live or come from.
3.2 The importance of the environment
First, let us estimate the role of the average level of education among the population. Within the
TvL model, the latter could be obtained by changing the parameters of the normal distribution
of talent. Actually, assuming that talent and skills of individuals, if stimulated, could be more
effective in exploiting new opportunities, an increase in either the mean mTor the standard
deviation σTof the talent distribution could be interpreted as the effect of policies targeted,
respectively, either at raising the average level of education or at reinforcing the training of the
most gifted people.
In the two panels of Figure 13 we report the final capital/success accumulated by the best
performers in each of the 100 runs, as function of their talent. The parameters setup is the same
than in subsection 2.2 (N= 1000, I= 80, δt= 6, C(0) = 10, NE= 500 and pL= 50%) but
with different moments for the talent distributions. In particular, in panel (a) we left unchanged
mT= 0.6 but increased σT= 0.2, while in panel (b) we made the opposite, leaving σT= 0.1
but increasing mT= 0.7. In both cases, a shift on the right of the maximum success peaks can
be appreciated, but with different details.
Actually, it results that increasing σTwithout changing mT, as shown in panel (a), enhances
the chances for more talented people to get a very high success: the best performer is, now, a very
talented agent with T= 0.97, who reaches an incredible level of capital/success Cbest = 655360.
This, on one hand, could be considered positive but, on the other hand, it is an isolated case
and it has, as a counterpart, an increase in the gap between unsuccessful and successful people.
Looking now at panel (b), it results that increasing mTwithout changing σTproduces a best
performer, with Cbest = 327680 and a talent T= 0.8, followed by other two with C= 163840
and, respectively, T= 0.85 and T= 0.92. This means that also in this case the chances for more
talented people to get a very high success are enhanced, while the gap between unsuccessful and
successful people is lower than before.
Finally, in both considered examples, the average value of the capital/success for the most
talented people over the 100 runs is increased with respect to the value Cmt 63 found in
subsection 2.2. In particular, we found Cmt 319 for panel (a) and Cmt 122 for panel (b), but
Figure 13: The final capital of the most successful individuals in each of the 100 runs is reported as
function of their talent for populations with different talent distributions parameters: (a) mT= 0.6
and σT= 0.2 (which represent a training reinforcement for the most gifted people); (b) mT= 0.7 and
σT= 0.1 (which represents an increase in the average level of education). The corresponding mTand
mT±σTvalues are also indicated as, respectively, vertical dashed and dot lines.
these values are quite sensitive to the specific set of simulation runs. A more reliable parameter in
order to quantify the effectiveness of the social policies investigated here is, again, the indicator
PTintroduced in the previous subsection, i.e. the average percentage of individuals with talent
T > mT+σTand with final success/capital Cend >10, over the total number of individuals
with talent T > mT+σT(notice that now, in both the cases considered, mT+σT= 0.8). In
particular, we found PT= 38% for panel (a) and PT= 37.5% for panel (b), with a slight net
increment with respect to the reference value PT0= 32% (obtained for a talent distribution with
mT= 0.6 and σT= 0.1).
Summarizing, our results indicate that strengthening the training of the most gifted people
or increasing the average level of education produce, as one could expect, some beneficial effects
on the social system, since both these policies raise the probability, for talented individuals, to
grasp the opportunities that luck presents to them. On the other hand, the enhancement in
the average percentage of highly talented people who are able to reach a good level of success,
seems to be not particularly remarkable in both the cases analyzed, therefore the result of
the corresponding educational policies appears mainly restricted to the emergence of isolated
extreme successful cases.
Of course, once a given level of education has been fixed, it is quite obvious that the abun-
Figure 14: The final capital of the most successful individuals in each of the 100 runs is reported as
function of their talent, for populations living in environments with a different percentage pLof lucky
events: (a) pL= 80%; (b) pL= 20%. The values of mT= 0.6 and mT±σT, with σT= 0.1 are also
indicated as, respectively, vertical dashed and dot lines.
dance of opportunities offered by the social environment, i.e. by the country where someone
accidentally is born or where someone choose to live, it is another key ingredient able to influence
the global performance of the system.
In Figure 14 we show results analogous to those shown in the previous figure, but for another
set of simulations, with 100 runs each, with the same parameters setup as in subsection 2.2
(N= 1000, mT= 0.6, σT= 0.1, I= 80, C(0) = 10, NE= 500) and with different percentages
pLof lucky events (we remind that, in subsection 2.2., this percentage was set to pL= 50%).
In panels (a) we set pL= 80%, in order to simulate a very stimulating environment, rich
of opportunities, like that of rich and industrialized countries such as the U.S. [26]. On the
other hand, in panels (b), the value pL= 20% reproduces the case of a much less stimulating
environment, with very few opportunities, like for instance that of Third World countries.
As visible in both panels, the final success/capital of the most successful individuals as
function of their talent strongly depend on pL.
When pL= 80%, as in panel (a), several agents with medium-high talent are able to reach
higher levels of success compared to the case pL= 50%, with a peak of Cbest = 163840. On the
other hand, the average value of the capital/success for the most talented individuals, Cmt 149,
is quite high and, what is more important, the same holds for the indicator PT= 62.18% (about
twice with respect to the reference value PT0= 32%), meaning that, as expected, talented people
benefits of the higher percentage of lucky events.
Completely different outcomes are obtained with pL= 20%. Indeed, as visible in panel (b),
the overall level of success is now very low, if compared to that found in the simulations of
subsection 2.2, with a peak value Cbest of only 5120 units: it is a footprint of a reduction in the
social inequalities, which is an expected consequence of the flattening of success opportunities.
According with these results, also the PTindicator reaches a minimal value, with an average
percentage of only 8.75% of talented individuals able to increase their initial level of success.
In conclusion, in this section we have shown that a stimulating environment, rich of op-
portunities, associated to an appropriate strategy for the distribution of funds and resources,
are important factors in exploiting the potential of the most talented people, giving them more
chances of success with respect to the moderately gifted, but luckier, ones. At the macro level,
any policy able to influence those factors and to sustain talented individuals, will have the result
of ensuring collective progress and innovation.
4 Conclusive remarks
In this paper, starting from few very simple and reasonable assumptions, we have presented an
agent-based model which is able to quantify the role of talent and luck in the success of people’s
careers. The simulations show that although talent has a Gaussian distribution among agents,
the resulting distribution of success/capital after a working life of 40 years, follows a power law
which respects the ”80-20” Pareto law for the distribution of wealth found in the real world.
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 - another
stylised fact often reported in the literature. The model shows the importance, very frequently
underestimated, of lucky events in determining the final level of individual success. Since rewards
and resources are usually given to those that have already reached a high level of success,
mistakenly considered as a measure of competence/talent, this result is even a more harmful
disincentive, causing a lack of opportunities for the most talented ones. Our results highlight the
risks of the paradigm that we call ”naive meritocracy”, which fails to give honors and rewards
to the most competent people, because it underestimates the role of randomness among the
determinants of success. In this respect, several different scenarios have been investigated in
order to discuss more efficient strategies, which are able to counterbalance the unpredictable
role of luck and give more opportunities and resources to the most talented ones - a purpose
that should be the main aim of a truly meritocratic approach. Such strategies have also been
shown to be the most beneficial for the entire society, since they tend to increase the diversity
of ideas and perspectives in research, thus fostering also innovation.
We would like to thank Robert H. Frank, Pawel Sobkowicz and Constantino Tsallis for fruitful
discussions and comments.
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... Inner talent, in this view, makes the main difference in career development. However, many recent studies have shown that talent does not vary so widely among people and that its probability distribution is limited and concentrated around a well defined mean value [1][2][3][4]. ...
... For each fencer, P k depends both on his/her talent T k and on the chance parameter L k . In analogy with previous studies [2,3,5,6], we represent talent with a real variable T k 2 (0, 1], randomly extracted from a Gaussian distribution with mean μ = 0.6 and standard deviation σ = 0.1; thus, T k envelopes all the inner qualities of an athlete (intelligence, skills, ability, training, motivation, etc.). Talent should be broadly interpreted as the maximum potential that can be expressed by the athletes throughout the competitions. ...
... During this phase, the bout has its canonical structure, three periods of three minutes each and a maximum score of 15 points, each touch being assigned with the same procedure implemented for the bouts in the Round of pools (Eqs (1) and (2). Again, when the score is tied, an extra minute of priority is given, as described in Fencing rules and implemented in the same way as in Round of pools. ...
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It is a widespread belief that success is mainly due to innate qualities rather than external forces. This is particularly true in sports competitions, where individual talent is usually considered the main, if not the only, ingredient to reach success. In this study, we explore the limits of this belief by quantifying the relative weight of talent and chance in fencing, a combat sport involving a weapon, with the help of both real data and agent-based simulations. Fencing competitions are structured as direct elimination tournaments, where randomness is explicitly present in some rules. We focused on épée, which is one of three disciplines. We collected data on international competition results and annual rankings, in the range 2008–2020, for male and female fencers under 20 years old (Junior category). Then, we built the model calibrated on our dataset and parametrized by just one free variable a , describing the importance of talent—and, consequently, of chance—in competitions ( a = 1 indicates the ideal scenario where only talent matters, a = 0 the complete random one). Our agent-based approach can reproduce the main stylized facts observed in data, at the level of both single tournaments and the entire careers of a given community of épée fencers. We find that simulations approximate very well the data for both Junior Men and Women when talent weights slightly less than chance, i.e. when a is around 0.45. We conclude that the role of chance in fencing is unusually high and it probably represents an extreme case for individual sports. Our findings shed light on the importance of external factors in both athletes’ results in tournaments and throughout their career, making even more unfair the “winner-takes-all” disparities that often occur between the winner and the other classified competitors.
... The specific advantage of this class of models is that they study the rise of bottom-up decentralized decisions, which is particularly helpful to analyze collective problems, specially with reference to complex aggregate contexts. Simulative models can be, then, particularly helpful in studying behavioral attributes, as in previous studies of socio-economic and financial markets analysis, as in Pluchino et al. (2010Pluchino et al. ( , 2018, Biondo et al. (2013), Squazzoni et al. (2014) and Biondo (2019). Dealing with tax evasion, agent-based models can replicate the importance of social norms and auditing, as in Hokamp and Pickhardt (2010), the effect of social networks on the tax compliance, as in Vale (2015), or even the impact of network configurations on the compliance, as in Andrei et al. (2014), and in Gamannossi degl'Innocenti and Rablen 2020. ...
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In this paper we study tax evasion by means of a unified framework, based on a behavioral approach, where each individual decision with respect to tax compliance is driven by either personal evaluations of the available information, correlated to income and the perception of the quality of the public good, and social influences, derived by the known decision of neighbors. Our model relies on individual utility functions and describes the tax-evasion problem by means of a personal evolutionary scheme, in which each citizen dynamically adapts her behavior as a response to changing economic and social factors. We will show basic economic intuitions on the relevance of penalties, imitation, satisfaction and risk aversion by means of an analytical model and its agent-based companion version, in order to analyse different elements influencing tax evasion and their dynamic effects. In particular, it is shown how the tax-evasion probability changes as a function of the risk-aversion and specific focus is dedicated to the role played by non-monetary elements of utility in inducing high levels of tax compliance also at substantially reduced fines.
... Koch and Soto (2016) found that the number of song plays per artist for different users follows a truncated power-law distribution. Much attention has been paid to reveal the factors behind success of cultural products (Pongnumkul and Motohashi 2018;Pluchino et al. 2018;Sornette et al. 2019). The phenomenon of cumulative advantage is one of the leading candidate mechanisms to explain the formation of the power law-like distributions found in, e.g., the sales of music recordings or the popularity of songs/ artists (Haampland 2017). ...
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Online music communities reflect and influence people’s music tastes, providing a detailed digital record of individuals’ behavior. There have been extensive studies on human musical preference; however, the further questions of how the preferences correlate, how intensive and extensive a musical preference can spread in social networks and an individual’s preference is like his/her neighbors, and which factors are most relevant to the diversity of individual music preference are not well explored. In this paper, we analyze the music preference of users in a large online music community in China. We find that there exists obvious correlated musical preference for certain pairs of genres or languages. The preference locality leads to the decay of preference similarity between users and their neighbors with network distance, and the decay is asymmetric for fans and followees in terms of preference probability, preference distribution similarity and list similarity. Users’ musical preference well reflects their ethnic, cultural, and demographic features. We quantify preference diversity, reveal the factors which are significantly correlated with or can predict the diversity, and find that the mean diversity of users’ nearest fans can be the most important predictor. This study reveals the characteristics of users’ music preference, producing new sights on musical tastes, their diversity determinants, and their correlation with surrounding communities and cultures.
... Yet, recent research [8,9] into the origins of success in science and beyond highlights the role of other factors -such as chance. Some [10,11] claim that luck contributes more than the beneficiaries are eager to admit. ...
Full-text available
We consider a version of the D.J.Price's model for the growth of a bibliographic network, where in each iteration a constant number of citations is randomly allocated according to a weighted combination of accidental (uniformly distributed) and preferential (rich-get-richer) rules. Instead of relying on the typical master equation approach, we formulate and solve this problem in terms of the rank-size distribution. We show that, asymptotically, such a process leads to a Pareto-type 2 distribution with an appealingly interpretable parametrisation. We prove that the solution to the Price model expressed in terms of the rank-size distribution coincides with the expected values of order statistics in an independent Paretian sample. We study the bias and the mean squared error of three well-behaving estimators of the underlying model parameters. An empirical analysis of a large repository of academic papers yields a good fit not only in the tail of the distribution (as it is usually the case in the power law-like framework), but also across the whole domain. Interestingly, the estimated models indicate higher degree of preferentially attached citations and smaller share of randomness than previous studies.
... This concept is finding increasing traction in academic literature. In their well-publicized article on the role of randomness in success and failure, Pluchino et al. (2018) state, "It is rather common to underestimate the importance of external forces in individual successful stories" (1850014-1). By cataloging numerous seemingly uncorrelated attributes such as names and birthdates with professional success, they note, "There is nowadays an evergreater evidence about the fundamental role of chance, luck or, more in general, random factors, in determining successes or failures in our personal and professional lives" (1850014-2). ...
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Self-deception in leadership occurs when leaders make mistaken assessments about themselves and act according to those assessments. Results can be unhealthy, if not destructive. To help mitigate this natural tendency, we first seek to characterize the overall life cycle of self-deceived leadership. Second, we offer a model, rooted in Scripture and research, explaining the behavioral root of self-deception. Finally, we present an alternate path toward leadership self-awareness, reinforcing a lifelong commitment to Christian spiritual formation.
... And other researchers obviously see it the same way, as I was able to discover in the course of researching this commentary. Pluchino et al. (2018) demonstrated this in their model experiment "talent versus luck," using 40 fictitious simulation years: The influence of luck (especially on careers) should not be underestimated. As is also apparently the certainly part of getting the "right" client who asks the right questions and allows for original, unconventional scenarios-rather than demanding a "prediction of the lottery numbers." ...
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This commentary refers to the retrospective review by Rowland and Spaniol in Futures and Foresight Science (2021), which provides interesting insights into Kees van der Heijden's character and work 25 years after his famous book Scenarios: The art of strategic conversation was first published. The commentator draws on his own personal experience of Kees' work and book, including a seminar with him at the University of Oxford in 2011, as well as applying the book's fundamentals in his own research and advisory work over the past ten years.
... Crucially, these models prove that future states may differ significantly, even when initial states and developmental mechanisms are identical. In doing so, Pólya's urn models illuminate a third source of developmental differences (Molenaar, Boomsma, & Dolan, 1993) by means of a developmental mechanisms that is often overlooked: chance (Pluchino, Biondo, & Rapisarda, 2018). ...
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Twentieth century theory formation in human intelligence was dominated by factor theories; network theories will dominate the twenty first. Network theories answer a broad call for formal theories in psychological science, provide a strong approach to an idiographic science, and create an opportunity to study the developmental mechanisms of human's cognitive dynamics. Although the current century already delivered two formal stationary network theories of human intelligence—mutualism and wired intelligence—integrating dynamic mechanisms remains a serious challenge. This challenge translates into clear priorities: the identification of robust developmental phenomena, the study of the biological and cognitive mechanisms that drive these phenomena, the integration of these mechanisms into network theories of growth, the integration of network theories from different explanatory levels, and the empirical characterization of the structure of network theories.
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Cumulative advantage–commonly known as the Matthew Effect–influences academic output and careers. Given the challenge and uncertainty of gauging the quality of academic research, gatekeepers often possess incentives to prefer the work of established academics. Such preferences breach scientific norms of universalism and can stifle innovation. This article analyzes repeat authors within academic journals as a possible exemplar of the Matthew Effect. Using publication data for 347 economics journals from 1980–2017, as well as from three major generalist science journals, we analyze how articles written by repeat authors fare vis-à-vis less-experienced authors. Results show that articles written by repeat authors steadily decline in citation impact with each additional repeat authorship. Despite these declines, repeat authors also tend to garner more citations than debut authors. These contrasting results suggest both benefits and drawbacks associated with repeat authorships. Journals appear to respond to feedback from previous publications, as more-cited authors in a journal are more likely to be selected for repeat authorships. Institutional characteristics of journals also affect the likelihood of repeat authorship, as well as citation outcomes. Repeat authorships–particularly in leading academic journals–reflect innovative incentives and professional reward structures, while also influencing the intellectual content of science.
The role of luck on individual success is hard to be investigated empirically. Simplified mathematical models are often used to shed light on the subtle relations between success and luck. Recently, a simple model called “Talent versus Luck” showed that the most successful individual in a population can be just an average talented individual that is subjected to a very fortunate sequence of events. Here, we modify the framework of the TvL model such that in our model the individuals’ success is modelled as an ensemble of one-dimensional random walks. Our model reproduces the original TvL results and, due to the mathematical simplicity, it shows clearly that the original conclusions of the TvL model are the consequence of two factors: first, the normal distribution of talents with low standard deviation, which creates a large number of average talented individuals; second, the low number of steps considered, which allows the observation of large fluctuations. We also show that the results strongly depend on the relative frequency of good and bad luck events, which defines a critical value for the talent: in the long run, the individuals with high talent end up very successful and those with low talent end up ruined. Last, we considered two variations to illustrate applications of the ensemble of random walks model.
Any collection can be ranked. Sports and games are common examples of ranked systems: players and teams are constantly ranked using different methods. The statistical properties of rankings have been studied for almost a century in a variety of fields. More recently, data availability has allowed us to study rank dynamics: how elements of a ranking change in time. Here, we study the rank distributions and rank dynamics of 12 datasets from different sports and games. To study rank dynamics, we consider measures that we have defined previously: rank diversity, change probability, rank entropy, and rank complexity. We also introduce a new measure that we call “system closure” that reflects how many elements enter or leave the rankings in time. We use a random walk model to reproduce the observed rank dynamics, showing that a simple mechanism can generate similar statistical properties as the ones observed in the datasets. Our results show that while rank distributions vary considerably for different rankings, rank dynamics have similar behaviors, independently of the nature and competitiveness of the sport or game and its ranking method. Our results also suggest that our measures of rank dynamics are general and applicable for complex systems of different natures.
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A classic thesis is that scientific achievement exhibits a "Matthew effect": Scientists who have previously been successful are more likely to succeed again, producing increasing distinction. We investigate to what extent the Matthew effect drives the allocation of research funds. To this end, we assembled a dataset containing all review scores and funding decisions of grant proposals submitted by recent PhDs in a €2 billion granting program. Analyses of review scores reveal that early funding success introduces a growing rift, with winners just above the funding threshold accumulating more than twice as much research funding (€180,000) during the following eight years as nonwinners just below it. We find no evidence that winners' improved funding chances in subsequent competitions are due to achievements enabled by the preceding grant, which suggests that early funding itself is an asset for acquiring later funding. Surprisingly, however, the emergent funding gap is partly created by applicants, who, after failing to win one grant, apply for another grant less often.
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Confocal laser endomicroscopy (pCLE) provides real-time histologic imaging of human tissues at a depth of 60-70 μm during endoscopy. pCLE of the extrahepatic bile duct after fluorescein injection demonstrated a reticular pattern within fluorescein-filled sinuses that had no known anatomical correlate. Freezing biopsy tissue before fixation preserved the anatomy of this structure, demonstrating that it is part of the submucosa and a previously unappreciated fluid-filled interstitial space, draining to lymph nodes and supported by a complex network of thick collagen bundles. These bundles are intermittently lined on one side by fibroblast-like cells that stain with endothelial markers and vimentin, although there is a highly unusual and extensive unlined interface between the matrix proteins of the bundles and the surrounding fluid. We observed similar structures in numerous tissues that are subject to intermittent or rhythmic compression, including the submucosae of the entire gastrointestinal tract and urinary bladder, the dermis, the peri-bronchial and peri-arterial soft tissues, and fascia. These anatomic structures may be important in cancer metastasis, edema, fibrosis, and mechanical functioning of many or all tissues and organs. In sum, we describe the anatomy and histology of a previously unrecognized, though widespread, macroscopic, fluid-filled space within and between tissues, a novel expansion and specification of the concept of the human interstitium.
While there has been extensive interest in how intraspecific trait variation affects ecological processes, outcomes are highly variable even when individuals are identical: some are lucky, while others are not. Trait variation is therefore important only if it adds substantially to the variability produced by luck. We ask when trait variation has a substantial effect on variability in lifetime reproductive success (LRS), using two approaches: (1) we partition the variation in LRS into contributions from luck and trait variation and (2) we ask what can be inferred about an individual’s traits and with what certainty, given their observed LRS. In theoretical stage- and size-structured models and two empirical case studies, we find that luck usually dominates the variance of LRS. Even when individuals differ substantially in ways that affect expected LRS, unless the effects of luck are substantially reduced (e.g., low variability in reproductive life span or annual fecundity), most variance in lifetime outcomes is due to luck, implying that departures from “null” models omitting trait variation will be hard to detect. Luck also obscures the relationship between realized LRS and individual traits. While trait variation may influence the fate of populations, luck often governs the lives of individuals.
Five years ago, the Declaration on Research Assessment was a rallying point. It must now become a tool for fair evaluation, urges Stephen Curry.