633 research outputs found
The problem of shot selection in basketball
In basketball, every time the offense produces a shot opportunity the player
with the ball must decide whether the shot is worth taking. In this paper, I
explore the question of when a team should shoot and when they should pass up
the shot by considering a simple theoretical model of the shot selection
process, in which the quality of shot opportunities generated by the offense is
assumed to fall randomly within a uniform distribution. I derive an answer to
the question "how likely must the shot be to go in before the player should
take it?", and show that this "lower cutoff" for shot quality depends
crucially on the number of shot opportunities remaining (say, before the
shot clock expires), with larger demanding that only higher-quality shots
should be taken. The function is also derived in the presence of a
finite turnover rate and used to predict the shooting rate of an
optimal-shooting team as a function of time. This prediction is compared to
observed shooting rates from the National Basketball Association (NBA), and the
comparison suggests that NBA players tend to wait too long before shooting and
undervalue the probability of committing a turnover.Comment: 7 pages, 2 figures; comparison to NBA data adde
Fluctuation scaling in complex systems: Taylor's law and beyond
Complex systems consist of many interacting elements which participate in
some dynamical process. The activity of various elements is often different and
the fluctuation in the activity of an element grows monotonically with the
average activity. This relationship is often of the form "", where the exponent is predominantly in
the range . This power law has been observed in a very wide range of
disciplines, ranging from population dynamics through the Internet to the stock
market and it is often treated under the names \emph{Taylor's law} or
\emph{fluctuation scaling}. This review attempts to show how general the above
scaling relationship is by surveying the literature, as well as by reporting
some new empirical data and model calculations. We also show some basic
principles that can underlie the generality of the phenomenon. This is followed
by a mean-field framework based on sums of random variables. In this context
the emergence of fluctuation scaling is equivalent to some corresponding limit
theorems. In certain physical systems fluctuation scaling can be related to
finite size scaling.Comment: 33 pages, 20 figures, 2 tables, submitted to Advances in Physic
Router-level community structure of the Internet Autonomous Systems
The Internet is composed of routing devices connected between them and
organized into independent administrative entities: the Autonomous Systems. The
existence of different types of Autonomous Systems (like large connectivity
providers, Internet Service Providers or universities) together with
geographical and economical constraints, turns the Internet into a complex
modular and hierarchical network. This organization is reflected in many
properties of the Internet topology, like its high degree of clustering and its
robustness.
In this work, we study the modular structure of the Internet router-level
graph in order to assess to what extent the Autonomous Systems satisfy some of
the known notions of community structure. We show that the modular structure of
the Internet is much richer than what can be captured by the current community
detection methods, which are severely affected by resolution limits and by the
heterogeneity of the Autonomous Systems. Here we overcome this issue by using a
multiresolution detection algorithm combined with a small sample of nodes. We
also discuss recent work on community structure in the light of our results
Who is the best player ever? A complex network analysis of the history of professional tennis
We consider all matches played by professional tennis players between 1968
and 2010, and, on the basis of this data set, construct a directed and weighted
network of contacts. The resulting graph shows complex features, typical of
many real networked systems studied in literature. We develop a diffusion
algorithm and apply it to the tennis contact network in order to rank
professional players. Jimmy Connors is identified as the best player of the
history of tennis according to our ranking procedure. We perform a complete
analysis by determining the best players on specific playing surfaces as well
as the best ones in each of the years covered by the data set. The results of
our technique are compared to those of two other well established methods. In
general, we observe that our ranking method performs better: it has a higher
predictive power and does not require the arbitrary introduction of external
criteria for the correct assessment of the quality of players. The present work
provides a novel evidence of the utility of tools and methods of network theory
in real applications.Comment: 10 pages, 4 figures, 4 table
Hot Streaks in Artistic, Cultural, and Scientific Careers
The hot streak, loosely defined as winning begets more winnings, highlights a
specific period during which an individual's performance is substantially
higher than her typical performance. While widely debated in sports, gambling,
and financial markets over the past several decades, little is known if hot
streaks apply to individual careers. Here, building on rich literature on
lifecycle of creativity, we collected large-scale career histories of
individual artists, movie directors and scientists, tracing the artworks,
movies, and scientific publications they produced. We find that, across all
three domains, hit works within a career show a high degree of temporal
regularity, each career being characterized by bursts of high-impact works
occurring in sequence. We demonstrate that these observations can be explained
by a simple hot-streak model we developed, allowing us to probe quantitatively
the hot streak phenomenon governing individual careers, which we find to be
remarkably universal across diverse domains we analyzed: The hot streaks are
ubiquitous yet unique across different careers. While the vast majority of
individuals have at least one hot streak, hot streaks are most likely to occur
only once. The hot streak emerges randomly within an individual's sequence of
works, is temporally localized, and is unassociated with any detectable change
in productivity. We show that, since works produced during hot streaks garner
significantly more impact, the uncovered hot streaks fundamentally drives the
collective impact of an individual, ignoring which leads us to systematically
over- or under-estimate the future impact of a career. These results not only
deepen our quantitative understanding of patterns governing individual
ingenuity and success, they may also have implications for decisions and
policies involving predicting and nurturing individuals with lasting impact
Mesoscopic structure conditions the emergence of cooperation on social networks
We study the evolutionary Prisoner's Dilemma on two social networks obtained
from actual relational data. We find very different cooperation levels on each
of them that can not be easily understood in terms of global statistical
properties of both networks. We claim that the result can be understood at the
mesoscopic scale, by studying the community structure of the networks. We
explain the dependence of the cooperation level on the temptation parameter in
terms of the internal structure of the communities and their interconnections.
We then test our results on community-structured, specifically designed
artificial networks, finding perfect agreement with the observations in the
real networks. Our results support the conclusion that studies of evolutionary
games on model networks and their interpretation in terms of global properties
may not be sufficient to study specific, real social systems. In addition, the
community perspective may be helpful to interpret the origin and behavior of
existing networks as well as to design structures that show resilient
cooperative behavior.Comment: Largely improved version, includes an artificial network model that
fully confirms the explanation of the results in terms of inter- and
intra-community structur
Universality, limits and predictability of gold-medal performances at the Olympic Games
Inspired by the Games held in ancient Greece, modern Olympics represent the
world's largest pageant of athletic skill and competitive spirit. Performances
of athletes at the Olympic Games mirror, since 1896, human potentialities in
sports, and thus provide an optimal source of information for studying the
evolution of sport achievements and predicting the limits that athletes can
reach. Unfortunately, the models introduced so far for the description of
athlete performances at the Olympics are either sophisticated or unrealistic,
and more importantly, do not provide a unified theory for sport performances.
Here, we address this issue by showing that relative performance improvements
of medal winners at the Olympics are normally distributed, implying that the
evolution of performance values can be described in good approximation as an
exponential approach to an a priori unknown limiting performance value. This
law holds for all specialties in athletics-including running, jumping, and
throwing-and swimming. We present a self-consistent method, based on normality
hypothesis testing, able to predict limiting performance values in all
specialties. We further quantify the most likely years in which athletes will
breach challenging performance walls in running, jumping, throwing, and
swimming events, as well as the probability that new world records will be
established at the next edition of the Olympic Games.Comment: 8 pages, 3 figures, 1 table. Supporting information files and data
are available at filrad.homelinux.or
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