Mass gathering events and the spread of infectious diseases: Evidence from the early growth phase of COVID-19

This paper studies the impact on reported coronavirus 2019 (COVID-19) cases and deaths in Spain resulting from large mass gatherings that occurred from March 6 to March 8, 2020. To study these outcomes, the geographic differences in the planned pre-pandemic major events that took place on these dates were exploited, which is a quasi-random source of variation for identification purposes. We collected daily and detailed information about the number of attendees at football (soccer) and basketball matches in addition to individuals participating in the Women’s Day marches across Spain, which we merged with daily data on reported COVID-19 cases and deaths at the provincial level. Our results reveal evidence of non-negligible COVID-19 cases related to the differences in the percentage of attendees at these major events from March 6 to March 8. In a typical province, approximately 31% of the average daily reported COVID-19 cases per 100,000 inhabitants between mid-March and early April 2020 can be explained by the participation rate in those major events. A back-of-the-envelope calculation suggests that this implies almost five million euros (169,000 euros/day) of additional economic cost in the health system of a typical province with one million inhabitants in the period under consideration. Several mechanisms behind the spread of COVID-19 are also examined.     

Basketball Shot Types and Shot Success in Different Levels of Competitive Basketball

The purpose of our research was to investigate the relative frequencies of different types of basketball shots (above head, hook shot, layup, dunk, tip-in), some details about their technical execution (one-legged, two-legged, drive, cut, …), and shot success in different levels of basketball competitions. We analysed video footage and categorized 5024 basketball shots from 40 basketball games and 5 different levels of competitive basketball (National Basketball Association (NBA), Euroleague, Slovenian 1^st Division, and two Youth basketball competitions). Statistical analysis with hierarchical multinomial logistic regression models reveals that there are substantial differences between competitions. However, most differences decrease or disappear entirely after we adjust for differences in situations that arise in different competitions (shot location, player type, and attacks in transition). Differences after adjustment are mostly between the Senior and Youth competitions: more shots executed jumping or standing on one leg, more uncategorised shot types, and more dribbling or cutting to the basket in the Youth competitions, which can all be attributed to lesser technical and physical ability of developing basketball players. The two discernible differences within the Senior competitions are that, in the NBA, dunks are more frequent and hook shots are less frequent compared to European basketball, which can be attributed to better athleticism of NBA players. The effect situational variables have on shot types and shot success are found to be very similar for all competitions.     

Predicting performance and injury resilience from movement quality and fitness scores in a basketball team over 2 years

The purpose of this study was to see if specific tests of fitness and movement quality could predict injury resilience and performance in a team of basketball players over 2 years (2 playing seasons). It was hypothesized that, in a basketball population, movement and fitness scores would predict performance scores and that movement and fitness scores would predict injury resilience. A basketball team from a major American university (N = 14) served as the test population in this longitudinal trial. Variables linked to fitness, movement ability, speed, strength, and agility were measured together with some National Basketball Association (NBA) combine tests. Dependent variables of performance indicators (such as games and minutes played, points scored, assists, rebounds, steal, and blocks) and injury reports were tracked for the subsequent 2 years. Results showed that better performance was linked with having a stiffer torso, more mobile hips, weaker left grip strength, and a longer standing long jump, to name a few. Of the 3 NBA combine tests administered here, only a faster lane agility time had significant links with performance. Some movement qualities and torso endurance were not linked. No patterns with injury emerged. These observations have implications for preseason testing and subsequent training programs in an attempt to reduce future injury and enhance playing performance.     

The effect of players' standard and tactical strategy on game demands in men's basketball

The purpose of the present study was to examine the effects of competitive level and team tactic on game demands in men's basketball. Sixteen international-level male basketball players (INPs) and 22 national-level male basketball players (NLPs) were studied during 6 games. Time-motion analysis was performed to track game activities. Game physiological demands were assessed by monitoring heart rate (HR) and blood-lactate concentration. Results showed that INPs sprinted significantly more and performed more high-intensity shuffling than did NLPs (p < 0.05). Game-activity changes and frequency of high-intensity bouts were similar in man-to-man and zone-marking games (1,053 vs. 1,056 and 253 vs. 224, respectively, p > 0.05). Time spent in the maximal (>95% of HRmax) and high-intensity zone (85-95% of HRmax) was greater in the INPs than in the NLPs (17.8 vs. 15.2%, p < 0.01 and 59.1 vs. 54.4%, p < 0.05, respectively). No significant differences in mean HR were evident between man-to-man and zone-marking games (93.3 ± 2.1 vs. 92.8 ± 1.8% of HRmax, p > 0.05). Blood-lactate concentration was higher in the INPs than in the NLPs (6.60 ± 1.22 vs. 5.66 ± 1.19 mmol·L?1 at halftime and 5.65 ± 1.21 vs. 4.43 ± 1.43 mmol·L?1 at full time, p < 0.05). No mean or peak blood-lactate concentration differences resulted between man-to-man and zone-marking games (5.15 ± 1.32 vs. 5.83 ± 1.10 and 5.90 ± 1.25 vs. 6.30 ± 1.27 mmol·L?1, respectively, p > 0.05). These results suggest an effect of competitive level over game demands in men's basketball. No marking strategy effect was evident. Basketball coaches and fitness trainers should develop the ability to repeatedly perform high-intensity activity during the game. Repeated sprinting and high-intensity shuffling ability should be trained to successfully play man-to-man and zone defense, respectively.     

Bodychecking Rules and Concussion in Elite Hockey

Athletes participating in contact sports such as ice hockey are exposed to a high risk of suffering a concussion. We determined whether recent rule changes regulating contact to the head introduced in 2010–11 and 2011–12 have been effective in reducing the incidence of concussion in the National Hockey League (NHL). A league with a longstanding ban on hits contacting the head, the Ontario Hockey League (OHL), was also studied. A retrospective study of NHL and OHL games for the 2009–10 to 2011–12 seasons was performed using official game records and team injury reports in addition to other media sources. Concussion incidence over the 3 seasons analyzed was 5.23 per 100 NHL regular season games and 5.05 per 100 OHL regular season games (IRR 1.04; 95% CI 1.01, 1.50). When injuries described as concussion-like or suspicious of concussion were included, incidences rose to 8.8 and 7.1 per 100 games respectively (IRR 1.23; 95% CI 0.81, 1.32). The number of NHL concussions or suspected concussions was lower in 2009–10 than in 2010–11 (IRR 0.61; 95% CI 0.45, 0.83), but did not increase from 2010–11 to 2011–12 (IRR 1.05; 95% CI 0.80, 1.38). 64.2% of NHL concussions were caused by bodychecking, and only 28.4% of concussions and 36.8% of suspected concussions were caused by illegal incidents. We conclude that rules regulating bodychecking to the head did not reduce the number of players suffering concussions during NHL regular season play and that further changes or stricter enforcement of existing rules may be required to minimize the risk of players suffering these injuries.     

Basketball exercise and secretory immunoglobulin A.

This study examined saliva levels of immunoglobulin A (IgA) before and after three games and three practice sessions during the basketball season. Saliva was collected from 27 prepubescent boys (10-12 years) in a small Fry league and 23 postpubescent boys (16-18 years) on a high school varsity team. Saliva samples were frozen for later assay using a standard enzyme-linked immunosorbent assay technique. IgA levels were significantly increased after games 1 and 3 in both age groups and after practice 3 in the high school athletes. Over the 2 months of saliva collections the pre-exercise IgA increased significantly with games 2 and 3 higher than game 1, and practice 3 higher than practices 1 and 2, in both age groups. These results indicate that basketball exercise can increase saliva IgA levels and that chronic exercise over the basketball season may increase the resting levels of IgA. These changes may give athletes more protection against respiratory infections both after exercise and in the resting state later in the season.     

Reciprocity on the Hardwood: Passing Patterns among Professional Basketball Players

Past theory and research view reciprocal resource sharing as a fundamental building block of human societies. Most studies of reciprocity dynamics have focused on trading among individuals in laboratory settings. But if motivations to engage in these patterns of resource sharing are powerful, then we should observe forms of reciprocity even in highly structured group environments in which reciprocity does not clearly serve individual or group interests. To this end, we investigated whether patterns of reciprocity might emerge among teammates in professional basketball games. Using data from logs of National Basketball Association (NBA) games of the 2008–9 season, we estimated a series of conditional logistic regression models to test the impact of different factors on the probability that a given player would assist another player in scoring a basket. Our analysis found evidence for a direct reciprocity effect in which players who had “received” assists in the past tended to subsequently reciprocate their benefactors. Further, this tendency was time-dependent, with the probability of repayment highest soon after receiving an assist and declining as game time passed. We found no evidence for generalized reciprocity – a tendency to “pay forward” assists – and only very limited evidence for indirect reciprocity – a tendency to reward players who had sent others many assists. These findings highlight the power of reciprocity to shape human behavior, even in a setting characterized by extensive planning, division of labor, quick decision-making, and a focus on inter-group competition.     

The Advantage of Playing Home in NBA: Microscopic,Team-Specific and Evolving Features

The idea that the success rate of a team increases when playing home is broadly accepted and documented for a wide variety of sports. Investigations on the so-called “home advantage phenomenon” date back to the 70’s and ever since has attracted the attention of scholars and sport enthusiasts. These studies have been mainly focused on identifying the phenomenon and trying to correlate it with external factors such as crowd noise and referee bias. Much less is known about the effects of home advantage in the “microscopic” dynamics of the game (within the game) or possible team-specific and evolving features of this phenomenon. Here we present a detailed study of these previous features in the National Basketball Association (NBA). By analyzing play-by-play events of more than sixteen thousand games that span thirteen NBA seasons, we have found that home advantage affects the microscopic dynamics of the game by increasing the scoring rates and decreasing the time intervals between scores of teams playing home. We verified that these two features are different among the NBA teams, for instance, the scoring rate of the Cleveland Cavaliers team is increased ≈0.16 points per minute (on average the seasons 2004–05 to 2013–14) when playing home, whereas for the New Jersey Nets (now the Brooklyn Nets) this rate increases in only ≈0.04 points per minute. We further observed that these microscopic features have evolved over time in a non-trivial manner when analyzing the results team-by-team. However, after averaging over all teams some regularities emerge; in particular, we noticed that the average differences in the scoring rates and in the characteristic times (related to the time intervals between scores) have slightly decreased over time, suggesting a weakening of the phenomenon. This study thus adds evidence of the home advantage phenomenon and contributes to a deeper understanding of this effect over the course of games.     

Did Covid-19 hit harder in peripheral areas? The case of Italian municipalities

The first wave of Covid-19 pandemic had a geographically heterogeneous impact even within the most severely hit regions. Exploiting a triple-differences methodology, we find that in Italy Covid-19 hit relatively harder in peripheral areas: the excess mortality in peripheral areas was almost double that of central ones in March 2020 (1.2 additional deaths every 1000 inhabitants). We leverage a rich dataset on Italian municipalities to explore mechanisms behind this gradient. We first show that socio-demographic and economic features at municipal level are highly collinear, making it hard to identify single-variable causal relationships. Using Principal Components Analysis we model excess mortality and show that areas with higher excess mortality have lower income, lower education, larger households, lower trade and higher industrial employments, and older population. Our findings highlight a strong centre-periphery gradient in the harshness of Covid-19, which we believe is also highly relevant from a policy-making standpoint.     

Basketball Teams as Strategic Networks

We asked how team dynamics can be captured in relation to function by considering games in the first round of the NBA 2010 play-offs as networks. Defining players as nodes and ball movements as links, we analyzed the network properties of degree centrality, clustering, entropy and flow centrality across teams and positions, to characterize the game from a network perspective and to determine whether we can assess differences in team offensive strategy by their network properties. The compiled network structure across teams reflected a fundamental attribute of basketball strategy. They primarily showed a centralized ball distribution pattern with the point guard in a leadership role. However, individual play-off teams showed variation in their relative involvement of other players/positions in ball distribution, reflected quantitatively by differences in clustering and degree centrality. We also characterized two potential alternate offensive strategies by associated variation in network structure: (1) whether teams consistently moved the ball towards their shooting specialists, measured as “uphill/downhill” flux, and (2) whether they distributed the ball in a way that reduced predictability, measured as team entropy. These network metrics quantified different aspects of team strategy, with no single metric wholly predictive of success. However, in the context of the 2010 play-offs, the values of clustering (connectedness across players) and network entropy (unpredictability of ball movement) had the most consistent association with team advancement. Our analyses demonstrate the utility of network approaches in quantifying team strategy and show that testable hypotheses can be evaluated using this approach. These analyses also highlight the richness of basketball networks as a dataset for exploring the relationships between network structure and dynamics with team organization and effectiveness.     

An ESS maximum principle for matrix games

Previous work has demonstrated that for games defined by differential or difference equations with a continuum of strategies, there exists a G-function, related to individual fitness, that must take on a maximum with respect to a virtual variable v whenever v is one of the vectors in the coalition of vectors which make up the evolutionarily stable strategy (ESS). This result, called the ESS maximum principle, is quite useful in determining candidates for an ESS. This principle is reformulated here, so that it may be conveniently applied to matrix games. In particular, we define a matrix game to be one in which fitness is expressed in terms of strategy frequencies and a matrix of expected payoffs. It is shown that the G-function in the matrix game setting must again take on a maximum value at all the strategies which make up the ESS coalition vector. The reformulated maximum principle is applicable to both bilinear and nonlinear matrix games. One advantage in employing this principle to solve the traditional bilinear matrix game is that the same G-function is used to find both pure and mixed strategy solutions by simply specifying an appropriate strategy space. Furthermore we show how the theory may be used to solve matrix games which are not in the usual bilinear form. We examine in detail two nonlinear matrix games: the game between relatives and the sex ratio game. In both of these games an ESS solution is determined. These examples not only illustrate the usefulness of this approach to finding solutions to an expanded class of matrix games, but aids in understanding the nature of the ESS as well.     

A dynamic over games drives selfish agents to win–win outcomes

Understanding human institutions, animal cultures and other social systems requires flexible formalisms that describe how their members change them from within. We introduce a framework for modelling how agents change the games they participate in. We contrast this between-game ‘institutional evolution’ with the more familiar within-game ‘behavioural evolution’. We model institutional change by following small numbers of persistent agents as they select and play a changing series of games. Starting from an initial game, a group of agents trace trajectories through game space by navigating to increasingly preferable games until they converge on ‘attractor’ games. Agents use their ‘institutional preferences'' for game features (such as stability, fairness and efficiency) to choose between neighbouring games. We use this framework to pose a pressing question: what kinds of games does institutional evolution select for; what is in the attractors? After computing institutional change trajectories over the two-player space, we find that attractors have disproportionately fair outcomes, even though the agents who produce them are strictly self-interested and indifferent to fairness. This seems to occur because game fairness co-occurs with the self-serving features these agents do actually prefer. We thus present institutional evolution as a mechanism for encouraging the spontaneous emergence of cooperation among small groups of inherently selfish agents, without space, reputation, repetition, or other more familiar mechanisms. Game space trajectories provide a flexible, testable formalism for modelling the interdependencies of behavioural and institutional evolutionary processes, as well as a mechanism for the evolution of cooperation.     

Game-related statistics that discriminated winning and losing teams from the Spanish men's professional basketball teams

The purpose of the present study was to analyse men's basketball competitions, trying to identify which game-related statistics allow to discriminate winning and losing teams. The sample used corresponded to 306 games from the 2004-2005 Regular Season of the Spanish Men's Professional League. The game-related statistics gathered were: 2 and 3 points field-goals (both successful and unsuccessful), free-throws (both successful and unsuccessful), offensive and defensive rebounds, blocks, assists, fouls, turnovers and steals. The data were analysed in two groups: balanced games (final score differences equal or below 12 points) and unbalanced games (final score differences above 12 points). Discriminant analysis allowed to conclude the following: (i) in balanced games, the variable that best differentiate both groups were the defensive rebounds; (ii) in unbalanced games, the variables that discriminate between both groups were the successful 2 points field-goals, the defensive rebounds and the assists; and (iii) in all games, the statistical analysis identified two variables that discriminate winning and losing teams (defensive rebounds and assists). The defensive rebounds were the only game-related statistic that discriminates both groups in all performed analysis. Coaches and players should be aware of these different profiles in order to increase knowledge about game cognitive and motor solicitation and, therefore, to enhance specificity at the time of practice and game planning.     

Relationship of anthropometrical, physiological and motor attributes to sport-specific skills

The purpose of this pilot study was to investigate the importance of the athlete's motor capabilities in success in sport. More precisely, the association of anthropometrical and physiological attributes, as well as motor abilities of elite basketball players with play elements of basketball. The subjects were seven elite basketball players. At the end of the competitive season, the anthropometrical and physiological features were measured to establish the physical fitness of the subjects. Both general and sport-specific motor tests were done. The coach estimated the performance of each player during the games of the competitive season. The coach's data sheet incorporated 14 parameters of the game. Regression analyses indicated significant correlation between certain variables of the laboratory tests and the data of the coach's estimation statistics. Knowing these relationships provides us with valuable predictive information about player's capabilities in sport.     

Close encounters during a pandemic: Social habits and inter-generational links in the first two waves of COVID-19

Social habits are ingrained in a community and affect human behaviour. Have they played any role in the spread of the pandemic? We use high-frequency data for 220 regions in 15 European countries from March to December 2020 to compare the association between social contacts outside the family and within inter-generational families, on the one hand, and cases and excess mortality on the other. We find that a standard deviation increase in the percentage of people having daily face-to-face contacts outside the household is associated with 5 new daily cases and 2.6 additional weekly deaths, while the incidence of inter-generational households exhibits a less robust association with both COVID-19 transmission and mortality. We compare results across the first and the second wave of pandemic and show that differences are related to the average age of the most affected groups. Our findings are robust to the inclusion of a number of controls, fixed effects, the chosen sample of countries, and the estimation method. We argue that type and frequency of social interactions are interweaved with a region culture and habits and are informative on the potential transmission of contagion and on its lethality.     

Failure to Demonstrate That Playing Violent Video Games Diminishes Prosocial Behavior

Background

Past research has found that playing a classic prosocial video game resulted in heightened prosocial behavior when compared to a control group, whereas playing a classic violent video game had no effect. Given purported links between violent video games and poor social behavior, this result is surprising. Here our aim was to assess whether this finding may be due to the specific games used. That is, modern games are experienced differently from classic games (more immersion in virtual environments, more connection with characters, etc.) and it may be that playing violent video games impacts prosocial behavior only when contemporary versions are used.

Methods and Findings

Experiments 1 and 2 explored the effects of playing contemporary violent, non-violent, and prosocial video games on prosocial behavior, as measured by the pen-drop task. We found that slight contextual changes in the delivery of the pen-drop task led to different rates of helping but that the type of game played had little effect. Experiment 3 explored this further by using classic games. Again, we found no effect.

Conclusions

We failed to find evidence that playing video games affects prosocial behavior. Research on the effects of video game play is of significant public interest. It is therefore important that speculation be rigorously tested and findings replicated. Here we fail to substantiate conjecture that playing contemporary violent video games will lead to diminished prosocial behavior.     

Unpredictability induced by unfocused games in evolutionary game dynamics

Evolutionary game theory is a basis of replicator systems and has applications ranging from animal behavior and human language to ecosystems and other hierarchical network systems. Most studies in evolutionary game dynamics have focused on a single game, but, in many situations, we see that many games are played simultaneously. We construct a replicator equation with plural games by assuming that a reward of a player is a simple summation of the reward of each game. Even if the numbers of the strategies of the games are different, its dynamics can be described in one replicator equation. We here show that when players play several games at the same time, the fate of a single game cannot be determined without knowing the structures of the whole other games. The most absorbing fact is that even if a single game has a ESS (evolutionary stable strategy), the relative frequencies of strategies in the game does not always converge to the ESS point when other games are played simultaneously.     

N-player quantum games in an EPR setting

The N-player quantum games are analyzed that use an Einstein-Podolsky-Rosen (EPR) experiment, as the underlying physical setup. In this setup, a player's strategies are not unitary transformations as in alternate quantum game-theoretic frameworks, but a classical choice between two directions along which spin or polarization measurements are made. The players' strategies thus remain identical to their strategies in the mixed-strategy version of the classical game. In the EPR setting the quantum game reduces itself to the corresponding classical game when the shared quantum state reaches zero entanglement. We find the relations for the probability distribution for N-qubit GHZ and W-type states, subject to general measurement directions, from which the expressions for the players' payoffs and mixed Nash equilibrium are determined. Players' N x N payoff matrices are then defined using linear functions so that common two-player games can be easily extended to the N-player case and permit analytic expressions for the Nash equilibrium. As a specific example, we solve the Prisoners' Dilemma game for general N ≥ 2. We find a new property for the game that for an even number of players the payoffs at the Nash equilibrium are equal, whereas for an odd number of players the cooperating players receive higher payoffs. By dispensing with the standard unitary transformations on state vectors in Hilbert space and using instead rotors and multivectors, based on Clifford's geometric algebra (GA), it is shown how the N-player case becomes tractable. The new mathematical approach presented here has wide implications in the areas of quantum information and quantum complexity, as it opens up a powerful way to tractably analyze N-partite qubit interactions.     

Ecological theatre and the evolutionary game: how environmental and demographic factors determine payoffs in evolutionary games

In the standard approach to evolutionary games and replicator dynamics, differences in fitness can be interpreted as an excess from the mean Malthusian growth rate in the population. In the underlying reasoning, related to an analysis of “costs” and “benefits”, there is a silent assumption that fitness can be described in some type of units. However, in most cases these units of measure are not explicitly specified. Then the question arises: are these theories testable? How can we measure “benefit” or “cost”? A natural language, useful for describing and justifying comparisons of strategic “cost” versus “benefits”, is the terminology of demography, because the basic events that shape the outcome of natural selection are births and deaths. In this paper, we present the consequences of an explicit analysis of births and deaths in an evolutionary game theoretic framework. We will investigate different types of mortality pressures, their combinations and the possibility of trade-offs between mortality and fertility. We will show that within this new approach it is possible to model how strictly ecological factors such as density dependence and additive background fitness, which seem neutral in classical theory, can affect the outcomes of the game. We consider the example of the Hawk–Dove game, and show that when reformulated in terms of our new approach new details and new biological predictions are produced.     

Training load,recovery and game performance in semiprofessional male basketball: influence of individual characteristics and contextual factors

This study examined the effects of individual characteristics and contextual factors on training load, pre-game recovery and game performance in adult male semi-professional basketball. Fourteen players were monitored, across a whole competitive season, with the session-RPE method to calculate weekly training load, and the Total Quality Recovery Scale to obtain pre-game recovery scores. Additionally, game-related statistics were gathered during official games to calculate the Performance Index Rating (PIR). Individual characteristics and contextual factors were grouped using k-means cluster analyses. Separate mixed linear models for repeated measures were performed to evaluate the single and combined (interaction) effects of individual characteristics (playing experience; playing position; playing time) and contextual factors (season phase; recovery cycle; previous game outcome; previous and upcoming opponent level) on weekly training load, pre-game recovery and PIR. Weekly load was higher in guards and medium minute-per-game (MPG) players, and lower for medium-experienced players, before facing high-level opponents, during later season phases and short recovery cycles (all p < 0.05). Pre-game recovery was lower in centers and high-experience players (p < 0.05). Game performance was better in high-MPG players (p < 0.05) and when facing low and medium-level opponents (p < 0.001). Interestingly, players performed better in games when the previous week’s training load was low (p = 0.042). This study suggests that several individual characteristics and contextual factors need to be considered when monitoring training load (playing experience, playing position, playing time, recovery cycle, upcoming opponent level), recovery (playing experience, playing position) and game performance (opponent level, weekly training load, pre-game recovery) in basketball players during the competitive season.