Do soccer players play the mixed-strategy Nash equilibrium?

Mixed-strategy Nash equilibrium (MSNE) is a commonly-used solution concept in game-theoretic models in various fields in economics, management, and other disciplines, but the experimental results whether the MSNE predicts well actual play in games is mixed. Consequently, evidence for naturally-occurring games in which the MSNE predicts the outcome well is of great importance, as it can justify the vast use of MSNE in models. The game between the kicker and goalkeeper in soccer penalty kicks is a real-world game that can be used to examine the application of the MSNE concept or its accuracy because payoffs are a common knowledge, the players have huge incentives to play correctly, the game is simple enough to analyze, its Nash equilibrium is in mixed strategies, and players' actions can be observed. We collected and analyzed data on the direction of kicks and jumps in penalty kicks in various top leagues and tournaments. Our analysis suggests that the MSNE predictions are the closest to the actual sample data, even though some other prediction methods use information on the marginal distribution of kicks or jumps whereas the MSNE does not.Soccer; Football; MSNE; Mixed-strategies; Mixed-strategy Nash equilibrium; Sports; Penalty kicks

Action bias among elite soccer goalkeepers: The case of penalty kicks

In soccer penalty kicks, goalkeepers choose their action before they can clearly observe the kick direction. An analysis of 286 penalty kicks in top leagues and championships worldwide shows that given the probability distribution of kick direction, the optimal strategy for goalkeepers is to stay in the goal's center. Goalkeepers, however, almost always jump right or left. We propose the following explanation for this behavior: because the norm is to jump, norm theory (Kahneman and Miller, 1986) implies that a goal scored yields worse feelings for the goalkeeper following inaction (staying in the center) than following action (jumping), leading to a bias for action. The omission bias, a bias in favor of inaction, is reversed here because the norm here is reversed - to act rather than to choose inaction. The claim that jumping is the norm is supported by a second study, a survey conducted with 32 top professional goalkeepers. The seemingly biased decision making is particularly striking since the goalkeepers have huge incentives to make correct decisions, and it is a decision they encounter frequently. Finally, we discuss several implications of the action/omission bias for economics and management.Decision Making; Uncertainty; Choice Behavior; Sport Psychology; Behavioral Economics; Action Bias; Omission Bias; Commission Bias; Action Effect; Inaction Effect; Actor Effect; Economic Psychology; Heuristics and Biases; Soccer; Goalkeepers; Penalty Kicks; Risk; Norms

Do soccer players play the mixed-strategy Nash equilibrium?

Mixed-strategy Nash equilibrium (MSNE) is a commonly-used solution concept in game-theoretic models in various fields in economics, management, and other disciplines, but the experimental results whether the MSNE predicts well actual play in games is mixed. Consequently, evidence for naturally-occurring games in which the MSNE predicts the outcome well is of great importance, as it can justify the vast use of MSNE in models. The game between the kicker and goalkeeper in soccer penalty kicks is a real-world game that can be used to examine the application of the MSNE concept or its accuracy because payoffs are a common knowledge, the players have huge incentives to play correctly, the game is simple enough to analyze, its Nash equilibrium is in mixed strategies, and players' actions can be observed. We collected and analyzed data on the direction of kicks and jumps in penalty kicks in various top leagues and tournaments. Our analysis suggests that the MSNE predictions are the closest to the actual sample data, even though some other prediction methods use information on the marginal distribution of kicks or jumps whereas the MSNE does not

Do soccer players play the mixed-strategy Nash equilibrium?

Mixed-strategy Nash equilibrium (MSNE) is a commonly-used solution concept in game-theoretic models in various fields in economics, management, and other disciplines, but the experimental results whether the MSNE predicts well actual play in games is mixed. Consequently, evidence for naturally-occurring games in which the MSNE predicts the outcome well is of great importance, as it can justify the vast use of MSNE in models. The game between the kicker and goalkeeper in soccer penalty kicks is a real-world game that can be used to examine the application of the MSNE concept or its accuracy because payoffs are a common knowledge, the players have huge incentives to play correctly, the game is simple enough to analyze, its Nash equilibrium is in mixed strategies, and players' actions can be observed. We collected and analyzed data on the direction of kicks and jumps in penalty kicks in various top leagues and tournaments. Our analysis suggests that the MSNE predictions are the closest to the actual sample data, even though some other prediction methods use information on the marginal distribution of kicks or jumps whereas the MSNE does not

Searching for Judgment Biases Among Elite Basketball Referees

An attacking basketball player initiating significant physical contact with a defender who has already established a legal and stationary position, should be called with an offensive foul. Offensive foul situations are particularly ambiguous and complex, making the referee’s task a difficult one. In such conditions of complexity and constraints of time, the referee is likely to be prone to systematic biases, as has been documented by previous research in other sport settings. We analyzed the referees’ decisions in 250 instances of collisions between an attacking player and a defender. In these collisions the defender fell, and potentially an offensive foul could be called. We found no evidence of favoritism granted to the home team, to star players, or to high-reputation teams, or of small players being tackled by significantly larger opponents. The findings suggest that these biases are not very robust, and are sensitive to the context, and that proper training of referees and enhanced awareness can help to alleviate referees’ biases

Analysis of 3.5 Million SARS-CoV-2 Sequences Reveals Unique Mutational Trends with Consistent Nucleotide and Codon Frequencies

Background: Since the onset of the SARS-CoV-2 pandemic, bioinformatic analyses have been performed to understand the nucleotide and synonymous codon usage features and mutational patterns of the virus. However, comparatively few have attempted to perform such analyses on a considerably large cohort of viral genomes while organizing the plethora of available sequence data for a month-by-month analysis to observe changes over time. Here, we aimed to perform sequence composition and mutation analysis of SARS-CoV-2, separating sequences by gene, clade, and timepoints, and contrast the mutational profile of SARS-CoV-2 to other comparable RNA viruses.Methods: Using a cleaned, filtered, and pre-aligned dataset of over 3.5 million sequences downloaded from the GISAID database, we computed nucleotide and codon usage statistics, including calculation of relative synonymous codon usage values. We then calculated codon adaptation index (CAI) changes and a nonsynonymous/synonymous mutation ratio (dN/dS) over time for our dataset. Finally, we compiled information on the types of mutations occurring for SARS-CoV-2 and other comparable RNA viruses, and generated heatmaps showing codon and nucleotide composition at high entropy positions along the Spike sequence.Results: We show that nucleotide and codon usage metrics remain relatively consistent over the 32-month span, though there are significant differences between clades within each gene at various timepoints. CAI and dN/dS values vary substantially between different timepoints and different genes, with Spike gene on average showing both the highest CAI and dN/dS values. Mutational analysis showed that SARS-CoV-2 Spike has a higher proportion of nonsynonymous mutations than analogous genes in other RNA viruses, with nonsynonymous mutations outnumbering synonymous ones by up to 20:1. However, at several specific positions, synonymous mutations were overwhelmingly predominant.Conclusions: Our multifaceted analysis covering both the composition and mutation signature of SARS-CoV-2 gives valuable insight into the nucleotide frequency and codon usage heterogeneity of SARS-CoV-2 over time, and its unique mutational profile compared to other RNA viruses

Action bias among elite soccer goalkeepers: The case of penalty kicks

In soccer penalty kicks, goalkeepers choose their action before they can clearly observe the kick direction. An analysis of 286 penalty kicks in top leagues and championships worldwide shows that given the probability distribution of kick direction, the optimal strategy for goalkeepers is to stay in the goal's center. Goalkeepers, however, almost always jump right or left. We propose the following explanation for this behavior: because the norm is to jump, norm theory (Kahneman and Miller, 1986) implies that a goal scored yields worse feelings for the goalkeeper following inaction (staying in the center) than following action (jumping), leading to a bias for action. The omission bias, a bias in favor of inaction, is reversed here because the norm here is reversed - to act rather than to choose inaction. The claim that jumping is the norm is supported by a second study, a survey conducted with 32 top professional goalkeepers. The seemingly biased decision making is particularly striking since the goalkeepers have huge incentives to make correct decisions, and it is a decision they encounter frequently. Finally, we discuss several implications of the action/omission bias for economics and management

Endoplasmic spreading requires coalescence of vimentin intermediate filaments at force-bearing adhesions

10.1091/mbc.E12-05-0377Molecular Biology of the Cell24121-30MBCE

Multi-camera real-time three-dimensional tracking of multiple flying animals

Automated tracking of animal movement allows analyses that would not otherwise be possible by providing great quantities of data. The additional capability of tracking in real time—with minimal latency—opens up the experimental possibility of manipulating sensory feedback, thus allowing detailed explorations of the neural basis for control of behaviour. Here, we describe a system capable of tracking the three-dimensional position and body orientation of animals such as flies and birds. The system operates with less than 40 ms latency and can track multiple animals simultaneously. To achieve these results, a multi-target tracking algorithm was developed based on the extended Kalman filter and the nearest neighbour standard filter data association algorithm. In one implementation, an 11-camera system is capable of tracking three flies simultaneously at 60 frames per second using a gigabit network of nine standard Intel Pentium 4 and Core 2 Duo computers. This manuscript presents the rationale and details of the algorithms employed and shows three implementations of the system. An experiment was performed using the tracking system to measure the effect of visual contrast on the flight speed of Drosophila melanogaster. At low contrasts, speed is more variable and faster on average than at high contrasts. Thus, the system is already a useful tool to study the neurobiology and behaviour of freely flying animals. If combined with other techniques, such as ‘virtual reality’-type computer graphics or genetic manipulation, the tracking system would offer a powerful new way to investigate the biology of flying animals