Does playing several competitions influence a team’s league performance? Evidence from Spanish professional football

The sporting performance of professional football teams has often been assessed considering their results in the major regular competition, namely the national league. Here, we show that evaluating league performance without controlling for extra games played in other competitions might produce misleading results. Using Data Envelopment Analysis, we assess the performance of Spanish professional football teams in the League controlling for the extra games played in the King’s Cup, Champions League and UEFA Cup. Results show that assessing performance omitting extra games underestimates teams’ true performance in the League, the more extra games played leading to greater bias. Consequently, the multioutput nature of football must be considered when assessing team performance.     

Optimizing strategic behaviour in a dynamic setting in professional team sports

This article develops a dynamic game-theoretic model of optimizing strategic behaviour by football (soccer) teams. Teams choose between defensive and attacking formations and between a non-violent and a violent playing style, and can vary these choices continuously throughout each match. Starting from the end of the match and working backwards, the teams’ optimal strategies conditional on the current state of the match are determined by solving a series of two-player non-cooperative subgames. Numerical simulations are used to explore the sensitivity of strategic behaviour to variations in the structural parameters. The analysis demonstrates that the strategic behaviour of football teams can be rationalized in accordance with game-theoretic principles of optimizing strategic behaviour by agents when payoffs are uncertain and interdependent.     

Assessing the performance of German <Emphasis Type="Italic">Bundesliga</Emphasis> football players: a non-parametric metafrontier approach

This article presents a novel model for evaluating the performance of field players in football. Based upon Data Envelopment Analysis (DEA), we employ a non-concave metafrontier approach that permits estimation of players’ efficiency scores under consideration of their playing positions. The model is applied to a data set of Germany’s premier league football players covering the playing seasons 2002/03 to 2008/09. The results reveal a clear positive relationship between a team’s average player efficiency score and its rank in the league table at the end of the season. In addition, the metafrontier approach is used to identify a footballer’s optimal playing position in the team and to quantify the performance increase from moving to that position.     

A metric to quantify college football’s topsy-turvy season

Based on ranking change of college football teams from week to week in AP polls, a metric to measure the topsy-turviness of college football weeks has been developed. Six recent seasons (2002–2007) were used in the analysis. The 2007 season turned out to be the most topsy-turvy, while the 2004 season was the most stable. These findings were confirmed with other measurements, such as change in ranking from week to week and number of weeks deemed topsy-turvy or stable based on the average and standard deviation of all TT factor numbers. Other polls, such as the USA Today poll, resulted in similar trends. In-depth statistical analysis of the weekly TT factors did not indicate the presence of nonrandomness throughout the weekly topsy-turvy season. When using a randomized complete block design, statistically significant differences were detected in the mean TT factors across weeks and seasons. However, no significant trends were found in the TT factors, except for in the last week before the bowls are played.     

Unitary integrals and related matrix models

We briefly review the basic properties of unitary matrix integrals, using three matrix models to analyze their properties: the ordinary unitary, the Brezin—Gross—Witten, and the Harish—Chandra—Itzykson—Zuber models. We especially emphasize the nontrivial aspects of the theory, from the De Witt’Hooft anomaly in unitary integrals to the problem of calculating correlators with the Itzykson-Zuber measure. We emphasize the method of character expansions as a technical tool. Unitary integrals are still insufficiently investigated, and many new results should be expected as this field attracts increased attention.     

Carathéodory, Helly and the Others in the Max-Plus World

Carathéodory’s, Helly’s and Radon’s theorems are three basic results in discrete geometry. Their max-plus or tropical analogues have been proved by various authors. We show that more advanced results in discrete geometry also have max-plus analogues, namely, the colorful Carathéodory theorem and the Tverberg theorem. A conjecture connected to the Tverberg theorem—Sierksma’s conjecture—although still open for the usual convexity, is shown to be true in the max-plus setting.     

The welfare effects of public opinion polls

This paper presents an experimental study of the effects of polls on voters’ welfare. The analysis shows that polls have a different effect on closely divided and lopsided divided electorates. The data show that in closely divided electorates (and only for these electorates) the provision of information on the voters’ distribution of preferences significantly raises the participation of subjects supporting the slightly larger team relative to the smaller team. This causes a substantial increase on the frequency of electoral victories of the larger team. As a consequence, we observe a steep decrease in the welfare of the members of the smaller team because they vote more often and yet they loose the elections more frequently. Polls are detrimental to aggregate welfare in closely divided electorates because the decrease in the payoffs of the minority is stronger than the increase in the payoffs of the majority. In lopsided divided electorates polls don’t have a significant different effect on the voters’ turnout conditional on their team size. We do observe an increase on the frequency of electoral victories of the larger team after the provision of information, but this is in part due to smaller teams’ members voting less frequently and saving the participation costs. As a consequence, while polls have a negative effect on the relative payoffs of the minority for these electorates as well, they have a positive effect on total welfare.     

Infinite highly connected planar graphs of large girth

We construct infinite planar graphs of arbitrarily large connectivity and girth, and study their separation properties. These graphs have no thick end but continuum many thin ones. Every finite cycle separates them, but they corroborate Diestel’s conjecture that everyk-connected locally finite graph contains a possibly infinite cycle — see [3] — whose deletion leaves it (k — 3)-connected.     

A bilevel fuzzy principal-agent model for optimal nonlinear taxation problems

This paper presents a bilevel fuzzy principal-agent model for optimal nonlinear taxation problems with asymmetric information, in which the government and the monopolist are the principals, the consumer is their agent. Since the assessment of the government and the monopolist about the consumer’s taste is subjective, therefore, it is reasonable to characterize this assessment as a fuzzy variable. What’s more, a bilevel fuzzy optimal nonlinear taxation model is developed with the purpose of maximizing the expected social welfare and the monopolist’s expected welfare under the incentive feasible mechanism. The equivalent model for the bilevel fuzzy optimal nonlinear taxation model is presented and Pontryagin maximum principle is adopted to obtain the necessary conditions of the solutions for the fuzzy optimal nonlinear taxation problems. Finally, one numerical example is given to illustrate the effectiveness of the proposed model, the results demonstrate that the consumer’s purchased quantity not only relates with the consumer’s taste, but also depends on the structure of the social welfare.     

Kvanvig on Pointless Truths and the Cognitive Ideal

Jonathan Kvanvig has recently attempted to reconcile the problem of (apparently) pointless truths with the claim that the value of truth is unrestricted—that truth is always and everywhere valuable. In this paper, I critically evaluate Kvanvig’s argument and show it to be defective at a crucial juncture. I propose my own alternative strategy for generating Kvanvig’s result—an alternative that parts ways with Kvanvig’s own conception of the cognitively ideal.     

Investment under ambiguity with the best and worst in mind

Recent literature on optimal investment has stressed the difference between the impact of risk and the impact of ambiguity—also called Knightian uncertainty—on investors’ decisions. In this paper, we show that a decision maker’s attitude towards ambiguity is similarly crucial for investment decisions. We capture the investor’s individual ambiguity attitude by applying α-MEU preferences to a standard investment problem. We show that the presence of ambiguity often leads to an increase in the subjective project value, and entrepreneurs are more eager to invest. Thereby, our investment model helps to explain differences in investment behavior in situations which are objectively identical.     

Dancy Cartwright: Particularism in the philosophy of science

This paper aims to explore the space of possible particularistic approaches to Philosophy of Science by examining the differences and similarities between Jonathan Dancy’s moral particularism—as expressed in both his earlier writings (e.g., Moral Reasons, 1993), and, more explicitly defended in his book Ethics without Principles (2004)—and Nancy Cartwright’s particularism in the philosophy of science, as defended in her early collection of essays, How the Laws of Physics Lie (1983), and her later book, The Dappled World: A Study of the Boundaries of Science (1999). I shall argue that Dancy’s particularism is more radical, but also more plausible, than Cartwright’s, concluding that we have good reason to embrace a scientific particularism that is far closer to Dancy’s ethical particularism than any view defended by Nancy Cartwright, or any other philosopher from the ‘Stanford school’ of scientific theory.     

Evaluating the performance of Brazilian university hospitals

In order to demonstrate how DEA modeling can be helpful to aid decision making relative to the Brazilian Teaching Hospital Policy by means of hospital performance assessment, we develop a case study with 30 general hospitals linked to Brazilian Federal Universities. We consider data on medical care (Medical Model—MM), teaching and research (Teaching-Research Model—TRM) and use the software IDEAL (Interactive Data Envelopment Analysis Laboratory) as a tool for the units’ efficiency evaluation. IDEAL, developed in Brazil, is unique in providing a 3-D frontiers visualization, assisting in exploratory analysis and allowing a better understanding of the DEA modeling (envelopment and multiplier). Both models are input-oriented and each hospital is categorized according to its relative efficiency in the MM and TRM. In this phase, it is very important to discuss with the decision-makers the results and patterns of the DEA models. Finally, the modelling indicates the necessary changes for the inefficient units and generates recommendations for teaching ratios and public financing.     

Reasons and passions

Jonathan Dancy has argued that agents’ reasons for their actions are facts or features of the situations rather than their psychological states. The purpose of the paper is to show that even if we grant that this is so in most of the cases, there is a class of mental states that can be reasons. Although beliefs and desires are not reasons for actions, some emotional states—like loving, liking or disliking someone—can generate reasons. The distinctive feature of these states is that their content is a particular, and not a proposition. Hence in certain situations their love or admiration can provide agents with reasons to do one particular thing rather than another.     

Networks metrics and ball possession in professional football

This study aimed to verify the network of interactions resulting from the collective behavior of professional football teams and the influence of ball possession. A dataset of 30 matches of one highly successful team from the Portuguese Premier League, season 2010/2011, was considered. From these 30 matches, 13,958 passes (e.g., 11,127 successfully passes and 2831 unsuccessfully passes) and 7583 collective offensive actions were analysed. The data were analysed using Node XL Template that allows to characterize networks and team activity profiles. The results showed that football players' interactions tended to occur, preferentially, during the offensive phase, wherein the network of contacts was mainly organised in the central and lateral areas of the field. We concluded that the ball possession during a football match endows the team with a larger domain in terms of game actions. Moreover, the results of this study also allow concluding that the ball possession does not significantly influence the final outcome of the game. This study has practical implications for coaches, since it provides a multidimensional analysis of the football match (e.g., networks and ball possession) and offers relevant insights on how creative and organizing individuals might act to orchestrate team strategies. © 2016 Wiley Periodicals, Inc. Complexity 21: 342–354, 2016     

Algebras that satisfy Auslander’s condition on vanishing of cohomology

Auslander conjectured that every Artin algebra satisfies a certain condition on vanishing of cohomology of finitely generated modules. The failure of this conjecture—by a 2003 counterexample due to Jorgensen and Şega—motivates the consideration of the class of rings that do satisfy Auslander’s condition. We call them AC rings and show that an AC Artin algebra that is left-Gorenstein is also right-Gorenstein. Furthermore, the Auslander–Reiten Conjecture is proved for AC rings, and Auslander’s G-dimension is shown to be functorial for AC rings that are commutative or have a dualizing complex.     

The planar algebra associated to a Kac algebra

We obtain (two equivalent) presentations — in terms of generators and relations — of the planar algebra associated with the subfactor corresponding to (an outer action on a factor by) a finite-dimensional Kac algebra. One of the relations shows that the antipode of the Kac algebra agrees with the ‘rotation on 2-boxes’.     

Euler’s constant, q-logarithms, and formulas of Ramanujan and Gosper

The aim of the paper is to relate computational and arithmetic questions about Euler’s constant γ with properties of the values of the q-logarithm function, with natural choice of~q. By these means, we generalize a classical formula for γ due to Ramanujan, together with Vacca’s and Gosper’s series for γ, as well as deduce irrationality criteria and tests and new asymptotic formulas for computing Euler’s constant. The main tools are Euler-type integrals and hypergeometric series. 2000 Mathematics Subject Classification Primary—11Y60; Secondary—11J72, 33C20, 33D15 The work of the second author is supported by an Alexander von Humboldt research fellowship Dedication: To Leonhard Euler on his 300th birthday.     

Measuring and investigating strategic knowledge about drawing to solve geometry modelling problems

We report on the construction, validation, and implementation of an instrument for measuring students’ strategic knowledge about drawing for geometry modelling problems, namely, the strategic knowledge about drawing scale. We conducted a qualitative study and a quantitative study to validate the proposed construction and interpretation of the scale and to obtain initial findings on students’ strategic knowledge about drawing. Results showed that ninth-grade students in the intermediate achievement track had less elaborated strategic knowledge about drawing than their peers in the high achievement track. Further, strategic knowledge about drawing was found to be related to drawing accuracy and modelling performance even when cognitive abilities and interest were controlled for. The current study suggests that promoting strategic knowledge about drawing might be a means to increase drawing and modelling performance—especially among non-high-achieving students.