Modeling Pitch Trajectories in Fastpitch Softball

The fourth-order Runge–Kutta method is used to numerically integrate the equations of motion for a fastpitch softball pitch and to create a model from which the trajectories of drop balls, rise balls and curve balls can be computed and displayed. By requiring these pitches to pass through the strike zone, and by assuming specific values for the initial speed, launch angle and height of each pitch, an upper limit on the lift coefficient can be predicted which agrees with experimental data. This approach also predicts the launch angles necessary to put rise balls, drop balls and curve balls in the strike zone, as well as a value of the drag coefficient that agrees with experimental data. Finally, Adair’s analysis of a batter’s swing is used to compare pitches that look similar to a batter starting her swing, yet which diverge before reaching the home plate, to predict when she is likely to miss or foul the ball

Measuring Systems Engineering Success: Insights from Baseball

Optimizing the efficiency of socio-technical systems and determining accurate measurements of performance is a critical issue in many systems engineering enterprises. In our analysis we explore some of the recurring themes of Michael Lewis’s study of baseball, depicted in the best selling book Moneyball, and we make the connection to corresponding systems engineering principles of interest. The paper will focus on the systems engineering roadmap inspired by Lewis’ study for developing and refining a meaningful set of metrics for organizational transformation. The following steps are highlighted to convey this transformation with the assistance of metrics: identify and understand value in the enterprise and your organization; consider an integrated system focus in your organization; use cost analysis methods to implement a strategy for executing the transformation; and manage risk throughout operations and improve the process continuously

Mixed Tournaments, Common Shocks, and Disincentives: An Experimental Study

Two well-known hypotheses from the literature on tournaments are that (1) tournaments can filter out common shocks thereby reducing agents risk exposure; and (2) disincentive effects can arise when a tournament scheme is administered on a group of mixed ability agents. While handicapping and/or the creation of homogeneous groups have been suggested as mechanisms for mitigating disincentive effects, it is often impractical to use handicapping schemes and nearly impossible to create a completely homogeneous labor force. Hence, contract administrators who intend to use tournaments to elicit effort must be able to assess the positive effects of tournaments (eliminate common shocks) against the negative effects (disincentive effects). Using economic experiments, we find evidence of disincentive effects under tournaments, although these effects are not as strong as predicted. Moreover, tournaments can be effective at reducing earnings variability when common shocks are important. These results suggest that the benefits of risk reduction from eliminating common shocks might outweigh the disincentive effects arising from mixed tournaments.mixed tournaments, incentives, relative performance contracts, experimental economics, Research Methods/ Statistical Methods, C91 D01, D81, D82, D86,

Why do firms fail to engage diversity? A behavioral strategy perspective

The persistent failure of organizations to engage diversity—to employ a diverse workforce and fully realize its potential—is puzzling, as it creates labor-market inefficiencies and untapped opportunities. Addressing this puzzle from a behavioral strategy as arbitrage perspective, this paper argues that attractive opportunities tend to be protected by strong behavioral and social limits to arbitrage. I outline four limits—cognizing, searching, reconfiguring, and legitimizing (CSRL)—that deter firms from sensing, seizing, integrating, and justifying valuable diversity. The case of Moneyball is used to illustrate how these CSRL limits prevented mispriced human resources from being arbitraged away sooner, with implications for engaging cognitive diversity that go beyond sports. This perspective describes why behavioral failures as arbitrage opportunities can persist and prescribes strategists, as contrarian theorists, a framework for formulating relevant behavioral and social problems to solve in order to search for and exploit these untapped opportunities

It\u27s Not About the Money: The Role of Preferences, Cognitive Biases, and Heuristics Among Professional Athletes

Professional athletes are often regarded as selfish, greedy, and out-of-touch with regular people. They hire agents who are vilified for negotiating employment contracts that occasionally yield compensation in excess of national gross domestic products. Professional athletes are thus commonly assumed to most value economic remuneration, rather than the love of the game or some other intangible, romanticized inclination. Lending credibility to this intuition is the rational actor model, a law and economic precept which presupposes that when individuals are presented with a set of choices, they rationally weigh costs and benefits, and select the course of action that maximizes their wealth, happiness, or satisfaction. Since athletes are generally presumed to most value financial compensation, they simply behave rationally by selecting the most lucrative offer. Intriguingly, however, for every apparent athletic mercenary, there appear to be many who significantly discount financial compensation. Indeed, for a variety of expressed motivations, professional athletes regularly select the non-optimal contract offer, at least in a traditional sense of optimality. Risk aversion and other deliberative strategies occasionally provide explanation, but more often explanatory is value in intangibles, such as loyalty, regional affinity, weather preferences, familiarity with certain teammates or coaches, prospects for team success, and demographic traits. A law and economic explanation for such behavior would illuminate the ranking of alternative preferences, and then, as reflected by choice, a maximization of such ranking. Put differently, by accepting a less remunerative offer, professional athletes may consciously substitute subjective value for objective value, and their choice simply reflects that which makes them most happy. Though diagrammatic in many instances, preferences may not universally explain decision-making among professional athletes. Indeed, like all individuals, professional athletes appear vulnerable to cognitive biases, which are subconscious mental errors triggered by simplified informational processes, and heuristics, which are convenient, if unfinished predictive cues. Though cognitive biases and heuristics enable individuals to manage a complex array of stimuli, they often distort preferences and adversely affect decision-making. For instance, because of confirmation bias, individuals are subject to ignore or discount information that challenges existing beliefs. Alternatively, optimism bias leads individuals to assume that general risks do not apply with equal force to themselves. In the context of professional sports, these and other cognitive distortions may impair not only the pursuit of objective value, but also rational assessment of subjective value. This is especially true when teams adroitly manipulate distortions, such as impressing illusory variances among themselves and other teams. Accordingly, when accepting a less remunerative offer, professional athletes may have unknowingly misinterpreted their preferences and rankings. To date, no published analysis has addressed the potential influence of behavioral tendencies on professional athletes in contemplation of contract offers. Perhaps this is not surprising, given the relative paucity of professional athletes among the general population, their presumptively unique modes of employment, and a general aversion among academics for the study of sports. A more scrupulous assessment of professional athletes, however, suggests a uniquely desirable group for examination. Indeed, aside from their striking influence on the world and economy around them, professional athletes, unlike most groups commonly studied by academics, furnish published commentary of their thought processes, typically through newspaper, television, and radio interviews. Accordingly, professional athletes offer a wealth of narration as to their values, beliefs, and priorities, and, equally important, such narration occurs in real world settings, rather than in experimental circumstances. Along those lines, by evading the alleged experimental flaw of many behavioral law and economic studies, analysis of decision-making among professional athletes may prove extraordinarily salient in the broader discussion of behavioral sciences and their influence on traditional law and economics. In pursuit of the above phenomena, this Article will begin by exploring the rational actor model, and how individuals utilize preferences in determining their optimal choice. This Article will then discuss limitations to the rational actor model, namely the role of cognitive biases and heuristics. Thereafter, this Article will canvass decision-making among professional athletes in contemplation of contract offers. In that regard, this Article will examine why some professional athletes pursue the most lucrative offer, while others do not, and to what extent cognitive biases and heuristics influence their decision-making. This Article will conclude by highlighting implications for professional sports and proposing recommendations for further analysis by economists, psychologists, and legal academics

Examples of Mental Mistakes Made by Systems Engineers While Creating Tradeoff Studies

Problem statement: Humans often make poor decisions. To help them make better decisions, engineers are taught to create tradeoff studies. However, these engineers are usually unaware of mental mistakes that they make while creating their tradeoff studies. We need to increase awareness of a dozen specific mental mistakes that engineers commonly make while creating tradeoff studies. Aims of the research: To prove that engineers actually do make mental mistakes while creating tradeoff studies. To identify which mental mistakes can be detected in tradeoff study documentation. Methodology: Over the past two decades, teams of students and practicing engineers in Bahill’s Systems Engineering courses wrote the system design documents for an assigned system. On average, each of these document sets took 100 man-hours to create and comprised 75 pages. We used 110 of these projects, two dozen government contractor tradeoff studies and three publicly accessible tradeoff studies. We scoured these document sets looking for examples of 28 specific mental mistakes that might affect a tradeoff study. We found instances of a dozen of these mental mistakes. Results: Often evidence of some of these mistakes cannot be found in the final documentation. To find evidence for such mistakes, the experimenters would have had to be a part of the data collection and decision making process. That is why, in this paper, we present only 12 of the original 28 mental mistakes. We found hundreds of examples of such mistakes. We provide suggestions to help people avoid making these mental mistakes while doing tradeoff studies. Conclusions: This paper shows evidence of a dozen common mental mistakes that are continually being repeated by engineers while creating tradeoff studies. When engineers are taught about these mistakes, they can minimize their occurrence in the future

What Law Schools Can Learn From Billy Beane and the Oakland Athletics

In Moneyball, Michael Lewis writes about a story with which he fell in love, a story about professional baseball and the people that play it. A surprising number of books and articles have been written by law professors who have had long love affairs with baseball. These books and articles are a two-way street, with baseball and law each informing and enriching the other. For example, law professors versed in antitrust, labor, property, tax, and tort law have brought their legal training to bear on particular aspects of baseball. Law professors also have mined their passion for baseball in extracting from the diamond lessons for the law in areas as diverse as The Common Law Origins of the Infield Fly Rule (and the almost cult-like following it spawned,) statutory construction, legal theory, comparisons of Supreme Court Justices to famous baseball players, and, our favorite, The Jurisprudence of Yogi Berra. Indeed, one commentator has called baseball and law “America\u27s Two National Pastimes.