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1 This article was downloaded by: [Deutsche Sporthochschule Koeln] On: 07 September 2012, At: 04:18 Publisher: Routledge Informa Ltd Registered in England and Wales Registered Number: Registered office: Mortimer House, Mortimer Street, London W1T 3JH, UK International Review of Sport and Exercise Psychology Publication details, including instructions for authors and subscription information: Simple heuristics in sports Markus Raab a a Institute of Psychology, German Sport University, Cologne, Germany Version of record first published: 09 Feb 2012 To cite this article: Markus Raab (2012): Simple heuristics in sports, International Review of Sport and Exercise Psychology, 5:2, To link to this article: PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.

2 International Review of Sport and Exercise Psychology Vol. 5, No. 2, September 2012, Simple heuristics in sports Markus Raab* Institute of Psychology, German Sport University, Cologne, Germany (Received 13 April 2011; final version received 21 December 2011) How do people make decisions under conditions of limited knowledge, time, and cognitive capacity in real-life situations such as sports? In this review I will introduce the concept of simple heuristics rules of thumb that are based on the building blocks of decision making: how to search for information, stop information search, and decide quickly and accurately and how they can help us understand the decisions made by athletes, coaches, referees, managers, and fans in tasks involving high uncertainty, such as predicting tournament outcomes, allocating balls to teammates, or determining when to buy or sell a talented player. I will present an adaptive toolbox of such heuristics, that is, a collection of strategies that work effectively in specific environments. Additional building blocks will be added to explain motor behavior itself, which is central to many sport applications. Finally, principles for studying the use of simple heuristics by people involved in sports will be presented to guide future applications. Keywords: decision making; simple heuristic; sport Simple heuristics in sports In our daily lives we encounter many situations in which, due to our limited resources, time, or cognitive capacity, we rely on simple decision strategies called heuristics, rules of thumb based on the building blocks of decision making: how to search for information, stop information search, and decide quickly and accurately. For instance, if you have never heard of the term simple heuristics and you type simple heuristic into your internet search engine, it will come up with roughly 6 million hits. Surely you will not read all of these hits but will search through the items from the top, knowing that the system lists the hits in decreasing order of fit to your search. After scanning some of the items you may stop when one appears to fit your search and examine the information it provides to determine if it satisfies your request. Thus for the choice which page to open a simple heuristic might be takethe-first-appropriate. Its building blocks would consist of a top-down search rule, a stopping rule of matching, and a choice rule of choosing the first matching page. To illustrate for the sports context, consider a basketball game in which the perspectives and decisions of the people involved are quite different. The playmaker must choose in milliseconds to whom to allocate the ball; the referee must decide in less than a second if the playmaker foot-touched the three-point line when shooting; the coach, within minutes, must decide whether to keep the playmaker on the court; the manager might have a week to decide whether to sell this playmaker and buy * raab@dshs-koeln.de ISSN X print/issn online # 2012 Taylor & Francis

3 International Review of Sport and Exercise Psychology 105 a new one; and the fan sitting at home thinks ahead to whether this playmaker will lead the team to win the championship, and if therefore a bet on that future outcome will be won. Because these different tasks, which occur on different timescales, require different kinds of heuristics, it is crucial to structure heuristics according to the tasks and the people who make the decisions. In this review I will summarize simple heuristics for the domain of sports, where recently different laboratories have applied the simple heuristics framework. Highlighting a set of heuristics that are used by different people in sports settings, I will present the current state of the art, discuss how applying the simple heuristics framework to sports requires extending the framework, and finally provide some principles for studying heuristics in sports in the future. This review will provide a new theoretical perspective on the behavior of athletes and others involved in sports that can describe, explain, and predict behavior more consistently and with fewer premises than alternative perspectives, such as ecological dynamics or computational approaches (e.g., Araújo, Davids, & Hristovski, 2006; Johnson, 2006), while using simpler principles. Simpler principles would seem particularly desirable for studying fast sport choices. As Moran (2009, p. 420) recently noted, given the limitations of the traditional information processing approach to the mind, cognitive sport psychology researchers should consider alternative theoretical perspectives postulated in cognitive psychology and cognitive neuroscience. Simple heuristics framework A heuristic has been defined as a strategy that ignores part of the information, with the goal of making decisions more quickly, frugally, and/or accurately than more complex methods (Gigerenzer & Gaissmaier, 2011, p. 454). Complex methods, in comparison, would be tools from logic or statistics that use many pieces of information, weighting them to come to a decision. The debate on whether for specific tasks a simpler or more complex method is advantageous has spread to the domain of sports. For instance, Bennis and Pachur (2006) described situations in sports in which simple heuristics could have been applied and would have predicted the same or better sport choices than more complex models. Such simple heuristics can rely on the concept that less can be more, as when a simpler decision strategy outperforms a more complex one (Glöckner, Heinen, Johnson, & Raab, 2011), or when fewer fixations provide good choices (Williams & Ward, 2007), or having fewer options results in appropriate decisions (Raab & Johnson, 2007). This less-is-more benefit (described in more detail below) is connected to the idea that humans do not maximize (i.e., consider all options) but rather satisfice (i.e., consider one or a few options to reach an adequate, rather than the optimal solution; Simon, 1956). Evidence against pure rational behavior and supporting less-is-more behavior has been found in many other decision situations sharing similar dynamics with sports, such as medical treatment decisions (Wegwarth, Gaissmaier, & Gigerenzer, 2009), investment decisions in the stock market (Boyd, 2001), and bail decisions in courts of law (Dhami & Ayton, 2001). The heuristics that have been suggested in other environments with potentially highly similar behaviors, such as emergency rooms, fire scenes, and military situations, have not been applied to sports. Overviews on applied heuristics have not included sports as a domain of study (e.g., Koehler & Harvey, 2004; Todd & Gigerenzer, 2012).

4 106 M. Raab The range of heuristics we have at our disposal has been called the mind s adaptive toolbox, from which we are able to select the best tool, or strategy, for a given task in an uncertain world (Gigerenzer, Todd, & the ABC Research Group, 1999). Each simple heuristic is composed of building blocks that define how to search for information, how to stop information search, and how to decide between two or more options. These building blocks can be combined in multiple ways to describe behavior. For illustration, consider a well-known and very simple rule of thumb in cognitive science: the recognition heuristic. It states that in the case of two options (e.g., which city has more citizens, Kappeln or Berlin?), where one option is recognized and the other not, choose the option that is recognized. The recognition heuristic has been applied to many domains (Gigerenzer, Hertwig, & Pachur, 2011), has been modeled formally (Goldstein & Gigerenzer, 2008), and is neurophysiologically supported (Volz et al., 2006). Recently it was applied in the sports domain to predict who would win at Wimbledon. Participants in an experiment using the recognition heuristic predicted the recognized player would win the next match with an accuracy of 70% (Scheibehenne & Bröder, 2007). Obviously this heuristic cannot be applied if the options, in this case the players, are both known or both unknown. In the sports domain, simple heuristics are rules of thumb that allow athletes, coaches, referees, managers, or fans to make efficient decisions under internal and external constraints. When focusing primarily on the fast choices of athletes, internal constraints would be attention and memory limits and external constraints would be time pressure and options available. Recently, specific building blocks for search, stopping, and decision rules in sports behavior have been studied extensively. For instance, search rules have been compared using the gaze behavior of athletes, such as the amount or duration of fixations or sequence patterns, as a variable (Glöckner et al., 2011). Stopping rules have been studied in coaches, looking at whether they rely on further cues than the base rate of a player to define allocation strategies for playmakers (Raab, Gula, & Gigerenzer, 2011). Finally, decision rules have been tested in athletes by examining whether they prefer the first or last generated option as the final choice in an optiongeneration paradigm (Raab & Johnson, 2007). Whether a heuristic is effective is a matter of how well it fits the information structure of the environment, that is, its so-called ecological rationality (Gigerenzer et al., 1999). Ecological rationality means that heuristics are not good or bad per se, but only relative to their environment. Their success depends on being matched to the structure of a particular environment; thus heuristics are embodied and situated, able to exploit the core capacities of the brain (Gigerenzer & Gaissmaier, 2011). Heuristics are therefore perfectly suited to being applied in the uncertain, complex, and dynamic domain that is sports. There are many situations in sports where rules of thumb might lead to better choices. However, we have limited knowledge to guide athletes in deciding within milliseconds whether to shoot to the basket or pass to a teammate, to aid coaches in choosing their starting team for a weekend competition, to help referees recognize fouls, and to assist managers in deciding whom to buy or sell. From this list of tasks it is obvious that situations vary on many dimensions, such as the time available for a decision, the decision s importance, or whether it is part of a sequence of behaviors. Given this array of situations, researchers in the simple heuristics framework have suggested that humans are equipped with or have developed a number of heuristics

5 International Review of Sport and Exercise Psychology 107 and core capacities. Core capacities are the general abilities, such as working memory, used by heuristics. Advanced capacities, such as a large working-memory span, can affect the use of heuristics (Bröder, 2003; Gaissmaier, Schooler, & Mata, 2008). For instance, in sports a large working-memory capacity may influence a playmaker s allocation strategy given that she can use a different amount of information compared to a playmaker with a smaller memory span. Furthermore, specific attributions a person has learned could impact heuristics use, such as stereotype threat (Beilock, Jellison, Rydell, McConnell, & Carr, 2007). Scope of the review and application to sports In this review I consider applications to sports of heuristics previously explored in cognitive science, addressing the lack of alternative theories mentioned above (e.g., Moran, 2009). I will not reiterate the current dominant viewpoints and theories from the related cognitive literature that extend or are in contrast to simple heuristics, focusing instead purely on sports (see Hammond, 1990, and Stanovich & West, 2000, for overviews and debates in cognitive science). In sports, heuristic is broadly interpreted. For instance, referees have been said to use gender as a heuristic cue in their decisions (Souchon et al., 2010), and orienteers have been said to use heuristic reasoning in planning routes (Eccles, Walsh, & Ingledew, 2002). These examples do not fit the full definition of heuristics as formal descriptions of simple decision strategies, as they refer solely to the description of information or cues used for achieving an outcome. The definition I use requires us to define formal models of heuristics from building blocks that specify how the information is processed. Previous reviews have provided a list of such heuristics applied in different domains (Raab & Gigerenzer, 2005) and presented as different forms of choices, such as social or moral, and in recognition-based decisions (Gigerenzer & Gaissmaier, 2011). In this review I focus on what is known and what should be known about simple heuristics in sports by the people who use them the athletes, coaches, referees, managers, and fans. Looking at heuristics from the perspectives of the various people involved in sports allows us to examine the different behaviors simple heuristics are meant to capture and apply the theoretical concept to specific sport situations. Athletes It is clear from the basketball example above that the different people involved in sports have different tasks, and that the decisions they make differ greatly in their importance and in how quickly they must be made. For the purpose of contrasting with the temporally more leisurely choices made by managers and coaches, I will focus here on athletes quick decisions involving sensorimotor behavior. The most researched simple heuristics for allocation decisions are take-the-first and take-thebest (Bennis & Pachur, 2006). These heuristics and others described below are applied, for instance, when playmakers must choose quickly from a number of options, such as whether to pass the ball (and if so, to whom) or shoot to the basket. Take-the-first is simply this: choose the first alternative that comes to mind (Raab & Johnson, 2007). Empirical evidence has shown that between 60 and 90% of athletes decisions meet the description of take-the-first in basketball, Australian football, and team handball (Farrow, 2011; Hepler & Feltz, 2011; Johnson & Raab,

6 108 M. Raab 2003). In more detail, it has been shown that the search pattern uses option similarity for search (Raab & Johnson, 2007). Search starts with the first appropriate option (Glöckner et al., 2011); stop is modulated by a preference for intuitive decision making and is often realized after two or three options (Raab & Laborde, 2011). In addition, the number of options generated can be modulated by mood (Laborde & Raab, 2011). The take-the-best heuristic describes searches for cues in the order of their cue validity. Cue validity indicates the proportion of correct choices relative to all choices if this specific cue is used. Search stops when one object has a positive cue value and the other does not, and the object with the positive cue value is chosen. For instance, our basketball player choosing which teammate to pass to may consider cues such as the teammates distance to the basket, distances of defense players to the teammates, average base rate of players or players recent performance (e.g., evidence of a hot hand ; Gilovich, Vallone, & Tversky, 1985). It has been shown that playmakers rank these cues such that they rely on the hot hand cue first and then use a probabilistic matching function based on players base rates (Raab et al., 2011). In a computer experiment, playmakers in volleyball chose between two players who varied in the hotness of their performance sequence and/or their base rate. Participants in this experiment allocated the balls in pseudorandom sequences to the players matching their base rates. However, when the base rates favored one player but the other player s recent performance was higher, participants preferred more allocations to the player with the hot hand (Raab et al., 2011). The combination of heuristics and core capacities in complex behaviors has rarely been studied empirically (but see Raab, Masters, & Maxwell, 2005). Research on athletes heuristics has also varied on the extent to which descriptions are formalized and on whether different heuristics are compared to each other. For instance, Eccles et al. (2002) found two heuristics that expert and novice orienteers use in route planning. Experts searched backward from the control (the point that must be located) to the start of a route. The search strategy was reversed for novices. The authors did not identify the building blocks of the heuristics or formalize their descriptions so they could be used to predict athletes behavior. As mentioned above, such conceptualizations seem to treat the term heuristic as synonymous with cue use. Coaches In basketball, coaches tasks include decisions about strategy, player replacement, and time outs, to name just a few. Here I will focus on coaches judging the performance of their own players over a longer period, that is, over the course of a game. Heuristics for coaches have been prominently discussed in the general literature on sports coaching but have not been experimentally tested or formally modeled (e.g., Lyle, 2002, p. 136), with the exception of studies that demonstrated specific problem-solving and information-selection strategies (e.g., Hagemann, Strauß, & Büsch, 2008). Again, the identified heuristics were not formally described or empirically tested against competing strategies. Empirical tests of competing strategies of coaches have been recently tested in a study of sequential decisions using hot hand beliefs (Raab et al., 2011). The coaches were asked to watch a volleyball match and produce instructions for the playmakers. Unbeknown to the

7 International Review of Sport and Exercise Psychology 109 coaches, the sequence structure of two players who had the same performance (equal base rates) varied only in their sequences of three hits in a row. Coaches used a simple heuristic that relies on the sequence information to decide whether a specific player should receive more balls from the playmaker. Referees and judges Sports officials include referees, who often make split-second judgments of rule violations, and judges, who rate athletes performances. Both have recently become the subject of interest in heuristics research. For instance, Souchon et al. (2010) found that referees making split-second decisions seem to apply heuristic strategies to reduce the complexity of the situation. Other researchers have argued that using cues leads them to wrong decisions (Nevill, Balmer, & Williams, 2002); still others have focused more on the beneficial aspects of heuristic use (Dosseville, Laborde, & Raab, 2011). Concerning biases, crowd noise was found to influence the decisions of soccer referees in favor of the home team (Downward & Jones, 2007; Nevill et al., 2002). Others found that cues used to call penalties or give yellow cards continued to influence subsequent decisions, resulting in bias (Plessner & Haar, 2006; Unkelbach & Memmert, 2008). Another bias is rooted in perception, such as when a linesman s perception of whether a soccer player is offside is influenced by the linesman s own position on the field (Baldo, Ranvaud, & Morya, 2002; Oudejans et al., 2000). Finally it has been shown that referees sometimes use irrelevant cues, such as when they attribute more foul calls to teams wearing black uniforms (Frank & Gilovich, 1988) or award more points to combat sport participants wearing red (Hagemann, Strauß, & Leißing, 2008). As these biases should be avoided, strategies have been developed to train referees to optimize their behavior (Bar-Eli, Plessner, & Raab, 2011; Catteeuw, Gilis, Wagemans, & Helsen, 2010). Concerning the positive use of cues, it has been shown that judges can use simple heuristics to perform with less bias (Schweizer, Plessner, Kahlert, & Brand, 2011). For instance, there have been indications that judges who themselves have motor experience in gymnastics make better judgments of movements on the balance beam (Pizzera, in press). These studies showing that crowd noise, reprimands, position on the field, and even color can bias referees decisions in sports shed light on what cues referees and judges may use. However, they fail to describe the specific building blocks of the heuristics; we still know little about how the process that leads from perception to choice is implemented. Managers and fans The tasks of managers and fans in the basketball example are quite different, as each group has only a limited set of choices during a game. Given the scant research that has been done and the limited decisions they make during actual games, I will present them together. Sports managers and fans are often analyzed by economists who are interested in the choices they make from a behavioral economics perspective. This perspective often results in complex but formally described models that try to maximize the

8 110 M. Raab outcome for each decision of a manager (e.g., buying/selling players) or fan (e.g., betting on a team). This is a quite different approach from that of the simple heuristics program, as discussed elsewhere (e.g., Bar-Eli & Azar, 2009). There have been no research programs on heuristics use in sport managers or fans. For instance, heuristics for making policy or individual decisions have been proposed (e.g., Chalip, 1995), but neither a coherent description of these heuristics nor a formalization has been developed. The situation is somewhat better for fans. For instance, the hot hand phenomenon has been studied among fans as well as in players, and it has been shown that fans judge whether a player is hot. They rely on simple heuristics, such as comparing the current performance of a player to the player s average performance, as opposed to comparing the performance to other players performances or to chance (Raab et al., 2011). A further line of research on the betting behavior of fans (or bettors) has shown that fans use simple heuristics when predicting the chance of a team winning (Gröschner & Raab, 2006). Gröschner and Raab (2006) asked participants before the 2002 World Cup in soccer to predict the matches in the group phase, and in another study in the same paper to predict the individual outcomes of all games for the next season of the German Football League. For each presentation of two teams the authors provided the participants with a number of cues from the previous season, such as rank in the final standings, winning percentage, home advantage, and goals scored. The choices of the participants could be best modeled by very simple heuristics, such as take-the-last-ranking, which uses the rank from the previous season or World Cup. Concerning the predictions of the league games, the team predicted to win was the one with the higher memorized or presented rank; if both teams had earned the same number of points (or in the World Cup did not pass beyond the group phase) the heuristic predicted a draw. Studies have shown that experts (in terms of their knowledge of soccer or betting) were not better than novices (Andersson, Memmert, & Popowicz, 2009; Cantinotti, Ladouceour, & Jacques, 2004), an example of the less-is-more effect. Elsewhere, the recognition heuristic explained why Turkish fans predicted English Premier League games more accurately than English soccer fans did (Ayton, Önkal, & McReynolds, 2011). A limitation of most of these studies is that outcome comparisons of experts and novices have been provided, rather than heuristic descriptions of their choices. Table 1 lists the heuristics applied to sports or developed in sports so far. Beyond the need for further empirical evidence for or against the use of heuristics in sports, the framework itself needs to be evaluated in reference to its limitations and in comparison to other theories. Limitations of the framework and comparisons The simple heuristics framework, as demonstrated above, has been applied to sport situations, but relatively rarely. Research on simple heuristics and empirical tests have long been carried out in the laboratory, where options and cues can be clearly defined. Recently, however, researchers have become interested in studying heuristics in the wild (Gigerenzer et al., 2011), yet not in the domain of sports, even though, as argued above, this domain provides an appropriate test bed and reasonable boundaries for such an approach. What would be gained by doing so? Athletes and others involved in sports would learn how heuristics can aid their decisions, and researchers would extend their knowledge of the generalization of simple heuristics.

9 Table 1. Heuristics and their sports applications. International Review of Sport and Exercise Psychology 111 Heuristic Search Stop Decision Application Recognition heuristic (Pachur & Biele, 2007) Take-the-best heuristic (Todorov, 2001) Take-the-first heuristic (Raab & Johnson, 2007) Take-the-lastranking heuristic (Gröschner & Raab, 2006) Search for option that is recognized Search through cues in order of validity Generate options in the order of validity Search for cues from previous success of a team or player Stop search if only one option is recognized Stop search as soon as a cue discriminates Stop after two or three options that can be implemented Stop search as soon as a previous success cue is found Choose the recognized option as being higher on cue validity Choose the alternative this cue favors Choose the first option generated Choose the team or player that has a higher rank; if ranks are equal predict a draw Sports betting, allocation in pick-up games Fans sports betting, athletes allocation, managers sell/ buy choices Athletes allocation choices, coaches replacement decisions Fans sports betting Note: See Raab and Gigerenzer (2005) and Gigerenzer and Gaissmaier (2011) for a list of heuristics in cognitive science. Yet before a more complex research enterprise is established, it seems important to describe the limitations of the approach in the sports domain. From there the framework can be discussed and compared to other theories in sports research. Limitations In recent reviews of the simple heuristics program, developments and challenges have been described that apply to the domain of sports (see Gigerenzer & Gaissmaier, 2011, for a general description). First, the simple heuristics program in the domain of sports is a new enterprise. Therefore empirical evidence and a list of heuristics and their fit to specific tasks, persons, and situations are still being assembled. Future efforts should focus on building testable heuristics in many sports applications and comparing them to alternative models. As the simple heuristics program is merely applied to cognitive tasks, sensorimotor behavior has yet to be explored. As introduced above, a number of questions have not been empirically explored. For instance, how do the decisions of people in sports change over their lifetime? How do they learn to use only important cues? How do they decide among possible heuristics? Are there any behaviors in the domain of sports where heuristics cannot be applied or where they systematically predict poorer performance than more complex models? How are heuristics built from core capacities in perception, cognition, and action? An important extension of the cognitive science program of simple heuristics to sports is the integration of building blocks that refer to the perceptual-motor system. In the above examples of athletes and referees, many choices are made in split

10 112 M. Raab seconds while fatigued or running fast in a dynamically changing environment. Simple heuristics have been criticized for being unable to describe such perceptual or motor levels of behavior and they do not describe very high forms of cognition well either, such as creativity (Gigerenzer et al., 1999). However, researchers have recently started to combine building blocks of search and execution to explain complex movements (Raab et al., 2005). Another required extension of the simple heuristics program should be based on the tasks people in sports need to solve. For instance, in most experimental applications of heuristics in cognitive science, the number of options is quite restricted, usually to two or three. Furthermore, the available options are usually predetermined and the sequence of choices does not matter much. As demonstrated in the basketball example, the athletes tasks, the information available to them, the time available to process that information, and the dynamics of the situation require a new set of heuristics to be developed in sports. Finally, sports settings are a complex, social, naturalistic environment primed to test simple heuristics under specific temporal and social parameters. For instance, most decisions are made in group settings or even by the group itself. Therefore issues of social learning, punishment, conformity, and competition are present, and social decisions tend to be the default. Comparison to other theories Any theory that proposes to describe or explain human behavior needs to be tested against other theories to be considered valid. One simple test would be to compare how well different models fit and predict individual behavior. Based on the principle of Occam s razor (Ariew, 1976), if two models predict the same amount of behavior or explain the same amount of variance, then the simpler model should be preferred. In practice, this is not so easy, as different models explain different dimensions of behavior and have different purposes (Pitt, Myung, & Zhang, 2002). For instance, in a recent overview of theories that could be applied to sport behavior in the context of judgment and decision-making processes, Bar-Eli et al. (2011) presented 264 potential theories, of which about 12 have so far been applied (Bar-Eli & Raab, 2006). Comparisons of the models derived from the theories used in sports to date are limited by the small number of theories and are restricted to a few dimensions. In order of simplicity I will focus on prototypical theoretical candidates an ecological dynamics approach from Araújo et al. (2006), a computational approach from Johnson (2006), and a simple heuristics approach from Raab and Gigerenzer (2005) to describe choices in sports. In short, the ecological dynamics approach describes a choice as relaxing the performer-environment system to the most attractive state in the potential landscape (Araújo et al., 2006, p. 662). For example, in a decision to start either on the left or the right side (two attractor states) of a starting line of a sailing regatta, the parameter wind direction is used in a function to explain or predict the probability of a sailor choosing the left or right side (Araújo et al., 2006). In the computational approach (see Johnson, 2006, p. 646 for parameters and equations), a decision is a result of a deliberate sequential sampling process. In this case, wind direction and other parameters (parameter importance defined by attention shifts) are sampled over time until a threshold of preference for

11 International Review of Sport and Exercise Psychology 113 one option is met that triggers the execution of the preferred option. In the simple heuristics approach (Raab & Gigerenzer, 2005) a choice is based on a sequence of search, stopping, and decision rules. Cues are searched for in order. If wind direction is the most valid information and the cue differentiates between the two options (left or right side of the starting line), search is stopped and the option with the higher or positive cue value is selected (see Bar-Eli et al., 2011, for extended comparison). I will use a limited number of dimensions for comparison (see Bar-Eli & Raab, 2006, for a two-dimension comparison of about 12 theories in sports science): (1) whether a behavior model is static, dynamic, or both. Static models are those that propose that all behavioral options are considered at the same time, and thus no time is modeled; (2) the nature of the model, that is, whether it is deterministic, probabilistic, or both. Probabilistic models predict different outcomes by assigning a probability to each option, whereas deterministic models predict one outcome; (3) the underlying personenvironment relationship; (4) the level of description; and (5) the prediction and explanation of empirical findings. Model characteristics The ecological dynamics model, the computational model, and the simple heuristics model are all dynamic in the sense that they describe processes rather than pure outcome of behavior in sports. The models under consideration differ in how they implement dynamics, using, for instance, a linear neural network approach (Glöckner et al., 2011), a nonlinear ecological dynamics approach (Araújo et al., 2006), or a nonlinear dynamical computational approach (Johnson, 2006). Nature of the model The models can be categorized as either deterministic or probabilistic. The simple heuristics approach is more deterministic and computational theory is more probabilistic, whereas the ecological dynamics model uses both approaches in its process description. However, any model can be transformed to any of these approaches. For instance, Glöckner et al. (2011) showed a transformation of deterministic to probabilistic in the same class of model by transforming a preferred choice to a probabilistic function of different options. The personenvironment relationship The models can be compared on the type of link between the person and the environment. The ecological dynamics approach (Araújo et al., 2006) emphasizes a much more direct link between the person and the environment than the computational (Johnson, 2006) or simple heuristics (Raab & Gigerenzer, 2005) approach. Level of description A further notable difference lies in the levels of description used. For instance, some mathematical description has been included in the application of the ecological

12 114 M. Raab dynamics approach to decision making in sports (Araújo et al., 2006); mathematical description has been more prominent in the computational approach (Johnson, 2006), and it is now beginning to be explored in simple heuristics (Glöckner et al., 2011). Neurophysiological correlates are still absent in most of the approaches and the simple heuristics approach is still limited to arm movements (Hill & Raab, 2005) or pure cognitive tasks (Volz et al., 2006). Empirical findings The first four dimensions refer to preferences in the theoretical framework that cannot be empirically tested. The fifth line of comparison discussed here is the models ability to predict and explain empirical findings. For instance, for the takethe-first heuristic we can demonstrate different predictions for option generation. Current models assume a pure recognition-primed decision that requires coming up with only one option (perception-action; Klein, 1997), generating a few options until a satisficing option is found (simple heuristics; Johnson & Raab, 2003), and finding all appropriate options based on a long-term working-memory model (LTWM) (computational approach; North, Ward, Ericsson, & Williams, 2011). Whereas take-the-first predicts a negative relationship between number of options generated and choice quality, a LTWM predicts the inverse relationship. There is empirical evidence for all the models and future research should evaluate what role personal, task-specific, or situation-specific factors play in these differences. More importantly, the generalization of take-the-first across different cross-sectional, longitudinal designs using different sports, paradigms, and expert groups indicates that it is a robust mechanism, one that has also been studied in applications outside sports, such as nursing (Whyte, Ward, & Eccles, 2009), navigation (Conlin, 2009), law (von Helversen & Rieskamp, 2009), medicine (Wegwarth et al., 2009), consumer choice (Nordgren & Dijkstershuis, 2009), and engineering (Simpson, 2008). Another line of comparison is whether a new theory can explain previous findings or is able to produce new hypotheses. For illustration, consider the empirical evidence that experts, compared to novices, have longer fixation durations and a lower number of fixations in a sport choice task, whereas in other experiments in the same sport the opposite has been found (Williams & Ward, 2007). From the simple heuristics perspective, I would predict that search is based on the importance of the cues and their relationships. If one cue is more important than the sum of the other cues, experts can use this knowledge, which they gain from experience, and stop search after considering one cue. However, if choosing between options requires more cues, then experts should focus on different cues, and more of them, than novices. Thus empirical evidence that seems contradictory can be integrated in one explanation. In sum, the simple heuristics approach serves as a good starting point for studying phenomena in sports because (a) it captures how cues and decisions are linked by search, stopping, decision, and execution rules; (b) it provides, through the description of individual heuristics, a formal account of information use that can be simulated and described on a mathematical level; and (c) it is neurophysiologically plausible to assume that such heuristics and processes exist.

13 International Review of Sport and Exercise Psychology 115 Principles for future research There have been proposals for principles for building simple heuristics, but these need to be evaluated in the contexts of their application. A recently published fiveprinciple program that can be applied to sports (Marewski, Schooler, & Gigerenzer, 2010) consists of the following principles: (1) build precise models of heuristics; (2) test heuristics comparatively; (3) conduct comparative model tests guided by theories of strategy selection; (4) examine how well models of heuristics predict new data; and (5) test heuristics in the real world or guided by models of the world. Let us consider each principle for the domain of sports. Build precise models To build a precise model of a heuristic one needs to describe its building blocks, the kinds of problems it can solve, and in which situations it is successful, as well as the core capacities the heuristic exploits. When studying athletes, this would require combining search, stopping, and decision rules with execution rules. For instance, consider search rules. The search rule needs to describe what information is looked up in what order. This might be done by measuring gaze behavior. If search refers to memory, the memory structure and the search strategy within that structure need to be described. The definition of problems and successful applications are another challenge, as we are unable to test each heuristic in all sports. Rather, we may need to use skill taxonomies to predict whether a specific sport-related behavior can be modeled with one particular heuristic and not others. For instance, research on the information structure of the decision on where to place the next serve may produce a successful heuristic that is applicable to a tennis, table tennis, volleyball, or badminton serve, but the same heuristic would not be applicable to many other situations in the same sports. Another caveat of the simple heuristics program is the description of the core capacities a heuristic exploits. In a memory search for different options in a tactical attack situation, multiple core structures (e.g., working memory, long-term memory) as well as multiple processes (e.g., intuitive, deliberative) could be used. These proposed processes could be tested and modeled on the level of outcome (Johnson & Raab, 2003), mechanisms (Glöckner et al., 2011), or their neurophysiological base (Volz et al., 2006). For the domain of sports many applications have focused purely on the first level of description. It seems important to discuss whether we need mathematical models or neurophysiological correlates of sports behavior. Test heuristics comparatively Recently a simple heuristic model was contrasted with the parallel constraint satisfaction model on predicting choices from the gaze of playmakers in team handball (Glöckner et al., 2011). Such an approach is preferable to simply fitting data to one model or providing alternatives using only vague labels. For instance, to study whether a heuristic is applicable to coaches replacement decisions in a competition, one needs to identify competing models within the simple heuristics program or between heuristics and alternative models. We have only limited information on how a coach decides whether a current drop in an individual s

14 116 M. Raab performance should result in that player s replacement. One heuristic might propose that the coach uses only the most important information, such as the importance of victory in the current game, the player s current performance variability, or the average performance of that player compared to the best bench player. Another heuristic might suggest that the coach sets a threshold (say, three failures in a row) that serves as a stopping rule and leads to the decision to replace the player. Other, more complex and nonheuristic models would use all available cues, such as the average base rate of a player s performance, the local base rate of the player s performance in this game (or subsets of it), and comparisons to base rates of bench players. From a practical viewpoint such descriptions of replacement decisions and their appropriateness could help counteract many of the biases that have been described in sports science. Conduct comparative model tests Model comparisons should be informed by the theories of strategy selection. In sports many simple heuristics have naturally evolved (Bennis & Pachur, 2006). More complicated are cases of movement behavior that even counteract evolved mechanisms, such as when a volleyball defender needs to overcome the instinctive reaction to avoid a fast-approaching object and instead protect the floor so the object does not hit the ground. How does a libero (a specialized defense player in volleyball) select between different defensive movements in milliseconds, based on the information the player perceives in the environment? A heuristics model can describe a libero s specific choices but it cannot describe how the libero learns the heuristic. Therefore models of learning motor or cognitive tasks could inform the development of heuristics and the choice among them. For instance, in longitudinal studies (e.g., a season in sports) it seems important to use a simple heuristics approach to describe how information pick-up and related movements and choices changes across the time span. Identifying the changes in the use of search, stopping, decision, and execution rules could help provide answers to how experience shapes the order of cues and the selection between strategies. To the best of my knowledge such programs have rarely been conducted (see Raab & Johnson, 2007, for an exception). Examine data prediction Heuristics should predict new data as well as or potentially better than more complex models. The idea is to go beyond data fitting, the core concept of many statistical tools. Rather, using a heuristic to predict new data allows for cross-validation, thereby reducing problems of overfitting. For instance, to develop a heuristic to help in talent identification, a model should describe a good fit between predictors in talent tests and the performance criterion of the sport, especially when applied to predict success in a new generation of talented athletes. Such an application, given the reduced number of children participating in sports worldwide, may help to test the limits of existing talent identification programs. Other examples are prediction models of sports events that demonstrate the advantages of heuristics in fitting data as well as in cross-validation (Pachur & Biele, 2007).

15 International Review of Sport and Exercise Psychology 117 Test in the real world The fifth principle, testing heuristics in the real world, is the most important one for applications in sports. Whereas much valued research has been conducted in sports laboratories, highlighting internal validity, a crucial test of an application is its use in real life. The sports domain is a gift for researchers using heuristics, as many sports researchers have access to experts and can test them in their real environments, on the ground, in the water, or in the air. Sports, compared to many other fields or professions, have a well-structured net of local, state, and national organizations, allowing the test of heuristics beyond the individual (see Reimer & Katsikopoulos, 2004). Researchers who only feel comfortable in the lab should derive samples of stimuli representative of the real world. Proposals of representative designs are not new in psychology (Brunswik, 1955) or in sports research (Pinder, Davids, Renshaw, & Araújo, 2011; Raab, de Oliveira, & Heinen, 2009). However, a theory of sampling information for stimuli in the lab is missing. Conclusion Simple heuristics that are shortcuts for fast decisions have spread to sports science in the last decade and have provided new insights into how people behave under conditions of limited cognitive capacity, time, and knowledge. Although there is abundant research in fields related to sports, within sports there is a paucity of applying simple heuristics, despite the many opportunities the sports environment provides. Studying how simple heuristics apply to sports will lead to new insights not only into sport decisions but into the theoretical development of simple heuristics. For instance, simple heuristics have rarely been applied to sensorimotor levels of behavior or social decisions, both present in myriad ways in sports. Finally, specific heuristics have been proposed for sports that have now been generalized to other domains. Heuristics as rules of thumb have been discussed since the days of the Greek philosophers. In sports the simple heuristics program has just started, but it has been able to provide a different account of why athletes, coaches, referees, managers, and fans behave so extraordinarily, ensuring our continued fascination. References Andersson, P., Memmert, D., & Popowicz, E. (2009). Forecasting outcomes of the World Cup 2006 in football: Performance and confidence of bettors and laypeople. Psychology of Sport and Exercise, 10, Araújo, D., Davids, K., & Hristovski, R. (2006). The ecological dynamics of decision making in sport. Psychology of Sport and Exercise, 7, Ariew, R. (1976). Ockham s razor: A historical and philosophical analysis of Ockham s principle of parsimony. Champaign-Urbana, IL: University of Illinois. Ayton, P., Önkal, D., & McReynolds, L. (2011). Effects of ignorance and information on judgments and decisions. Judgment and Decision Making, 6, Baldo, M.V.C., Ranvaud, R.D., & Morya, E. (2002). Flag errors in soccer games: The flash-lag effect. Perception, 31, Bar-Eli, M., & Azar, O.H. (2009). Penalty-kicks in soccer: An empirical analysis of shooting strategies and goalkeepers preferences. Soccer and Society, 10, Bar-Eli, M., Plessner, H., & Raab, M. (2011). Judgment, decision-making, and success in sport. Oxford, UK: Wiley.

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