The Contest Paradox

ABSTRACT

The paper introduces the “Contest Paradox”: on the one hand, rational competitors employ the most effective means to achieve the constitutive end of games - winning; On the other hand, apparently rational competitors often employ means that are sub-optimal for winning, e.g., playing beautifully or fairly. Nevertheless, the actions of such competitors are viewed as rational. Are such competitors rational? I reject the possibility of resolving the paradox by appealing to additional ends or norms to winning, such as playing sportingly. Instead, I argue that the constitutive end of games is not a win simpliciter, but a type of win, such as winning-beautifully or winning-fairly. This interpretive framework is theoretically advantageous because it accounts better for the ‘unity of action’ or ‘flow’ competitors experience, better deals with various cases, and accommodates different traditions of competing.

KEYWORDS:

• Contest
• interpretation
• paradox
• rationality
• winning
• Flow

1.

On 25 June 1982, the West Germany and Austria football teams met in Gijón, Spain for a group-stage world cup match, which was to become one of the most infamous in the history of the game. Coming into the match, both teams knew, based on the previous results in their group, that if West Germany wins by two goals or less, they will both qualify to the next stage, while other results will see one of the two teams eliminated. The first 10 minutes of the match gave no hint of its future notoriety. West Germany, the stronger team of the two, opened the match by storm, furiously attacking the Austrian goal. No later than 11 minutes into the game, German forward Horst Hrubesch scored. 1:0 West Germany. A great result for both teams, at the expense of Algeria, the third contender for qualification out of the group. However, there were still at least 79 minutes to be played, during which much could happen. Not much did, though. What ensued earned the match the infamous title ‘the Disgrace of Gijón’: both teams slid further and further back into their own halves of the pitch, employing careful tactics, to the sound of loud booing and angry chants from the outraged (mostly neutral) fans, who regarded this behavior to be, at best, a demonstration of poor sportitude and at worst, corrupt. When the match concluded, the result was still 1:0. Both West Germany and Austria had successfully qualified to the next stage, with West Germany progressing all the way to the final, which it lost to Italy. Algeria was sent home. In the aftermath of the match, an enquiry by FIFA found no evidence to back allegations of match fixing and concluded that no rules were broken.

Why, then, if everyone had just played by the rules, does this game still live in the collective memory of many football fans as a ‘Disgrace’? This puzzle, to which other similar ones can be readily added, raises a host of related issues: the rationality of athletes in competitive sports (henceforth: ‘competitors’), to what sporting excellence—virtue qua competitor and not only qua athlete—amounts, and whether and how different values in sport, such as efficiency and fairness, come together in performance.¹

The paper will focus on the question of competitors’ rationality, and specifically the puzzle I shall later dub the ‘Contest Paradox’, of seemingly rational competitors consistently behaving irrationally by opting for sub-optimal tactics for the sake of furthering values other than winning. The importance of puzzles (which clearly include paradoxes) to philosophical inquiry was elucidated by Russell (1905) in an influential passage: ‘A logical theory may be tested by its capacity for dealing with puzzles, and it is a wholesome plan, in thinking about logic, to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical science’. In the decades that followed, this methodology was adopted and explicitly advocated in various versions by philosophers such as Quine (1951, 1964) and more recently Williamson (2020, 2021), who also describes the role of, among others, thought experiments and puzzles.

1. Rational Choice Theory and the Interpretation of Actions

For competitors, rationality is a virtue. It is part of any ideal of excellence of competitors—the virtue of competitors qua competitors—and it is a norm that competitors should follow and by which they are judged. These seemingly mundane claims give rise to two constraints (or at least prima-facie constraints). First, any account of excellence in competition must accommodate rationality. Second, ideals of virtuous competitors come in various shapes and forms, stressing different virtues such as perseverance, nous, passion, or cool headedness. Any account of rationality in competition must cohere with the different ideals of virtuous competitors.

In the discussion to follow, I assume that to understand an action is to reveal how it was the rational response to the world from the agent’s point of view.² In particular, this applies to actions undertaken in sports: to understand why a competitor or a team did what they did is to understand why it was the rational thing to do from the competitor’s point of view.

If this task proves impossible, actions can at most be explained away in terms of underlying causal mechanisms, rather than in terms of reason. John McDowell (1985) summarizes this view thus: ‘To recognize the ideal status of the constitutive concept [of rationality] is to recognize that the concepts of the propositional attitudes have their proper home in explanations of a special sort: explanations in which things are made intelligible by being revealed to be, or to approximate being, as they rationally ought to be. This is to be contrasted with a style of explanation which makes things intelligible by representing their coming into being as a particular instance of how things generally tend to happen’.³

Rational Choice Theory plays an important role in such rational interpretation, outside as well as within sports.⁴ However, it has been shown that the application of Rational Choice Theory to several common practices, such as promises (Eylon 2009a, 2016), voting (Brennan 2020) and altruism (Kraut 2020), presents challenges. Prima-facie, voting, keeping a promise or acting altruistically are rational (or at least not irrational), and perfectly comprehensible practices. Nonetheless, we can produce an apparently convincing line of thought that leads to the conclusion that each of these actions is in fact irrational: keeping a promise despite costs is arguably contrary to one’s interest in some cases, a single vote in a general election is unlikely to change the results and voting could therefore be deemed to be a wasted effort, and acts of altruism, by their very definition, go against one’s interests.

Presenting these seemingly rational actions as irrational creates a puzzle. Given the role of rationality in explanations of actions, to explain a certain item of behavior, we should aim to show how it is rational, if possible. Therefore, ceteris paribus, an account of an action or a practice that deems them rational is preferable to one which does not.

Two main interpretative strategies were invoked to handle such puzzles. The first argues that despite appearances, the behavior in question is rational and we simply ought to get our sums right. The latter suggests that we bite the bullet and accept that certain practices, such as keeping promises, voting or acting altruistically, are indeed irrational or a-rational (Brennan and Lomasky 1997; Downs 1957). This strategy introduces amended models for action, such as the ‘Moral Person’ who takes over from the rational person and dutifully votes or keeps a promise (Adams 1993; Mackie 2015). In connection with our future discussion of rational competitors, it is important to note that the examples we mentioned so far—voting, keeping promises and altruism—are other-regarding or related to others in a relatively straightforward sense.⁵

The focus of this paper is competitive games, which seem like prime candidates for the application of Rational Choice Theory in interpretation. The end of competitions is winning, as determined by the rules of particular games or contests, and all that is required from the competitor is to select suitable means to achieve the end. The maxim for the interpreter seems to be ‘understand why the means chosen were thought to further winning, and you understand the competitor’.

However, as exemplified by the reactions to the Disgrace of Gijon, things are not so simple: the teams were criticized for doing the apparently rational thing—the only rational thing, in fact. As will be shown below, this is an instance of a similar paradox to those mentioned above: Prima-facie, there is nothing irrational about playing a game in a specific way (for example, fairly, sportingly or beautifully).⁶ Nevertheless, one can present a convincing argument why this is, in fact, irrational, since rational competitors—by definition—must play to win, and playing in ways which conflict with playing to win is therefore irrational.⁷

2. Winning

To clarify, when I argue that competing with the intention to win is necessary for playing a competitive game, I am not making a claim about the individual ends of competitors, which may vary. One might compete in order to make a living, impress the crowd, win sponsors, or a host of other desiderata which would be served by playing the game. Nevertheless, even in such cases, playing requires the intention to play to win (and in this sense aim to win).⁸ If the competitor, intent on impressing the crowd, focuses solely on style and on entertaining without any manifest preference for winning—without manifesting the intention to win—then they are not playing at all. To illustrate, consider the absurdity of an extreme case—someone who scores a spectacular own goal on purpose just to show off their kicking ability against the best goalkeeper in the match, who happens to be from their own team.

Another important point is that playing with the intention to win neither depends on, nor follows from, caring about winning. If one undertakes to play a competitive game, for whatever reason, then one commits to acting in certain ways and not in others, which amount to playing with the intention to win. One does not, however, commit to care about winning. Consequently, I will speak of an aim to win or a preference for winning thus-and-so only as relating to the intention to win, not to a desire or other state towards winning.⁹

What playing with the intention to win amounts to is that competitors act in ways that are presumably conducive to winning the game, such as sprinting to the line in a short race, passing the ball to a teammate rather than to a rival competitor or scoring in football or basketball. We have seen that personal ends do not necessarily constitute winning because someone might succeed in, for example, impressing the crowd while losing. But there remains an important question: is winning as defined by the rules of the game or by the rules of a competition, and how do the ends of competitors figure, if at all, in determining what counts as a win?

Competitions matter. In a league, the best result for a team might be to draw a particular match. Sometimes, this can lead to matches that are not zero-sum games, as the Disgrace of Gijon illustrates. For example, in football, a draw could sometimes be a good enough result—a ‘win’ – for both teams involved in a match. Coordination is the apparent obstacle in the way of cooperation in such cases: to actually discuss the situation and explicitly coordinate tactics would amount to match fixing and therefore to cheating, even if what is being ‘fixed’ is not a formal win. However, overt coordination is not always necessary for cooperation. There are myriad ways in which teams can respond to each other’s tactics during the match, leading to de facto coordination and thus cooperation. Given the mutual understanding of the situation, teams may well establish a set of ad hoc norms—with how many competitors each team attacks if at all, what type of effort to score can be made, and so forth. This type of mutual dance of caution can often suffice to guarantee a draw.

Employing cautions and defensive tactics does not mean a team, or even both teams, are not playing with the intention to win. A team can play for a draw, but with the intention to win. Thus, a team can adopt tactics to achieve at least a draw, but it still plays with the intention to win, albeit more cautiously: score if they can, stop the other team from scoring, keep the ball, etc. This is similar to a team playing cautiously to defend a lead. The aim and the tactics might differ, but the constitutive aim or intention (winning) is the same.

What about a team that would not mind losing a match, for example in order to secure a weaker opponent in the next stage of the competition and increase their chances of winning it? This is borderline case. Of course, even in such a match, a team that does not play with the intention to win—that ‘throws’ the game—is not playing the game and is guilty of cheating.

A related example is that of a team that opts to rest some of its starting players in an insignificant match (or even, as in the example above a match the team would rather lose), in order to conserve energy for subsequent, more important matches. This tactic is quite common in long tournaments and is generally considered legitimate. I suggest that this is because ‘downgrading’ the team in this way does not mean it is no longer playing to win, just as a basketball team resting some of its star players in the third quarter is still playing to win, as long as the substitute players make a genuine effort and play with the intention to win. Moreover, when we extend the scope of what constitutes a ‘win’ is to include the entire tournament, rather than just a single game, playing to win may actually call for this tactic.

This could be exemplified by the Denmark-West Germany match in the 1986 Football World Cup. By the time of the match, both teams secured qualification to the next round. However, the winner of the group would meet a strong Spain team, whereas the runners-up would end up playing the weaker Morocco. Denmark did not rest any players whereas West Germany did. Denmark won the match, lost a key player for the next match due to a red card, and were upset 5–1 by Spain. West Germany beat Morocco and made it to the final.

Who got it right then? Denmark, whose tactics were aimed to win the match as the rules of football prescribe, or West Germany, whose tactics were aimed at winning the tournament, as its rules prescribe? Arguably, the answer is that both of them did—as long as both teams played with an intention to win as specified above (score if they can, avoid conceding, not give the ball away, tackle opponents, etc).

Here, individual aims do make a difference: one team awards great importance to a particular match against a great rival, the other team is intent solely on winning the tournament. As long as both play with the intention to win, these differences are within the game.

3. Rational Competitors

The application of Rational Choice Theory to competitive sports games seems trivially warranted. Rational competitors are to be understood as treating tactics—the way in which a game is played—as means to an end: winning the competition. The idea that the choice of tactics is dictated by rational considerations is illustrated whenever tactics are altered in response to particular game situations, such as to defend a lead.

Rational Choice reasoning applies to teams as well as individuals. This raises some issues about the member-team relation, since the interests of members of teams might differ from those of the teams (Bar-Eli et al. 2007). However, so as not to overcomplicate this discussion, I will henceforth treat teams as single competitors, and ascribe competitors the same intentions as their team.

We can now turn to the discussion itself. The following schematic account of choosing tactics in competitive games suggests itself:

RM1. The constitutive aim of competitive games is winning, so that playing the game is necessarily playing with the intention to win.

RM2. Rational competitors act as best they can in order to win.

This account prescribes what playing (RM1) rationally (RM2) involves, broadly construed, and thus, serves as a general interpretive theory for competitive games. Note that this is not simply an analysis of the concept ‘playing a game’ but a normative claim about interpretations.¹⁰ If we accept the principle of charity—the claim that in attempting to make sense of the actions of others one must present them as rational and well-meaning as is possible given the evidence, then RM2 is an application of charity to the realm of competitive sports.¹¹ Note further that RM2 also serves to prescribe that since the virtuous competitor (qua competitor) is a rational competitor, then an ideal competitor is one whose actions are best suited to win the game. Thus, their sensitivities and abilities are such that they are able to identify the affordances and obstacles a situation presents and employ the most effective means to winning under such circumstances.¹²

4. Apparent Paradox

Both teams embracing the 11^th minute result in the Disgrace of Gijón was less than surprising, and readily comprehensible because it was a rational thing to do. The tactics utilized by the teams during the match were sensitive to the match situation and were the rational means to achieve the required end—qualification to the next round, in accordance with the rules of the game and the tournament. Thus, if we apply RM1 and RM2 to the match:

RM1-applied. The aim of each team was to win the tournament by qualifying for the next round.

RM2-applied. The teams—being rational competitors—did their best to get the required result by reverting to prudent tactics and maximizing the prospects of the desirable result.

It is important to note: the view encapsulated by RM1 and RM not only implies that rational competitors might employ the type of tactics employed by West Germany and Austria in Gijón, but also suggests that this is the right thing, that is what rational competitors should to do. Why, then, did the crowd berate the teams? Assuming they had a point, there is an evident challenge here to the Rational Choice Theory view. Of course, there is usually more than one way to win a match. There could be a reasonable disagreement about which tactics would be best under various conditions, and competitors might get the tactics wrong, or even play irrationally. That, though, does not seem to be what was agitating the crowds in Gijón. Rather, they were calling for something beyond the next-round qualification. Followers of competitive sports often encounter matches in which, assuming the rationality of the competitors, ‘playing with the intention to win’ does not seem to be a satisfactory account of what the competitors are doing. Rather, competitors may be committed to winning, but often also markedly display additional commitments, such as to playing fairly or to playing beautifully.

For example, in the 1982 Football World Cup tournament, the Brazilian national team (hereinafter: ‘Brazil 82’) played Italy for a place in the semi-finals. To qualify, Brazil only needed a draw. Nevertheless, they employed their signature all-out attack tactic displaying an unshakeable commitment to ‘the Beautiful Game’ (o jogo bonito). As a result of their tactics, Brazil ended up scoring but losing the match and consequently, the tournament. The Brazilians were undoubtedly trying to win the game, but they had more in mind than ‘just’ winning. Another dramatic example came about in the English Football Championship League 2019 match between Leeds United and Aston Villa, in which Leeds needed a win. Nevertheless, when a Leeds player scored while a Villa player was lying on the ground with an apparent injury—an action permitted under the rules of football but considered not to be in the spirit of fair play—the Leeds coach, Marcelo Bielsa, instructed his players to simply allow Aston Villa to immediately equalize (Taylor 2019). Again, Leeds seemingly played to win, but here they were, willing to hurt their own chances of winning for the sake of fairness and sportitude.

Both Brazil 82 and Leeds consciously chose to play in a manner seems to have adversely affected their chances to win, thus, prima facie, violating RM1. How, then, are we to interpret their actions?

In the context of our discussion, the key point about competitors like Brazil 82 or Bielsa’s Leeds is that, despite their apparent deviation from the requirements of Rational Choice Theory, their actions are readily comprehensible. In this, they are no different from the rational West German and Austrian teams from Gijón. Of course, this does not mean that the explanation of any such particular instance is immediately available—filling in the details might require interpretative ingenuity. But there is nothing prima facie mysterious or seemingly paradoxical about these performances and similar ones. The same holds for the contemptuous crowd in Gijón: we understand perfectly why they were protesting. This suggests a paradox: there are rational competitors, whose actions we can easily comprehend, who, prima facie, purposefully do not act as rational competitors. We can label this problem ‘the Contest Paradox’:

P1: Rational competitors in competitive games play with the intention to win.

P2: There are cases in which it seems that rational competitors intentionally are not playing to win.

5. Irrational Virtue?

It appears that if we take RM1 and RM2 seriously, the competitors described under P2 are revealed to be irrational, contra appearance. Is this conclusion necessary—must we bite the bullet and adopt this view? Let us look a bit more closely at the competitors in question. First, they often display a stable disposition: their commitment to playing fairly or beautifully is not a whim, and often it does not fade or diminish over time, even if it proves costly.

Second, their actions are typically chosen for their own sake—the competitor plays fairly because they believe fairness to be an ideal, not because they find it to be a more efficient mean to obtaining a win. The same goes for competitors committed to playing ‘the beautiful game’, which has become an explicit ideology. Thus, in many (though not all) instances, competitors display a conscious and overt, seemingly rational, choice to commit to playing fairly or beautifully.

In addition, competitors are neither blindly or passively following some tradition or social norm, nor are they merely adhering to tradition or social norms without question. Rather, they are choosing to play one way over another, despite being fully aware of the aspects of the particular situation that call for playing ‘ruthlessly’ (that is, as the case may be, unfairly or in an aesthetically unappealing manner), and reject that option, sometimes after deliberation or debate.

These points echo a typical view of virtues: stable dispositions to rationally choose actions for their own sake. Of course, this not a sufficient condition for being a virtue, and applies to some vices as well—but such vices would have to manifest a conscious choice, not merely a manifestation of Weakness of Will (akrasia) as, for example, some cases of cowardice do. In the circumstances of interest to us, our apparently irrational competitors knowingly and consciously choose to act in the supposedly irrational manner; they do not succumb to temptation or suffer a lapse pf judgment. This suggests that some ideal, some conception of excellence, is at work.

What these competitors highlight is that not only do we encounter a plurality of ways of playing a game, but we encounter different ideals about the way the game should be played: fairly, beautifully, with loyalty to a traditional formation or style, etc. Correspondingly, we encounter different sporting heroes—virtuous competitors—who embody the sensitivities and dispositions fitting a particular ideal of how the game should be played and function as role models. Marcelo Bielsa or the Brazil 82 team exemplify such ‘alternative’ ideals.

6. How to Rationalize

This paradox and the discussion above beg the question: can we interpret the actions of competitors with aims beyond ‘playing to win’ as rational?¹³ Two distinct interpretive frameworks offer competing possible solutions to this problem:

6.1. The Multiple Aims Framework (hereinafter: “Multiple”)

To interpret the actions of such competitors, we should adduce one or more additional intentions, separate aims or preferences, alongside winning, such as a taste for fairness, a taste for sportitude, or a taste for playing beautifully.

6.2. The Unified Account Framework (hereinafter: “Unified”)

There is only one intention or aim attributed to the competitor, and this aim is for a specific type of win. Possible aims can include the aim to win-fairly or the aim to win-beautifully, or even the aim to win simpliciter, which, under the Unified framework, is but one additional type of aim to win, taken to mean winning by all means permissible by the rules.¹⁴

How, then, are we to discern which of the two competing interpretive frameworks is most suitable to account for the actions of various competitors, including the apparently irrational ones we have been discussing? As a rule, theories are judged on how well they account for different phenomena, based on several criteria, and predominantly: adequacy, simplicity, and explanatory power. To assess the adequacy of the two frameworks, we will first test each of them in relation to certain typical scenarios related to the Contest Paradox. Further, we will discuss the ideal and experience of ‘flow’ in sports and weigh the competence of each of the two frameworks to account for it.

As noted above, puzzles such as the Contest Paradox had long served as the ‘experiments’ that help us put theories to the test and determine their value. Accordingly, examining the following typical scenarios relating to the Contest Paradox is crucial to appraising the rival interpretive theories¹⁵:

6.2.1. Playing Fairly or Beautifully As a Silver Lining

In this scenario, a competitor loses, but having played beautifully, their disappointment is greatly mitigated. They are even proud of having played beautifully.

This type of reaction is salient among fans of teams such as Brazil 82, as well as among competitors, who take pride in having played beautifully despite losing. This reaction does not appear to be irrational.

6.2.2. Winning Fairly or Beautifully Is the Only Way Worth Winning

In this scenario, a competitor does not attribute any value to winning achieved while playing unfairly or to winning while playing unattractively; the value of winning depends on also playing fairly or beautifully, respectively. Thus, an ugly win and a beautiful loss are on a par, and equally disappointing.¹⁶

6.2.3. Playing Fairly or Beautifully Is the Only Way Worth Playing

In this scenario, a competitor not only values winning fairly or winning beautifully but considers playing fairly or beautifully as the only thing giving value to the game. The difference between this scenario and the previous one is that that the value of playing at all, not just of winning, requires playing fairly or beautifully.

First, let us see how Multiple fares with these scenarios.

Multiple provides a simple account for Scenario A: the competitor who lost the match but played fairly or beautifully is, ceteris paribus, in a better state than a competitor who lost but does not share the preference for playing fairly or beautifully, and the same goes for fans. The satisfaction of the preference for beautiful play explains why the ill feeling for the loss is mitigated and explains why a losing competitor can feel proud and satisfied because they were successful in achieving some further ends.¹⁷

What about Scenario B? For one who values both winning and playing beautifully, tactics are a balancing act that depends on conditions. If conditions are such that winning is impossible, unless some beauty is sacrificed, sacrificing would be the rational thing to do. Can Multiple account for a competitor that refuses to adjust under any circumstances? One possibility is to ascribe such weight to playing beautifully so as to render sacrificing any beauty whatsoever not worth the value of winning.

Another possibility is to render the value of winning conditional on that of playing beautifully—playing beautifully does not simply weigh more, it is lexically prior. Each of these moves would suggest that in many circumstances, such competitors rationally play solely in order to maximize beauty.¹⁸ However, as claimed above, a competitor cannot be considered to be rationally trying to play (beautifully or otherwise) if they are playing without the intention to win. Therefore, the Multiple account of Scenario B misses the mark when it comes to Brazil 82 or Bielsa’s Leeds, teams who, at least prima facie, did play with the intention to win.

Multiple thus burdens the interpretation with having to view these competitors as only appearing to be playing football, while in fact doing something else, such as creating beauty or promoting fairness. This renders competitors in Scenario B similar to competitors that feign competing (for example, if a competitor is paid to cheat and intentionally loses the game). In such cases indeed the competitors are doing something else and only pretending to play. Not so for competitors who are committed to beautiful or fair play.

Unified fares better with these scenarios. According to Unified, competitors must play with the intention to win any type of win: win fairly, win beautifully, win simpliciter, etc. Unlike Multiple, Unified can easily account for Scenario B: a competitor that only values a fair win or a beautiful win simply has nothing to celebrate by winning if it is not fair or beautiful, respectively. Of course, they might also prefer winning simpliciter to losing, but not necessarily so: they might be indifferent, or they might even feel guilty and resent a win achieved non-beautifully. The reasons for valuing only a certain type of win vary, and often involve some conception of games (for example, the view that winning without playing fairly amounts to cheating or deprives the game of its conceived point, such as a mutual and respectful pursuit of athletic excellence (Simon 1984)).

Thus, Unified clarifies the relation between a commitment to beautiful play or fair play, to the means employed by the competitors. In so doing, it explicates the tactics pursued and reveals them to be rational, suitable for these particular ends, even if at the cost of winning simpliciter.

What about Scenario A, in which a losing competitor views playing beautifully as mitigating losing? At first glance, it seems that Unified, which describes competitors as playing to win-beautifully, will struggle with Scenario A, because losing frustrates the only aim of the competitors, regardless of whether they played beautifully or not.

To respond, it would be helpful to turn to another value that can mitigate a loss—doing one’s best, in particular against a superior opponent. In such cases, the competitor competed to win, and did so as well as they could. There was little they could have done and failed to do that would have changed the end result. Note that the competitor does not have two separate intentions, playing and playing well, but one. Trying to do as well as one can to achieve an end is internally related to having an end; it is (at least normally) already implied. Thus, to play for a particular kind of win means one tries to play well for this particular kind of win. The case of losing but playing beautifully is a case of losing but playing well, where ‘well’ means (also) beautifully. Thus, under Unified, when one aims to win-beautifully, then playing beautifully can be appreciated as an achievement, in the same way as losing despite doing one’s best.

Let us now turn to Scenario C. Unified highlights the fact that there is no presumption favoring playing to win simpliciter if winning beautifully is impossible—it may well be that the possibility of playing in a certain way is conceived as that which gives the game its value. Unified easily incorporates such a view of games. This is manifest when we consider winning fairly: if we view the fair competitor as someone who has two preferences, with winning being the prior, they should play to win when playing to win and playing fairly conflict. But Unified also allows for someone who does not value winning unfairly at all. It is not hard to imagine a rational competitor, who holds the view that an unfair win does not count as a genuine or worthy win.

Thus, Unified highlights the fact that what a rational competitor in a competitive game aims to achieve is not determined only by the rules of the game and cannot be defined a-priori. Instead, ways of playing the game, as they evolved in different traditions or chosen and shaped by various competitors can and do differ. Interpretative issues are not resolved by fiat, just as what is required for acting rationally is not.

7. Flow: What Is Wrong with Multiple?

Arguably, thus far Unified is ahead on points, with Multiple still in the game, perhaps requiring improved responses to the scenarios than those sketched above. But there is a deeper, more telling issue that separates Unified from Multiple, demonstrated by their treatment of the idea of ‘Flow’, the coveted psychological state of total absorption in a task, which is also sometimes depicted as ‘being in the zone’. The experience of flow has been explored in the sports literature from various aspects, emphasizing in particular the athlete’s single-mindedness and singularity of purpose.¹⁹ Athletes in a state of flow are fully focused, immersed in their task and experience a sense of unity and naturalness, which are in turn is associated with excellent performance. In other words, flow seems to capture what is meant by the idea of virtuous action as a habitual response to various situations chosen for its own sake—it manifests an internalization and mastery of the sensitivity and skills, that act out of a reasoned choice to move an athlete one way or the other. Consequently, an interpretive theory’s proficiency in addressing flow is an important indicator of its overall competence in elucidating what virtuous action in sports is and providing an account of it.

Multiple rephrases P1 so that when they play, competitors do not only intend to win: they have further intentions as well, and their actions are an exercise in balancing and optimization (on the basis of the weights they assign to the different preferences). As we saw above, Multiple cannot easily accommodate scenarios in which it seems that winning is abandoned to pursue other ends (as in the Leeds United-Aston Villa match), without portraying the competitors as irrational. This difficulty stems from the essential balancing nature of this view, and the fact that it renders competitors as either intending to win simpliciter, or else as burdened with additional intentions, perhaps belonging to their ethos. Thus, Multiple represents such competitors as engaged in a balancing of aims, that could, in some instances, practically contradict each other. Multiple depicts these competitors as being in two minds—the competitive mind and the fair play or beauty-seeking mind. This account is similar to accounts of irrational agents, suffering from weakness of the will or self deception.²⁰ According to Multiple, these types of competitors are ambivalent: they have conflicting motives. That is to say—they are not, and can never be, in a state of flow.

In opposition, the virtuous agent is traditionally presented as motivated only by the right thing to do in any situation (Aristotle 2000; Eylon 2009b; McDowell 1979). Excellence in action requires certainty and unity of mind, which lead to acting naturally and with ease, or in other words, to being in flow. With that in mind, it is clear that Multiple’s ‘Divided Mind’ account suggests that only competitors who intend to win simpliciter are virtuous competitors, who can serve as the model for rational and virtuous competition.

Note that Multiple does offer a solution of sorts to the Contest Paradox. Competitors that have preferences beyond winning simpliciter might still be deemed rational even if they play fairly or beautifully at the expense of winning. They would not, however, be rational qua competitors, and they certainly could not be considered ideal competitors, who are paradigms of excellence at competing. Under Multiple, that ‘status’ is reserved for one type of competitor, and that type only: those whose responses to the situation embody stable dispositions to utilize the best available tactics for winning simpliciter.

It is also important to note that it does not follow from Multiple that one ought (in the sense that attaches to acting rationally) to be a rational competitor rather than aim to play fairly. Nevertheless, it does follow that, qua rational competitor, conditionals such as ‘if you really want to play a competitive game, you must employ any legitimate tactic it takes’ are trivially true.

We can summarize the argument thus:

1. In competitive sports, excellent action is non-ambivalent action

2. teams and athletes that do not play to win simpliciter can (and often do) manifest excellence.

3. Multiple means that some teams display ambivalence.

4. Thus, according to Multiple, teams that choose to play beautifully or fairly rather than win simpliciter cannot manifest excellence.

To summarize: when dealing with competitors who do not play with the intention to win simpliciter, Multiple commits to a deliberative model that fails to do justice both to the ideal and to the experience of ‘flow’ and implies that teams like Brazil 82 or Bielsa’s Leeds could never achieve flow.²¹

8. Paradox Dissolved and Virtuous Competitors

Unlike Multiple, Unified allows and accounts for different ideals of rational and of virtuous competitors, who can meet the non-ambivalence requirement and exhibit flow, in accordance with the following argument:

1. In competitive sports, excellent action is non-ambivalent action.

2. teams and athletes that do not play to win simpliciter still can (and often do) manifest excellence.

3. Unified means that it is possible for teams that do not play to win simpliciter not to display any ambivalence.

4. Thus, according to Unified, teams that choose to play beautifully or fairly rather than win simpliciter can still manifest excellence.

Sports knows various ideals of competitors which fit different ends—virtuous competitors who embody excellences according to various and sometimes conflicting traditions and conceptions of competitive sports such as the fair competitor, the one committed to beautiful play, the hard worker, the defiant, the cunning. Conceptions of virtue may vary too. Indeed, Bielsa’s Leeds or Brazil 82 are viewed as virtuous competitors by those who value fairness or beauty, respectively, but as naïve, or even foolish, by those who hold different conceptions of virtue. Unified allows for this multiplicity and provides an interpretive framework that does not suggest that such competitors are stuck in eternal conflict.

Thus, under Unified, we can view Bielsa (if the description indeed fits) as embodying a conception of the ideal competitor that values sportitude and aims at winning fairly. Similarly, Brazil 82 can serve as a model for a team that embodies the ideal of the beautiful game.

Perhaps most saliently, Unified allows us to avoid the pitfall of viewing different traditions of playing the game as irrational traditions, that got things horribly wrong. Therefore, Unified accommodates a plurality of ways and traditions of playing the game, and (defeasibly) treats competitors committed to different conceptions of the game on a par qua competitors. Furthermore, by describing competitors as playing with the intention to win in a certain way, Unified allows for a direct relation between the specific circumstances of the game and the competitors’ action. In so doing, it both accounts for virtuous ideals of action.

Similarly, and unlike Multiple, Unified adequately allows for flow, and thus for diverse conception of the virtuous competitor that are each undivided and can thus respond directly to the demands presented by the game-situation. For example, given the type of competitor Bielsa is, it would be enough to describe the events of the match to account for Bielsa’s actions as the natural response to the requirements presented by the situation. No additional balancing or assignments of weights to different ends are required (Eylon 2009b; McDowell 1979). Bielsa’s actions would be non-ambivalent, as well as direct responses based on habituated sensitivities and dispositions, chosen for their own sake.

In conclusion, under Unified the Contest Paradox is dissolved because the aim of rational competitors could be any one of many types of win. This position is respectful of the normative nature of question ‘how to play a competitive game’, and can turn to an ethos of the game, traditions of playing the game, or subjective personal preferences in search of an answer. Rational and virtuous competitors employ tactics that serve the type of win that they aim for. A win simpliciter is but one possible candidate to fulfill this role.

Thus, a complete explanation of how a competitor plays must also account for their preferred type of win and present it as reasonable, and not as foreign to the game or unnecessarily burdensome. This type of explanation could invoke the relation between the competitor’s reasons to play and their choice of win, tradition, aesthetic norms, or other values, such as—among other things—valor, fighting spirit, or respect for one’s opponents.²²

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Notes

1. By ‘excellence’ and ‘virtue’, I will refer to those habits of action that make one excel at competing – i.e. that are conducive to winning according to the rules and ethos of the game. This does not preclude any conceptions of athletic excellence such as hard-work or fairness, and the proposed view allows for their inclusion at the most basic level of ideal competitors. See also McNamee (2008), for a discussion of various virtues and vices within sports.

2. See: Williamson (1996) for an illuminating discussion of the question of interpreting a practice.

3. For a recent discussion in support of this constraint on explaining actions, see Asarnow (2022), who defends a Davidsonian version of the constraint. For a discussion of the relation between such a Davidsonian view and McDowell’s views on action adduced here see Eylon (2009b). Dimitrakos (2020) provides a further exposition of McDowell’s brand of naturalism.

4. For a classic account that makes this relation explicit, see Davidson (1974). Bar-Eli et al. (2007) present an example within sports of applying rational choice theory to apparently puzzling behavior—goalkeepers opting for a sub-par strategy when facing penalties.

5. For a discussion of the different strategies of dealing with actions and practices that seem to challenge Rational Choice Theory, see Binmore (2010). Binmore (2022) further explores the issue of treating all agents in all cases as homo economicus. The view proposed below might seem to belong to the opposite camp, but the explanation of the actions of players must also rationalize their choice of type of win (rather than allow that it is an arbitrary preference).

6. By ‘playing fairly’, I mean something along the lines of showing ‘sportitude’ - a gender neutral term coined in (Holt 2020)—which is not identical to merely playing by the rules, or to not cheating.

7. Importantly, the responses invoked to justify treating other-regarding practices as a-rational rather than irrational are not available in this case: it seems clear that the teams got their sums right, and it would seem strange to invoke some ‘moral team’ that could serve the same function as the ‘moral citizen’ did in the account of voting. The discussion below elaborates on this claim.

8. For convenience, I use the terms ‘aim’ and ‘end’ as determined by intentions such as the intention to win or the intention to play fairly.

9. This also means that the discussion below is neutral regarding the ‘puzzle of caring’ about winning, although it does suggest a direction which ties winning to different values contra Baron-Schmitt (2023).

10. As a matter of terminology, I accept that in order to understand an action, one must explain it by interpreting it.

11. Donald Davidson has made a classical and influential case for the principle of charity. See in particular Davidson (2001).

12. By ‘virtuous competitor’ I mean someone who embodies the virtues of competition, not someone who is morally virtuous and also a competitor, perhaps in their spare time.

13. Note that this is a question about the interpretation of a practice, not a psychological or empirical hypothesis about individual players.

14. The ‘meaningful’ wins discussed by Laumakis, Laumakis, and Laumakis (2017) fall into this category as well.

15. In the scenarios that follow, I chose playing fairly or beautifully as examples for a specific type of playing or winning. The same argument could be applied to other types as well.

16. See Simon, Torres, and Hager (2015, ch.3) for relating playing unfairly to tainting a win or diminishing its value.

17. See Piller (2009), for a discussion of the value of trying in general and in sports, respectively.

18. One might hold that the preferences are mutually dependent. But such mutual dependence brings us to Unified.

19. Sports research, and in particular the philosophy of sport, takes the lead in the study of the concept of flow, which, despite being rarely discussed elsewhere yet, is a concept that can have broader applicability to general ethics, in particular to discussions about the validity and nature of the distinction between the actions of the virtuous agent and those of the merely strong-willed agent. See: Swann et al. (2012) and Swann et al. (2018) for a summary of some of the recent literature on the phenomenon of flow, and Frias and Lopez (2023) for a discussion of the importance of the flow experience and a summary of relevant literature in the philosophy of sport. Kimiecik and Stein (1992) discuss some methodological issues that also highlight the ‘given’ status of the experiences of flow, while Hunter and Csikszentmihalyi (2000) provide a phenomenological perspective.

20. With regard to both weakness of the will and self-deception, Davidsonian views are examples of the divided-mind account (Deweese-Boyd 2023; Stroud and Svirsky 2021). For a critique of such views that pertains to the view presented here, see McDowell (1994).

21. and see (McDowell 1979) for a related distinction between the actions of the virtuous agent in contrast to those of the strong-willed agent. See also Eylon (2009b).

22. I am grateful to Amir Horowitz, Michal Merling and anonymous readers of this journal for their invaluable suggestions and comments.