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Ich Bin The Champion | Of Tournaments and Pyramids


Above, a lovely match-by-match tournament illustration by the Estado de S. Paulo, dated prior to the beginning of sudden death matches.


Above, from Hierarchical structure and the prediction of missing links in networks: Nature,  453, 98-101 (1 May 2008). Notice the cut-vertices and bridges, which may be the locus of critical social stress and loss of cohesion, or as informal but intentional departures from formal rules in pursuit of collective goals.

As part of my own ongoing reading project on the subject, then, I wonder: What does social network theory have to say in such cases: a directed network  in which the loser transfers structural prestige to the winner, who parlays this relationship of winner and loser –if that is the proper way to say it? — into moving onward and upward.


Above: if victories transfer prestige from loser to winner, does the overall prestige of a winner reflect the prestige of its vanquished foes, according to some measure of performance? That is, is the tournament, a process designed to produce a world champion, a directed or an undirected network, apart from the initial, semi-random assignment of teams to round-robin groups?

The international governing body has published its criteria on the Web (PDF). They are pretty complex. Brazil enjoys a certain degree of immunity from the draw because of its status as host country.

Tournaments and Pyramids

Where is my copy of de Nooy, Mrvar and Batagel, Exploratory Network Analysis with Pajek?


In the meantime, in a 1994 study, Dagstuhl studied the level playing field which highlights the cognitive dissonance between professional and international careers.

Our network example describes the 22 soccer teams which participated in the World Championship in Paris, 1998.

Players of the national team often have contracts in other countries. This constitutes a players market where national teams export players to other countries. Members of the 22 teams had contracts in altogether 35 countries.

Screenshot from 2014-07-15 16:09:29

Screenshot from 2014-07-15 16:16:13

Counting which team exports how many players to which country can be described with a valued, asymmetric graph. The graph is highly unsymmetric: some countries only export players, some countries are only importers.

The social structure of a (round robin) tournament is described by Stanley Wasserman:


In its pure form, a round robin looks like this —

Screenshot from 2014-07-15 15:07:59

Actually, this definition seems not to deal with such complex questions as the nature of round-robin and single elimination tournaments and their combination in a case such as the World Cup, together with the methodology of the initial draw and the coin flip and all the other trappings of fine athletes giving it their all on a level — and, fortunately, well-drained, in one case — playing field.

Consider the community of wagerers as they place their bets, how they think about contingent events affecting the odds.  The shift in model with the commencement of sudden death imparts to the surviving athlete or team a different strategic position.

The obliteration of Brazil in this year’s 7 Germany x 1 Brazil, for example, suggests that it may not have deserved to represent the preliminary round-robin groups. That is, it might have been foreseeable — to some gambler, perhaps — that its prestige came at the cost of often nail-biting victories over weaker teams that weighed on it as it progressed through the later rounds toward sudden megadeath against the Germans.

The vast majority of Google searches on “social network tournament,” meanwhile, are basically marketing come-ons inviting audiences to get into the spirit of the game, using some app or other or executing some smart mob scheme.

In the scholarly literature — Google Scholar –on the other hand — and I have not got very far yet in my search — is N. Anand and Mary R. Watson, “Tournament Rituals in the Evolution of Fields: the Case of the Grammy Awards,” Academy of Management Journal (undated).

(I miss Brooklyn, where the public library provides free public access to databases of commercial scholarly journals.)

The paper seeks to learn

… how award ceremony rituals influence organizational field evolution through four critical processes: distributing prestige in “situated” performances; enacting a highly charged ceremonial form designed to attract the collective attention of a field; serving as a medium for surfacing and resolving conflicts about the legitimacy of field participants; and tightening horizontal linkages within the field. Using the Grammy Awards as a case study, we present a mixed-method, longitudinal analysis of these processes operating in tandem.

Now there is an interesting thought: the tournament as a mechanism for promoting cohesion, settling questions of structural prestige that have real, monetary value and move the markets for an entire infotainment industrial complex.

Tournament theory as the Chicago Boyz see it is a matter of a methodological choice for different competitive schemes for evaluating and rewarding productive workers.

But football players are millionaires beyond even the dreams of rank-and-file corporate CEOs. The extreme physical nature of their activity must imply a risk assessment that may shift the balance of motivations.


Flowing Data, meanwhile, contributes with a paper and lifts some nifty graphics — above — from the Los Angeles Times on the synergies between the nationality of players and the nationalities of the clubs they play for (Germany is full of Brazilian and Argentine players, and Neymar has signed with the almighty Barcelona, for example).

The notion of a round-robin design inherent to tournament competition is taken up by Marvin Washington and Edward J. Zajac in the AMJ   in a 2005 paper on the possibility viewing prestige as a structural decision not necessarily based on measurable aspects of the game. Their research focuses on the NCAA basketball tournament.

In this study, we (1) clarify and distinguish the concept of status, (2) identify and analyze the institutional and organizational factors that can lead to differences in organizational status over time, and (3) empirically assess the privileges implied by such differences. Using extensive longitudinal data on competitive intercollegiate athletics, we found that status was a significant predictor of whether a college was invited to participate in the NCAA postseason basketball tournament, independently of performance considerations.

The Brazilian enjoyed a status-based advantage in the assignment to tournament groups, did it not?

The Romanians Mihaela Balint, Vlad Posea, Alexandru Dimitriu, and Alexandru Iosup offer an event more intricate case: The effect of virtuality in face to face and online bridge tournament strategy.

Becoming Pelé


Anand and Watson cite another interesting piece of research, more directly related to the sociology of mass sporting events: «On Becoming Extraordinary: The Content and Structure of the Developmental Networks of Major League Baseball Hall of Famers,» (ACAD MANAGE J February 2011 54:1 15-46).

With that, I should busy myself with reading before raising my hand in  class again.

Interpreting the sociogram of the Cup seems like an interesting avenue, not especially well-traveled by mainstream social scientists, if at all, but honed to a sharp edge by marketing practitioners — a sport at which the Brazilians are unstoppable.

(I am waiting to see what Toni Negri has to say on the subject. Black blocs were stalemated with relative ease by security forces assigned to the stadium and surrounding areas.)