Numbers in play in psychosocial organization

Comprehension of Numbers Challenging Global Civilization (Part #3)

Work team size: This topic is usefully summarized in a Wikipedia entry on team size and in a Wharton knowledge base (Is Your Team Too Big? Too Small? What's the Right Number? Knowledge@Wharton, 14 June 2006). As succinctly stated by Susan Heathfield (What Team Size Is Optimum for Performance? About.com):

The team size that is optimum for team performance is a topic much researched and debated. The problem is that you need to consider a number of factors when determining optimum team size.... If you seek effective input, the optimal team size ranges from more than 2 up to 18-20 members, but these individuals are not expected to form a cohesive, highly interconnected team. It is much more likely that teams of a large size form sub-teams and working groups to accomplish the actual work of a project.

With respect to the "cultural message" conveyed as the size increases, according to the arguments of Meredith Belbin (Size matters: how many make the ideal team? Belbin, 24 November 2011) cited by Heathfield:

Four: We're well-balanced in our team and good at achieving agreement.
Five: One of us tends to be the odd one out.
Six: It takes longer to reach agreement, but we get there in the end.
Seven: Rather too many random contributions float about.
Eight: People speak freely but no one listens.
Nine: We could do with someone taking control.
Ten: We now have a leader, but their ideas are the only ones with a chance of acceptance.

Such issues are clearly fundamental to team building (Jon R. Katzenbach and Douglas K. Smith, The Wisdom of Teams: creating the high-performance organization, 2006). The many studies on team performance -- as a function of team size -- tend to conclude that optimum team size is between seven and eleven people. The lower constraint is due to unproductive limitations on diversity and expertise, whilst the higher constraint is due to reduction in open communication and fruitful participation.

The implications have necessarily been long explored with respect to the size of military units (platoon, legion), music groups, drama groups, and dance troupes. In each case there is a sense of what works and what does not at any particular size.

Sports team size and players on the field: It would seem to be both obvious and extraordinary to note the numbers typically chosen for sports teams and the manner by which they are constrained. The complexity in the case of football is indicated by the identified variants distinguished in Wikipedia (Present day codes and families):

The pattern is partially summarized in the following graphic, with the inclusion of other sports. This adds an indication of the players "on the field" from the opposing teams, but without any indication of those in reserve ("on the bench"). The dynamic of a competition between a set of teams (as in football) is designed to reduce the complexity of the numbers of many teams to a final game governed by the same constraints. Games with "hundreds of participants per side" are however characteristic of parliamentary debate.

Individual team-size and total players-on-the-field
(for a selection of 39 sports)

Individual team-size and total players-on-the-field for 39 sports

It is somewhat strange to recognize the problematic mix of assumptions governing the organizations of sports:

Gender: Typically there are few "mixed sports", tennis being the most notable exception. The mixed sports at the Olympics also include: badminton, ice dancing, and pair dancing. The assumption is that competition of male against female would be unfair, because men are better equipped in some way -- an argument which feminists have been happy to challenge over past decades. The subtext is that males in some cultures could not tolerate the possibility of being out-manoeuvered by females. The matter is further complicated in some sports through declarations of controversial gender orientation. Barely recognized by global media is the existence of of the FIFA Women's World Cup -- a situation perhaps appropriately to be described in the terms of Elise Boulding (The Underside of History: a view of women through time, 1976)
Size: In the light of the gender assumption, it is also strange to recognize the sports (male or female) in which size is specifically taken into account to ensure equality of chance. This is most obvious in the case of some contact sports, such as boxing (lightweight, heavyweight, etc). Rather than weight, this consideration is not however taken into account where height may constitute an unfair advantage, as in basketball. The very short are effectively excluded from sports intended to inspire the whole population
Age: Despite the handling of gender and size, significant consideration is given to age, in defining "junior" sports (as in ball sports, for example) for reasons which are obvious. Analogous exceptions are less evident in the case of "senior" sports -- although some account of age may be taken with respect to marathon records, for example. Curiously, skilled players in regulated sports may be expected to "retire" at an early age because of the disadvantage they experience in relation to "younger" players. No distinct provision is made for their further participation in competitive sport.
Skill: Sports tend to be organized such us to marginalize the unskilled and unrecognized. Especially embarrassing have been the cases of ski jumper Eddie "The Eagle" Edwards, the swimmers Eric Moussambani and Paula Barila Bolopa, and the Jamaican national bobsleigh team -- all competing with little skill on behalf of unrepresented countries in specific Olympic sports. They evoked a level of public (media) interest and sympathy which was intolerable to those more skilled and to the organizers. On the other hand some sports make explicit provision for a "handicap", most notably golf.
Disability: A further assumption is the special distinction with respect to the "handicapped" for which Paralympic Game provisions are made. Whilst this is comprehensible, it is is strange to note that some with disability have been allowed to compete against the non-handicapped, most notably in the case of the "blade runner", the double amputee Oscar Pistorius. This logic does not appear to have been accepted in the case of those "handicapped" by gender. On the other hand, whether framed as a "handicap" or not, considerable unresolved controversy is created by potential transgender participation, as in the case of Caster Semenya.

Individual sports are highly regulated. There is further regulation governing any acceptance of the sport as an Olympic sport. The rate of innovation (as indicated by introduction of new sports and variations) is remarkably slow, with the possible exception of winter sports employing new technologies (snow board, etc). Of particular relevance to this argument is that there is no experimentation with more than two teams playing against each other, or together, on the same field, with one or more balls, perhaps playing across each other to different sets of goals, possibly with players of varying skills and attributes. By contrast, there is considerable experimentation with board games and online gaming. What cognitive patterns are reinforced by team sizes and playing patterns in the total set of Olympis sports?

Team sport competition is universally framed to be between two opposing teams -- despite what this might be considered to reinforce in undermining what is upheld as the spirit and higher purpose of sport. The pattern is somewhat modified by use of a succession of two-sided games to engender a single "winner" from the resulting pool of "losers". There is a curious consequential conflation of "winning" with "positive" and "losing" with a "negativity" to be deprecated. This consequence has been usefully reviewed by Barbara Ehrenreich (Bright-sided: how the relentless promotion of positive thinking has undermined America, 2009; Smile Or Die: how positive thinking fooled America and the world, 2010) and separately discussed from a cybernetic perspective (Being Positive Avoiding Negativity Management challenge of positive vs negative, 2005).

This process naturally has implications for engagement with "others" and "alternatives" in other contexts. The commitment is then to winning, through becoming "number one", associated with the commitment to ensuring that the other is "annihilated" -- transformed into a nullity (a zero). In the absence of experimentation with other formats, conventional sport reinforces a pattern which does not correspond to the complexity of society and its disparate challenges.

Card and casino games: Given the importance of these as a focus for psychosocial energy -- and in terms of the money gambled on them -- they merit similar analysis to that of sports. What patterns of thinking and interaction are reinforced and how are they constrained by "numbers"? How many players, size of deck, etc? Of particular interest is the role of chance and (ignorance) non-transparency regarding the strength of the opponent.

Board games: A similar quest for pattern reinforcement could be made in the case of board games. Size of board, number of pieces, etc? Especially relevant to this argument are the strategic skills traditionally associated with those such as chess. The latter makes apparent the ambiguity associated with so-called Knight's move thinking. This is framed as a highly creative possibility in chess but is considered symptomatic of thought disorder by the medical world (Stratagems and ploys characteristic of Knight's move thinking, 2012).

This comparison can be used to make the point even more strongly in that conventional chess moves could be compared to the simplest of moves required of parading soldiers from whom "lockstep" is typically desirable. The Knight's move in chess could however be compared to one of the simpler dance steps, suggestive of the many more complex variants widely appreciated but excluded from "sports". As might be imagined, comparisons between the steps of the waltz and the Knight's move have long been made (but presumably not by psychoanalysts). The "Lockstep" could be usefully compared to "groupthink" in a period when failure of imagination is deplored as increasing vulnerability to civilizational collapse (Thomas Homer-Dixon, The Ingenuity Gap, 2000).

Online gaming: The virtual arenas offer the widest scope to experimentation and rapid innovation. With respect to multi-teams operating in the same arena, the possible organization into a number of "guilds" contrasts with the practice in conventional sports. This relates more closely to real-world dynamics in which shifting strategic alliances are of considerable significance. Also of significance is the degree of anonymity in participation avoiding the need to distinguish gender, handicap, or the like. Typically differences in skill can be handled through forms of "handicap" designed into the game -- "levels", etc. Again this variety merits careful analysis. Number of guilds? Participants per guild, etc?

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Numbers in play in psychosocial organization