Self-Organization, Economics &
Football Managers
Bernard Leong
3 June 2009

Self-Organization Long Tail
Self-Organized Criticality
Tipping Point

SOC implies scale invariance and “simple” microscopic
mechanism leads to an observed macroscopic effect.
Earthquakes History
Objects
Economic, Social &
Mechanism Classical Mechanics
Political Interactions
Self-Organization Formation of tectonic Formation of a social
Structure plates hierarchy
Criticality Earthquake Political Change
Power Law Plot the frequency of Plot the frequency of tenures
(Emergent Phenomenon) earthquakes vs Richter scale vs tenures of leaders

P (t) = At α
Measures how volatile the league is,
i.e. how frequent they fire managers.

Period Power Law α
England 1874-2005 ✔ -2.23
France 1928-2003 × n/a
Spanish 1910-2003 ✔ -2.75
Germany 1947-2003 ✔ -2.51
All Managers 1874-2005 ✔ -2.75
National Coaches 1902-2003 ✔ -2.92
American Baseball 1875-2003 ✔ -2.63
American Football 1920-2003 ✔ -2.08
Japanese Baseball 1936-2003 ✔ -2.41
Source: Aidt, Leong, Sgroi, Saslaw, Physica A, 370(2): 697-703

Can we explain this via a
microscopic model?
✤ We initialize 20 managers with two attributes: (1) Reputation and (2)
Tenure Length.
✤ Use the standard round robin (38 games) with each managers playing
against each other and a simple scoring system. The principles of
relegation, “Home” and “Away” apply.
✤ We use a set of criteria to decide how we fire a manager.
✤ Then run it for a hundred years (steady state) and see if we can
produce the power law distribution relating tenure length and
frequency.

When do we “fire” a manager?
✤ A manager is fired for poor performance - Firing threshold.
✤ A manager is poached by another club by good performance -
Poaching threshold
✤ A manager retires due to old age - Ossification threshold
✤ A manager is replaced when the team is relegated in the main league
after 38 games.
You are
fired !!!

“Home” & “Away” advantage (Model A)
or Equal Chances (Model B)

“Home” & “Away” advantage (Model A)
or Equal Chances (Model B)

Wage Cap of players
removed
Start of
TV coverage

Economics & Football Managers
✤ Competitive market forces might bring
sports leagues to a point of maximum
efficiency related to self-organized
criticality.
✤ Competition is a zero sum game where
what matters is relative, not absolute
performance.
✤ The Red Queen Principle: The more
things change, the more they stay the
same.