3. 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
4.
5.
6. P (t) = At α
Measures how volatile the league is,
i.e. how frequent they fire managers.
7. 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
8. 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.
9. 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 !!!
10. “Home” & “Away” advantage (Model A)
or Equal Chances (Model B)
11. “Home” & “Away” advantage (Model A)
or Equal Chances (Model B)
12.
13.
14.
15. Wage Cap of players
removed
Start of
TV coverage
16.
17. 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.