This document discusses chaos theory and its application to soccer. It begins with explanations of chaos theory and the butterfly effect. It then provides examples of how small changes can lead to large unpredictable outcomes, like a butterfly flapping its wings in Brazil potentially causing a tornado in Texas. It discusses how the complex interactions in a soccer game can be understood through chaos theory, with an example of how small changes to a scenario could alter the outcome of a game. It also discusses being "in the zone" and peak performance states that athletes can achieve through relaxation and imagery techniques. In under 3 sentences.

1. CHAOS, ZONES AND
IMAGERY IN SOCCER

2. CHAOS, ZONES AND
IMAGERY IN SOCCER
MAYBE IT’S THE BUTTERFLY’S
FAULT

3. CHAOS THEORY
• What is chaos theory?
Formally, chaos theory is defined as the study of
complex nonlinear dynamic systems. Complex
implies just that, nonlinear implies recursion and
higher mathematical algorithms, and dynamic
implies nonconstant and nonperiodic. Thus chaos
theory is, very generally, the study of forever
changing complex systems based on mathematical
concepts of recursion, whether in the form of a
recursive process or a set of differential equations
modeling a physical system.

4. BUTTERFLY EFFECT
The butterfly effect is a phrase that
encapsulates the more technical notion of
sensitive dependence on initial conditions in
chaos theory. Small variations of the initial
condition of a dynamical system may produce
large variations in the long term behavior of the
system. This is sometimes presented as esoteric
behavior, but can be exhibited by very simple
systems: for example, a ball placed at the crest
of a hill might roll into any of several valleys
depending on slight differences in initial position.

5. MORE BUTTERFLIES
Recurrence, the approximate return of a
system towards its initial conditions, together
with the sensitive dependence on initial
conditions, are the two main ingredients for
chaotic motion. They have the practical
consequence of making complex systems,
such as the weather, difficult to predict past
a certain time range—approximately a week,
in the case of weather.

6. LIKE A DROP OF WATER

7. A BUTTERFLY FLAPS ITS’ WINGS IN
BRAZIL
Inferface:
Please flap wings.
Click butterfly to see results.

8. AND WE GET A TORNADO IN TEXAS

9. •Brazil also wins another
World Cup, so go figure

10. WHY CHAOS
• Ever been to a soccer game?
– No really
• Chaos theory is an attempt to not only tell us
how something occurs, but also why

11. FROM HORST WEIN
• "One of the problems in coaching soccer is
the complexity and variety of situations
which the player is required to face. There is
also a considerable range of techniques and
skills which the handling of those situations
demands. "

12. COMPLEX SYSTEMS
• The application of complex systems theory to sports is
relatively new and there certainly is no guarantee that it will
lead to a complete understanding of sports-related
activities. On the other hand we tried to make the argument
that any theory that will be able to come close to this goal
will have to incorporate significant elements from complex
systems. We mentioned non-linearity and universality as
two of the most important characteristic features of complex
systems. An important consequence of those properties is
the appearance of chaotic attractors. The potential
application of chaos theory to sport behavior has been
discussed in the psychological literature:

13. • "(…)Current thinking has shifted from linear to nonlinear
and from uni-dimensional to multi-dimensional models for
research. Sport psychology scientists now believe that the
interactional approach of individual and situational factors
will take the field closer to the goal of understanding,
explaining, and predicting behavior (…). however, this focus
on multiple variables, complex systems, and nonlinear
relationships is in direct opposition to the current Newtonian
approach of trying to understand the world by examining
individual components (…). rather, a macroscopic
examination of complex, nonlinear systems is needed to aid
our understanding. Therefore, the purpose of this paper is
to provide a brief overview of such an approach, namely
chaos theory. We acknowledge that in our attempt to
explain and apply chaos theory to sport behavior, there is
the potential for over simplification of a complex
mathematical theory." Chaos Theory: A New Science for
Sport Behavior?, M.G. Mack, et al. [7]

14. We are convinced that eventually also the
other universal properties of complex
adaptive systems will prove to be helpful not
only in understanding but also in coaching
the multitude of current and most likely future
types of sports and games both on physical
as well as on virtual playing fields and
arenas.

15. SOCCER SCENARIO
• Game starts
• Star player runs into bench during warm-up
and is out
• Replacement player was up all night doing
homework, because they rarely get to play
• Coach and team have no confidence in
replacement

16. • Everyone tries to compensate for the sub
• Coach changes tactics
• Team mates compensate
• Team tries too hard and plays poorly
• Opponent sensing blood pours it on

17. • Players start to get CHIPPY
• No help from officials to keep things calm
• Other team reacts aggressively
• Coach asks a rhetorical question of the
referee

18. Coach gets
a red card!

19. FAULT
• If star player had been more careful, result
might have been different

20. SO WHAT
• What does this have to do with why we are
here today

21. BUTTERFLY EFFECT
• I’m here because of the butterfly's
• Actually I’M here to talk about Zones or Peak
Experience in soccer
• And more importantly, how we can help
athletes find their zone

22. ZONES & PEAK EXPERIENCE
• THAT SWEET SPOT IN TIME

23. CHARACTERISTICS OF
BEING IN THE ZONE

24. ANOTHER LOOK
• Flow
• Creativity
• Accomplishment
• Objective Space
• Mental Space
• Identity
• Locus of Knowing
• Content of Knowing
• Well-being
• Need and Fulfillment
• Feeling of Time
• Feeling of Reality

25. CHARACTERISTICS OF
BEING IN ZONE
• LOSS OF FEAR
• ABILITY TO EXECUTE BASIC SKILLS
• NO THINKING OF PERFORMANCE
• TOTAL IMMERSION IN ACTIVITY
• NARROW FOCUS OF ATTENTION
• TEMPORARY PHENOMENON
• FEELING OF BEING IN TOTAL CONTROL
• SELF VALIDATING
• INVOLUNTARY EXPERIENCE
• EXPERIENCE IS PERFECT

26. HOW CAN WE ENHANCE
OUR CHANCES
• Techniques for better performance
• A psychological approach

27. RELAXATION AND IMAGERY
• Relaxation demo and explanation

28. JACOBSON AND OTHERS
• Since the 30’s we have studied the
EFEECTS of RELAXATATION on muscle
tonus

29. IMAGERY
• In the 80’s I did a great deal of work using
relaxation and imagery to increase
awareness
• I found that it increased an athletes ability to
perform at a higher level
• Many reported afterwards experiences
related to Peak Experience

30. EXAMPLES OF IMAGERY
• Internal v. External References
• Learning v. Perfecting Technique
• Close your eyes for a minute, but keep your
hand near your wallet

31. BACK TO THE BUTTERFLY'S
• By understanding complex systems we may
one day better understand how to better
prepare players

32. SOCCER SCENARIO II
• Coach decides to have team manager move
bench because he doesn’t like where it is
• Star player does not run into bench
• Game is played well by everyone
• Coach does not ask a rhetorical question

33. • Coach is still shown a red, but
this time its’ the butterfly's fault

34. CHAOS, ZONES AND
IMAGERY IN SOCCER
• THANK YOU
• MIKE MARGOLIES
• Sport Psychology Consultants
• TheMental-Game.com
• (425) 241-6539

35. References
To be honest I’ve lost the exact references to this project. Some of
them came from an unmarked paper I have. Some of them come
from a reference sheet. I will supply those. It was never my
intention to not give credit to those that did all of the research.

36. References
• Chaos Theory
• References
• Blackerby, R.F. (1993). Application of chaos theory to psychological models. Austin, TX: Performance Strategies Publications.
• Davidson, R.J., & Schwartz, G.E. (1976). The psychobiology of relaxation and related states: A multi-process theory. In D.I. Mostofsky (Ed.),
Behavior control and modification of physiological activity (pp. 399-442). Englewood Cliffs, NJ: Prentice-Hall.
• Endler, N. S. (1978). The interaction model of anxiety: Some possible implications. In D.M. Landers & R.W. Christina (Eds.) , Psychology of
motor behavior and sport-1977 (pp. 332-351). Champaign, IL: Human Kinetics.
• Gleick, J. (1987). Chaos: Making a new science. New York: Penguin Books.
• Gould, D., & Krane, V. (1992). The arousal-athletic performance relationship: Current status and future directions. In T.S. Horn (Ed.),
Advances in sport psychology (pp. 119-142). Champaign, IL: Human Kinetics.
• Handford, C., Davids, K., Bennett, S., & Button, C. (1997). Skill acquisition in sport: Some applications of an evolving practice ecology.
Journal of Sports Sciences, 15, 621-640.
• Hardy, L. (1990). A catastrophe model of performance in sport. In J.G. Jones & L. Hardy (Eds.), Stress and performance in sport (pp. 81-
106). Chichester, England: Wiley.
• Hardy, L., & Fazey, J. (1987). The inverted-U hypothesis: A catastrophe for sport psychology. Paper presented at the meeting of the North
American Society for the Psychology of Sport and Physical Activity, Vancouver, BC.
• Hull, C.L. (1943). Principles of behavior. New York: Appleton-Century-Crofts.
• Kellert, S.H. (1993). In the wake of chaos: Unpredictable order in dynamical systems. Chicago: The University of Chicago Press.
• Jackson, S. A., & Csikszentmihalyi, M. (1999). Flow in sports. Champaign, IL: Human Kinetics.
• Kelso, J.A.S. (1981). On the oscillatory basis of movement. Bulletin of the Psychonomic Society, 18, 63.
• Kelso, J.A.S., & Schoner, G. (1988). Self-organization of coordinative moment patterns. Human Movement Science, 7, 27-46.
• Kerr, J.H. (1985). The experience of arousal: A new basis for studying arousal effects in sport. Journal of Sport Sciences, 3, 169-179.
• Krane, V., & Williams, J. (1987). Performance and somatic anxiety, cognitive anxiety, and confidence changes prior to competition. Journal of
Sport Behavior, 10, 47-56.
•

37. More References
• Martens, R., Burton, D., Vealey, R., Bump, L., & Smith, D. (1990). The development of the Competitive State Anxiety Inventory-2 (CSAI-2). In R.
Martens, R.S. Vealey, & D. Burton (Eds.), Competitive anxiety in sport (pp. 117-190). Champaign, IL: Human Kinetics.
• Martens, R., Vealey, R.S., & Burton, D. (Eds.) (1990). Competitive anxiety in sport. Champaign, IL: Human Kinetics.
• Masterpasqua, F. & Perna, P.A. (Eds.) (1997). The psychological meaning of chaos: Translating theory into practice. Washington, DC:
American Psychological Association.
• Perna, P.A. & Masterpasqua, F. (1997). Introduction: The history, meaning, and implications of chaos and complexity. In F. Masterpasqua &
P.A. Perna (Eds.), The psychological meaning of chaos: Translating theory into practice (pp. 1- 19).Washington, DC: American Psychological
Association.
• Quentmeyer, T. (1998). Chaos theory, dynamical systems, and fractal geometry. [On-line].
Http://hyperion.advanced.org/3493/noframes/chaos.html.
• Scholz, J.P., & Kelso, J.A.S. (1990). Intentional switching between patterns of bimanual coordination depends on the intrinsic dynamics of the
patterns. Journal of Motor Behavior, 22, 98-124.
• Spence, K.W. (1964). Anxiety (drive) level and performance in eyelid conditioning. Psychological Bulletin, 61, 129-139.
• Spence, K.W., Farber, I.E., & McFann, H.H. (1956). The relation of anxiety (drive) level to performance in competitional and noncompetitional
paired-associated learning. Journal of Experimental Psychology, 52, 296-305.
• Spence, J.T., & Spence, K.W. (1966). The motivational components of manifest anxiety: Drive and drive stimuli. In C.D. Spielberger (Ed.),
Anxiety and behavior. New York: Academic Press.
• Spielberger, C.D. (1971). Trait-state anxiety and motor behavior. Journal of Motor Behavior, 3, 265-279.
• Sternad, D. (1998). A dynamic systems perspective to perception and action. Research Quarterly for Exercise and Sport, 69, 319-325.
• Taylor, J., & Demick, A. (1994). A multidimensional model of momentum in sports. Journal of Applied Sport Psychology, 6, 51-70.
• Triplett, N. (1897). The dynamogenic factors in pacemaking and competition. American Journal of Psychology, 9, 507-553.
• Wallace, S.A. (1996). Dynamic pattern perspective of rhythmic movement: An introduction. In H.N. Zelaznik (Ed.), Advances in motor learning
and control (pp. 155- 194). Champaign, IL: Human Kinetics.
• Yerkes, R.M., & Dodson, J.D. (1908). The relationship of strength of stimulus to rapidity of habit formation. Journal of Comparative Neurology
and Psychology, 18, 459-482.

38. Mike Margolies
• Author of new book:
• The Athlete within You; A Mental Approach
to Sports and Business