Coaching for character development: insights from a simple mathematical model

Abstract

Problem statement: Character development is important for achieving sporting success. However, it cannot be presumed that athletes will develop healthy attitudes, values or beliefs about themselves, their sport or their opponents. Unfortunately, character development has lagged behind fitness and skills training in having recognised protocols able to consistently deliver positive outcomes for athletes. Approach: The logistic map is a simple mathematical model which has found applicability across disciplines when seeking to understand change. Indeed, the logistic map can model a variety of complex behaviours and has thus found favour in the biological sciences, including psychology. A simple variation of the logistic map has been developed and tested herein as a way to begin to understand the complexities of character development amongst athletes. Purpose: This paper sets forth a set of conditions, testable predictions, and some warnings useful for physical education teachers, coaches and sport psychologists alike when seeking to construct effective character development protocols for athletes. Results: The mathematical model provided three outcomes of note. First, it was capable of demonstrating substantial sustained positive growth (i.e. ≤184%) over time. It was therefore fit-for-purpose. Second, character development required at least moderate levels of adversity to develop and occurred by small increments over time (i.e. ≤81 iterations). Character development failed when threat was low and/or the initial amount of virtue (i.e. character) displayed by athletes was either similar to, or greater than, the threat faced. Usefully, each of these outcomes is also consistent with real-world experience and thus again validates the model. The implications of these outcomes are various but include: (1) the importance of promoting competition amongst junior athletes; (2) using a variety of experiences to spur character development so as to attain significant improvements in a time-limited way; and (3) avoiding hubris in elite athletes. The third, and perhaps most surprising, finding was that motivational messaging intended to improve athletes’ character may be counter-productive if not tempered. A ratio of approximately 2:1 between hope-based vs. temperance-based motivational messages is suggested. Conclusions: Character development is multi-facetted and therefore complex, but nevertheless essential to sporting success. The present model reduces character development to a limited set of variables. In doing so it provides: (1) guidance to physical education teachers and coaches for the development of efficient protocols intended to enhance athletes’ character development; and (2) testable predictions useful to sport psychologists in refining such protocols and optimising athletic performance.