Developing a Formula for the Comparison of Athletics Performances Across Gender, Age and Event Boundaries Based on South African Standards
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Vaal University of Technology Developing a formula for the comparison of athletics performances across gender, age and event boundaries based on South African standards SWJ Bekker (083 734-7079) 212118781 Dissertation Magister Technologiae: Information Technology In the FACULTY OF APPLIED AND COMPUTER SCIENCES Department of Information and Communication Technology At the Vaal University of Technology Supervisor: Dr J. F. Janse van Rensburg Declaration I, Sarel Wilhelmus Jacobus Bekker, ID number 4109185061087, hereby declare that the content of this dissertation is my own unaided work and that all quoted in this dissertation is properly acknowledged and referenced. Signed: ___________________ At Vanderbijlpark on 28/01/2018 i Acknowledgements Firstly and with humility, to GOD almighty for the ability and insight to conduct this work. To my departed wife who had to listen to my ideas and her support during the whole process of investigation, reading and writing. I wish to thank her mainly for being there for me as a soundboard when needed. To my daughters who are both involved in sport and have given me support and encouragement to continue. I want to thank Richard Stander (formerly from ASA and now with Boland Athletics) who has continually provided me with insight and information since 1985. I would also like to thank all the friends I have made through athletics, some only known by voice and a large number in person. Their continuous support (and criticism) has inspired me to continue with this work. My colleagues at Vaal University of Technology (especially Willem and Hannes) for their motivation to continue. Dr Pieter Conradie for giving initial direction to this work. ii Abstract The author addressed the need of parents, school teachers and athletic coaches to be able to assess the level of performance and to compare performances of individual athletes of either gender and in any age group. This was achieved by creating formulas for the following areas in track and field athletics: Correctly set base standards for all events from the results of 5 year weighted average performances. Use the base standards to determine comparative standards for all events in all age groups. Define a function to compare male and female performances in all events. For all events, generate tables with a range from 0 to 1000 as a comparative measurement. These formulae were created using data from international and national meetings. Different case studies were used for each of the areas and the results were evaluated using the data. In all four areas, it was possible to define hybrid functions with a confidence factor better than 99%. The final performance tables can be updated during revision periods (every 2 to 4 years) by using the national results for the last 5 years. These revisions will be required as implements, tracks and training methods change with time and this will then in turn influence the performances. This is evident from the continuous improvement of records in all events. iii These tables will not only assist coaches to improve training techniques but it will also facilitate team managers to improve team selections, and it will open the options of meeting organizers to arrange meetings using different formats. As this is a new and unique formulation for measuring performances at junior level in world athletics it can be used as a basis for future improvements in the field of comparative measurement for athletics. Using these tables at senior level it may assist to settle arguments of performance comparisons that are not addressed by the current tables used by the International Amateur Athletics Federation (IAAF). It will also avoid the use of different tables for the same events in standard track and field athletics compared to those used for combined event competitions. The author of the tables used by the IAAF has recognised this work as a new and unique development. Future development will include the automatic update of all functions and creation of tables for publication from a standard Windows® based application. A companion application, using the results from this research, will be developed. This application will address all the administration functions required to conduct a meeting. It will include the preparation for the meeting, capturing of results during the meeting and result reporting after the meeting. Keywords: Athletics, Performance, Comparison, Measurement, Tables, Age groups, Events, Competitions. iv Table of contents Declaration i Acknowledgements ii Abstract iii List of tables xi List of figures xiii List of annexures xvi Mathematical functions xvii Conventions xviii List of abbreviations xix Chapter 1: Motivation for the research 1 1.1 Introduction 1 1.2 Background of the study 2 1.3 Problem statement 5 1.4 Research objectives 5 1.4.1 Primary objetive 6 1.4.2 First sub-objevtive 6 1.4.3 Second sub-objective 6 1.4.4 Third sub-objective 7 1.5 Research method 7 1.6 Research ethics 8 1.7 Research layout 8 Chapter 2: Current systems literature review 10 2.1 Introduction 10 2.2 Measurement as a science 10 2.2.1 Metrology 10 2.2.2 Measuring instruments 11 2.2.3 Accuracy and Precision 12 2.2.4 Sensitivity, Threshold and Resolution 14 2.3 Measurement units 16 v 2.3.1 The need for standards and units 16 2.3.2 Standard systems 17 2.3.3 Dimensions 18 2.4 History of the Olympic Games 18 2.4.1 Ancient games and the origin of the Olympic Games 18 2.4.2 Modern Olympic Games – The revival 19 2.4.3 Rules and Regulations 20 2.5 Measurement in track and field events 21 2.5.1 The need for measurement 21 2.5.2 Measurement of Time 23 2.5.3 Measurement of distance 27 2.6 Combined events competitions 28 2.7 Comparitive tables 32 2.7.1 IAAF Scoring tables (previously Hungarian tables) 32 2.7.2 Purdy tables (Based on the Portuguese scoring tables) 33 2.7.3 Modified Purdy tables 34 2.7.4 Peter Riegel’s prediction formula 35 2.7.5 David F. Cameron model 35 2.7.6 Molvar conversion tables 35 2.7.7 English High Schools tables 36 2.7.8 Apple, SASOL, ABSA, ASA, APE tables 36 2.8 Best performance measurement 37 2.9 Scoring systems 38 2.9.1 Medal scoring system 39 2.9.1 Point scoring system 39 2.9.3 Table scoring system 40 2.10 Victor and Victrix Ludorum 41 2.11 Factors to consider in creating a table 43 2.11.1 Influence of training 43 2.11.2 Track and equipment development 44 2.11.3 Height above sea level 45 2.11.4 Wind resistance 45 vi 2.11.5 Reaction times of timekeepers 45 2.12 IAAF Coompetition rules 46 2.13 Summary 46 Chapter 3: Review of current systems 47 3.1 Introduction 47 3.2 Delimitations 49 3.3 Case considerations 50 3.4 Overview of current tables 51 3.4.1 IAAF tables 51 3.4.2 Hungarian tables 73 3.4.3 Purdy tables 73 3.4.4 Mercier tables 74 3.4.5 Running prediction tables 75 3.4.6 Graphical comparison of the existing tables 75 3.4.7 Criticism on the existing tables 77 3.5 Summary 79 Chapter 4: Data Analysis and Case Formulation 80 4.1 Data acquisition 80 4.2 Data ordering 80 4.3 Data analysis 87 4.4 Modeling possible cases 88 4.4.1 Linear model 89 4.4.2 Exponential model 89 4.4.3 Logarithmic model 90 4.4.4 Polynomial model 91 4.4.5 Least mean squares model 92 4.4.6 Exponential functions 93 4.4.7 Hybrid model 93 4.5 Scaling parameters 93 4.6 Model parameters 94 vii 4.7 Reasons why technical standards are required 94 4.7.1 Age differences 95 4.7.2 Gender differences 95 4.7.3 Race distances 96 4.7.4 Implement weight considerations 96 4.7.5 Height limitations and distance between obstacles 96 4.7.6 Events per athlete limitation 97 4.7.7 Starting heights and increments for vertical jumps 97 4.7.8 Consistency of event at different meetings 97 4.7.9 Order of events in combined events competitions 98 4.8 Current technical standards 98 4.9 Case development 101 4.10 Data to be used in the case evaluations 102 4.11 Summary 102 Chapter 5: Case evaluations 104 5.1 Introduction 104 5.2 Data selection 104 5.3 Model evaluations for the Senior Men case 111 5.3.1 Model comparisons 111 5.3.2 Comparison discussion 122 5.4 Relation between events 124 5.4.1 Track event relations for distances from 50m to 10 000m 125 5.4.2 Relation between track events and obstacle events 128 5.4.3 Race walking events 129 5.4.4 Relay events 130 5.4.5 Field events without implements 131 5.4.6 Field events with implements 132 5.4.7 Changing the constants for track events 132 5.5 Age difference effects for male athletes 133 5.5.1 Position progression per event 133 5.5.2 Age progression within specific events 136 viii 5.5.3 Age progression for hurdle events 140 5.5.4 Age progression for steeple chase and race walking events 141 5.5.5 Age progression for field events 141 5.5.6 Age progression for jumping events 141 5.5.7 Age progression for throwig events 143 5.5.8 Gender differences 146 5.6 Generation of comparitive tables 147 5.6.1 Table criteria 147 5.6.2 Table formula for 100 meter Junior Men 149 5.6.3 Alternative functions for 100 meter Junior Men 152 5.6.4 Selection of the table function 153 5.6.5 Verification of the table function for track events 154 5.6.6 Verification of the table function for field events 156 5.6.7 Verification of the table function for gender changes 156 5.6.8 Inverse table function 157 5.6.9 Hand timing changes 158 5.6.10 Height above sea level adjustment 159 5.7 Summary 160 Chapter 6: Contribution and relevance 162 6.1 Contribution to sport science 162 6.2 Peer review comments 162 6.3 Relevance to current problems 163 6.3.1 Assisting coaches and administrators 163 6.3.2 Combined event competitions 164 6.3.3 Extension to Masters