This thesis investigates problems of performance modelling in sport. Mathematical models are used to evaluate the performance of individuals, teams, and the competition rules under which they compete. The thesis comprises a collection of papers on applications of modelling to Australian rules football, soccer and cricket. Using variations of the model wij = ui + hi - uj + eij where wij is the home team winning margin when home team i plays away team j, ui is a team rating, hi is an individual ground effect and eij is random error, the evaluation of team home ground advantage effect (HA) is studied in detail. Data from the Australian Football League and English Association Football for 1980 to 1995 are investigated. The necessity of individual team HAs is demonstrated. The usual methods of calculating HA for competitions is shown to be inappropriate for individual teams. The existence of a spurious HA when home and away performances are compared is discussed. For a balanced competition, fitting the above model by least squares is equivalent to a simple calculator method using only data from the final ladder. A method of calculating HA by pairing matches is demonstrated. Tables of HA and paired HA in terms of points/game for each year are given. The resultant HAs for both Australian rules football and soccer are analysed. Clearly there is an isolation effect, where teams that are isolated geographically have large HAs. For English soccer, the paired HA is shown to be linearly related to the distance between club grounds. As an application of these methods, the development and implementation of a computer tipping program used to forecast Australian rules football by rating teams is described. The need for ground effects for each team and ground, and the use of heuristic methods to optimise the program is discussed. The accuracy of the prediction model and its implementation by publication in the media is discussed. International comparisons show prediction methods are limited by the data. Methods for evaluating the fairness of the League draw and the finals systems are given. The thesis also investigates the use of dynamic programming to optimise tactics in football and cricket. The thesis develops tables giving the optimal run rate and the expected score or probability of winning at any stage of a one-day cricket innings. They show a common strategy in one-day cricket to be non-optimal, and a heuristic is developed that is near optimal under a range of parameter variations. A range of dynamic programming models are presented, allowing for batsmen of different abilities and various objective functions. Their application to performance modelling are shown by developing a radically different performance measure for one day cricket, and applying it to a one-day series.
| Identifer | oai:union.ndltd.org:ADTP/216569 |
| Date | January 1997 |
| Creators | Clarke, Stephen R., sclarke@swin.edu.au |
| Publisher | Swinburne University of Technology. |
| Source Sets | Australiasian Digital Theses Program |
| Language | English |
| Detected Language | English |
| Rights | http://www.swin.edu.au/), Copyright Stephen R. Clarke |
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