A parametric model is developed and fitted to English league and cup football data from 1992 to 1995. The model is motivated by an aim to exploit potential inefficiencies in the association football betting market, and this is examined using bookmakers' odds from 1995 to 1996. The technique is based on a Poisson regression model but is complicated by the data structure and the dynamic nature of teams' performances. Maximum likelihood estimates are shown to be computationally obtainable, and the model is shown to have a positive return when used as the basis of a betting strategy.

Data from over 4000 recent association football (soccer) matches from the main English competitions show clear evidence that the rate of scoring goals changes over the course of a match. This rate tends to increase over the game but is also in¯uenced by the current score. We develop a model for a soccer match that incorporates parameters for both the attacking and the defensive strength of a team, home advantage, the current score and the time left to play. This model treats the number of goals scored by the two teams as interacting birth processes and shows a satisfactory ®t to the data. We also investigate football cliche  s and ®nd evidence that contradicts the cliche  that a team is more vulnerable just after it has scored a goal. Our model has applications in the football spread betting market, where prices are updated during a match, and may be useful to both bookmakers and bettors.

We focus on modelling the 92 soccer teams in the English Football Association League over the years 1992-1997 using refinements of the independent Poisson model of Dixon and Coles. Our framework assumes that each team has attack and defence strengths that evolve through time (rather than remaining constant) according to some unobserved bivariate stochastic process. Estimation of the teams' attack and defence capabilities is undertaken via a novel approach involving an approximation that is computationally convenient and fast. The results of this approximation compare very favourably with results obtained through the Dixon and Coles approach. We note that the full model (i.e. the model before the above approximation is made) may be implemented using Markov chain Monte Carlo procedures, and that this approach is vastly more computationally expensive. We focus on the probabilities of home win, draw or away win because these outcomes constitute the primary betting market. These probabilities are estimated for games played between any two of the 92 teams and the predictions are compared with the actual results.

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This paper introduces the concept of effective structural size in titanium alloys and its importance with respect to material production routes and component lifing/design. Traditionally, process route optimization has relied on optical microscopy, which may be misleading when predicting mechanical properties. Similarly, continuum mechanics and current lifing methods are based on empirical data analysis. The advent of advanced material characterization techniques, e.g. EBSD combined with crystal plasticity modelling, has the potential to provide the next generation of mechanistically sound methods that more accurately predict material behaviour in complex loading regimes. These benefits are reviewed in the context of industrial application. Crystal plasticity modelling techniques are presented and a particular structural unit -termed a rogue grain -in a model single-phase titanium alloy is considered. Cold dwell under both strain and stress control is then assessed in the structural unit.