Liam J. A. Lenten

Unobserved Components in Competitive Balance and Match Attendances in the Australian Football League, 1945–2005: Where is All the Action Happening?

A structural time-series model is estimated to investigate the relation between competitive balance, measured by the actual-to-idealised standard deviation ratio, and average match attendance in the Australian Football League from 1945 to 2005. The unobserved components approach allows the data to be modelled in ways new to the literature on this topic. A seemingly unrelated time-series version shows much of the explanatory power of the data to be in the irregular (fast-moving) component. An OLS regression produces robust goodness-of-fit and diagnostic results, and the coefficient estimates produce inferences in contrast to those of Schmidt and Berri (2001), with persistent shocks.

A Time-Series Analysis of the Demand for Life Insurance Companies in Australia: An Unobserved Components Approach

We systematically explore the time-series properties of life insurance demand using a novel statistical procedure that allows multiple unobservable (but interpretable) components to be extracted. This methodology allows the data to be modelled in new and innovative ways. We find univariate series decomposition allows us to more easily explain the behaviour of life insurance demand over the sample period (1981–2003), than would otherwise be possible. A multivariate model (including a number of variables thought to influence demand) produces quite pleasing results overall. A SUTSE model involving demand and each of the explanatory variables in turn shows evidence of common components in all cases but one. Finally, an out-of-sample forecast comparison shows the univariate model to outperform the multivariate model for accuracy.

Unbalanced Schedules and the Estimation of Competitive Balance in the Scottish Premier League

Since the season ending in 2001, the Scottish Premier League (SPL) has, unlike other European football leagues, utilised an unbalanced schedule, by which the strongest teams in a given season play each other an extra time, mutatis mutandis for the weakest teams. While this approach may make sense for several reasons, it also has implications for within-season measures of competitive balance, because it creates biases in the set of win ratios from the end-of-season league table. This paper applies a simple log-probability rule to calculate a set of adjusted win ratios correcting for this inherent bias. Such an adjustment is necessary if one wishes to compare within-season competitive balance of the SPL with other European leagues. It is shown that by correcting for the unbalanced schedule, the SPL is consistently less competitive over the sample period. The implications of this finding are discussed at length.

Towards a New Dynamic Measure of Competitive Balance: A Study Applied to Australia's Two Major Professional 'Football' Leagues

A new measure for competitive balance between seasons is proposed, which takes the form of a mobility gain function, based on each team’s win ratios from the current and previous seasons. This ‘dynamic’ function measures competitive balance within a oneperiod change framework. While it is not suggested that this measure replace useful existing within-season measures, such as the widely used actual-to-idealised standard deviation (ASD/ISD) ratio, this measure does overcome one of the shortcomings of within-season measures – that is, the ability to pick up uncertainty of outcome from season to season, rather than merely from round-to-round. Hence, it is suggested that this measure could be used in conjunction with within-season measures in time-series analysis. An application to Australia’s Australian Football League (AFL) and National Rugby League (NRL) over a century of data reveals numerous interesting comparisons.

An empirical investigation into long-term climate change in Australia

Abstract In this paper, we undertake an empirical investigation into the possibility of climate change in Australian centres using average monthly air temperatures for six sites around the country over the period 1901:1–1998:12. By estimating a multivariate structural time series model and carrying out the appropriate tests, it is concluded that the temperature series is I(1). A graphical inspection of the extracted trends reveals that temperature has an upward trend in many centres. Given that the data may involve measurement errors, the results should be treated with caution.

Measurement of Competitive Balance in Conference and Divisional Tournament Design

The conference and divisional system has long been a staple part of tournament design in the major pro-sports leagues of North America. This popular but highly rigid system determines on how many occasions all bilateral pairings of teams play each other during the season. Despite the virtues of this system, it necessitates removing the biases it generates in the set of win ratios from the regular season standings prior to calculating within-season measures of competitive balance. This article applies a modified version of a recent model, an extension that is generalizable to any unbalanced schedule design in professional sports leagues worldwide, to correct for this inherent bias for the NFL over the seasons 2002-2011, the results of which suggest the NFL is even more competitively balanced than thought previously.

Modelling the trend and seasonality in the consumption of alcoholic beverages in the United Kingdom

A univariate time series analysis of the consumption of beer, wine and spirits in the UK over the period 1964-1995 is presented. The analysis shows that the consumption of beer and wine exhibits stochastic seasonality while the consumption of spirits exhibits deterministic seasonality. Moreover, the three series are found to have stochastic trends. Analysis of the out-of-sample forecasting power of the various models reveals that the model with stochastic trend and seasonality is superior to other models. The results cast doubt on the validity and soundness of the practice of modelling the consumption of alcoholic beverages by assuming deterministic trend and seasonality.

When sports rules go awry

Wright (2014) recently presented a survey of sporting rules from an Operational Research (OR) perspective. He surveyed 21 sports, which consider the rules of sports and tournaments and whether changes have led to unintended consequences. The paper concludes: “Overall, it would seem that this is just a taster and there may be plenty more such studies to come”. In this paper we present one such study.

Secondary Behavioural Incentives: Bonus Points and Rugby Professionals

We examine the impact of secondary incentives by evaluating agent behaviour in a professional sport that rewards multiple outcomes. Our analysis focuses on the Super Rugby competition, which awards four points for a win and bonus points for scoring four or more tries and/or losing by seven or fewer points. Using binary response models, we find that significantly more tries are scored by teams late in matches when they can earn the try bonus point with one more try, but only when the match result itself is already likely decided. This result offers important evidence on multitasking by professionals.

IN DEFENCE OF MODEL-BASED SEASONAL ADJUSTMENT: AN ILLUSTRATION USING AUSTRALIAN DATA #

It is argued that the X-11 seasonal adjustment procedure suffers from severe drawbacks, and so it should be abandoned in favour of model-based seasonal adjustment. Furthermore, it is argued that Harveys structural time series model is superior to the conventional seasonal ARIMA models for the purpose of model-based seasonal adjustment. It is shown, with the help of a large number of Australian time series, that the nature of seasonality differs from one series to another, and this is why model selection is crucial for seasonal adjustment. It is further shown that model-based seasonal adjustment could produce results that are significantly different from those obtained by applying the X-11 procedure. Since the X-11 procedure is not based on an explicit model and in view of its other serious drawbacks, it is concluded that the procedure should be abandoned in favour of model-based seasonal adjustment.