Abstract
Like many professional sports leagues, the Australian Football League (AFL) operates an unbalanced schedule in which each team plays other teams an unequal number of times (once or twice) each season. This has led the AFL purposefully to schedule certain matches to be repeated each season with the remaining fixtures mostly randomly allocated. We explore the efficacy of this policy by estimating a fixed (rivalry) effects hedonic demand model for within-season AFL matches. Estimated rivalry effects are imputed into a binary integer program minimisation that provides an optimal profile of rematches against which we consider recent historic scheduling behaviour. As expected, rivalry effects are greatest for the large-market Melbourne ‘troika’ teams, which provides partial support for the AFL’s maintained policy. However, there exists scope for increasing aggregate attendance in the unbalanced part of the season by further attention to selection of rematches. We also observe some decline in interest of the second within-season meetings of popular troika teams and a rise in popularity of the intrastate derbies. Finally, we compare our results to alternative scheduling arrangements for the unbalanced part of the season.
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Notes
Throughout this paper we use the term ‘rival’ to refer to an opponent team, and the term ‘rivalry’ to refer to the implicit competition between a pair of teams. In the empirical part of the paper, we estimate ‘rivalry effects’ to provide a measurement of this effect over the 120 match pairings that we observe.
While not an explicit policy, per se, there is clear evidence from the AFL that attendance maximisation is one of their primary objectives in match scheduling. For example, in relation to the unbalanced portion of the season’s fixtures, the 2014 AFL Annual Report states: “…including the balancing of requests [from teams] and expectations from multiple stakeholders but with a focus on attendance and making the game more accessible for all fans around Australia.” (AFL Annual Report 2014, p. 36).
Although aggregate attendance maximisation appears to be the principal objective of the AFL, it is likely that they are also aware of potential problems with such a strategy over a longer time horizon: for example, shutting certain teams out of hosting popular revenue-generating clubs. Although, as Booth (2007) discusses, there is some compensation for small-market clubs who are adversely affected via a tax of gate revenues on the large-market matches.
The AFL as the elite national competition evolved out of the Victorian Football League, or VFL (known as such until 1989), which was primarily a Melbourne-suburban competition. When it sought to become a national-based league, it chose to do so by way of expansion from 1987, though that was preceded initially via the relocation of South Melbourne (Swans) to Sydney in 1982.
See AFL 2013 Annual Report http://www.afl.com.au/afl-hq/annual-reports.
This occurred when the number of teams increased from 12 to 14, while the ‘home-and-away’ (regular) season remained at 22 games. In the 1990s expansion continued to 16 teams. As discussed below, over our sample period the number of teams remained constant at 16 teams but the league has since expanded to 18 teams.
Television rights are also an important factor. The current (2012–2016) broadcast rights sold in April 2011 for A$1.253 billion (US$1.35 billion). This figure accounts for approximately 20–25 % of all club revenues. We do not consider TV viewership in the current study. Buraimo (2008) studies the trade-off between match attendance and TV viewership in the context of English football.
It should be noted that over the 1997–2010 sample, the correlation between win percentages and log of memberships (equivalent of season ticket holders in North American sports) is only 0.106, which indicates that playing large-market teams more often does not necessarily result in a tougher schedule.
The beginning of the sample coincides with Port Adelaide’s entrance into the competition that, with the amalgamation of Fitzroy and Brisbane in the same year, preserved the 16-team format in place since 1995 when Fremantle joined the league. We limit the sample to the year preceding the entry of Gold Coast into the league in 2011, which was subsequently followed by the entry of Greater Western Sydney in 2012 that expanded the league to the current 18-team format. This provides us the same set of 16 teams over the full sample period.
Another reason to exclude finals is that venue capacities often bind, which is almost never the case for regular-season games. In our sample, in only 13 of 2816 (i.e. less than 0.5 %) of matches did attendance exceed stated venue capacity less 500.
On occasions where teams meet a second time, both a home and away match is played for each team.
The reason for the relaxation of this sequencing constraint was to make easier the task of satisfying other practical constraints in the scheduling problem—for example, giving both teams a minimum 6-day break between games. However, this policy change ultimately has no implications for the difficulty-of-schedule problem (Goossens and Spieksma 2012).
Odds in this context are expressed in decimal terms: the return that would be generated for a one-unit wager in the event of a win. As an example, if Odds(Home) \(=\) 1.72 and Odds(Away) \(=\) 2.09, then \({{\mathrm{BOR}}}=\) ln(1.72/2.09) \(= -0.1948\).
Equation (2) is a simple re-specification of the actual standard deviation, i.e. \((\sum _{i=1}^N[w_{i,t} - 0.5]^2/N)^{0.5}\), to idealised standard deviation, i.e. \(0.5/t^{0.5}\), ratio. \({{\mathrm{RSD}}}\) is fixed to one for \(t = 1\).
Membership numbers are analagous to ‘season ticket holders’ in North American sporting terminology.
Although (absolute) ladder-rank difference may be interpreted in some sense as a measure of within-match competitive balance, we argue that betting odds provide a better measure. For example, in the second round of a season, the difference between first and last place on a ladder is only one win, but (potentially) constitutes an absolute rank difference of 15.
Scoring in Australian rules takes two forms: a goal (worth six points) for a kick between the center upright posts, or a behind (worth one point) for any other score.
ANZAC day commemorates the Battle of Gallipoli by Australian and New Zealand armed forces during World War I, and is a national public holiday in Australia. See http://www.awm.gov.au/commemoration/anzac/anzac_tradition.asp.
Since numerous AFL teams play home matches at multiple venues, inclusion of both home team and venue effects is permissible.
As discussed below, we consider it possible that rivalry effects can change both within season and across seasons.
We use Wooldridge’s (2002) test for serial correlation in panel data, which is robust to unbalanced panels as discussed by Drukker (2003). To operationalise the test, we subdivide each season into two panels: a complete (i.e. first time meetings) and an incomplete (i.e. second time meetings) cross section of team pairings. The test rejects the null of first-order serial correlation with a p value of 0.67.
Although qualitatively similar results are found, statistical equality between the two sets of coefficients is rejected formally by a Wald test.
Implicitly, we are still treating the first-meeting rivalry as fixed through time.
It is trivial to calculate the unconstrained number of possible pairings as \(\left( {\begin{array}{c}120\\ 56\end{array}}\right) \approx 7.4\cdot 10^{34}\). However, determining the actual number of constrained sets is not mathematically straightforward and is based on a numerical approximation. To calculate this, we systematically iterated over all possible candidates, counted them and approximated the overall number by multiplying the approximate occurrences per time with the approximate overall computation time.
Hypothetically, we could apply this optimisation approach to any process that ranks the 120 match pairings by a quantifiable metric and desires to maximise the sum of these values subject to the constraints described. For example, this could be a vote system rather than an econometric exercise.
See, for example, Bertsimas and Weismantel (2005).
To allow for a simple notation we introduce \(\hat{\alpha }_{ii} := -\infty\), s.t. \(\exp (\hat{\alpha }_{ii}) = 0\).
We solve the linear and binary integer program with the help of the optimisation toolbox (bintprog) of Matlab 2012b, MATLAB (2012).
The Spearman rank correlation between these two series is 0.99.
The average of the multipliers does not equal one exactly, because of the non-linear exponential transformation as expected by Jensen’s inequality.
As a common-sense check of our optimisation result, we applied the algorithm to the average attendances of Table 1. Using these we find that the optimised profile is similar, but not identical, to the one that is found using rivalry effects with 45/56 common team pairings for the full sample, and 44/56 for the reduced sample. This reduces the optimised (upper limit) gain in attendance by 0.85 and 1.1 %, respectively.
In reaching this estimate, we also utilise a parameter estimate from a simple regression of ‘Abs BOR’ on ‘Abs Rank Diff’.
The actual estimate of 0.6 % is calculated by multiplying the correlation with the estimate from (d).
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Acknowledgments
Earlier versions of this paper were presented at: (1) Internal Workshop, School of Economics, La Trobe University (May, 2012); (2) BET Seminar, Department of Economics, Monash University (May, 2012); (3) Western Economic Association International, 87th Annual Conference, San Francisco (July, 2012); and (4) Seminar, School of Economics, Finance and Marketing, RMIT University (October, 2012). Research assistance was provided by Blake Angell and Carmen Mezzadri. We are grateful for the comments of the Editor, Lawrence J. White, and two anonymous referees that have helped to improve this paper. We would also like to thank Jack Daniels for supplying betting data. All errors are our own.
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Lenor, S., Lenten, L. & McKenzie, J. Rivalry Effects and Unbalanced Schedule Optimisation in the Australian Football League. Rev Ind Organ 49, 43–69 (2016). https://doi.org/10.1007/s11151-015-9495-7
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DOI: https://doi.org/10.1007/s11151-015-9495-7