Playoff Uncertainty, Match Uncertainty and Attendance at Australian National Rugby League Matches

* The authors are grateful to Dan Farhat, LiamLenten, two anonymous referees and participants atthe Australian Conference of Economists ACE10,Sydney (September 2010), for helpful comments andsuggestions on earlier drafts. They also thank DanFarhat for advice on MATLAB coding.

JEL classifications: C23, L83Correspondence: Dorian Owen, Department of

Economics, University of Otago, PO Box 56, Dunedin

THE ECONOMIC RECORD, VOL. 88, NO. 281, JUNE, 2012, 262–277

9054, New Zealand. Email: [email protected]

Playoff Uncertainty, Match Uncertainty andAttendance at Australian National Rugby League

Matches*

NICHOLAS KING, P. DORIAN OWEN and RICK AUDAS

Department of Economics, University of Otago, Dunedin, New Zealand

� 2011 The Economdoi: 10.1111/j.1475

This article develops a new simulation-based measure of playoffuncertainty and investigates its contribution to modelling matchattendance compared with other variants of playoff uncertainty inthe existing literature. A model of match attendance incorporatingmatch uncertainty, playoff uncertainty, past home team perfor-mance and other relevant control variables is fitted to AustralianNational Rugby League data for seasons 2004–2008. The proba-bility of making the playoffs and home team success are moreimportant determinants of match attendance than match uncer-tainty. Alternative measures of playoff uncertainty based on pointsbehind the leader, although more ad hoc, also appear able tocapture broadly similar effects on attendance to the playoffprobabilities.

I IntroductionAccording to the ‘uncertainty of outcome

hypothesis’ (UOH; Rottenberg, 1956), closesporting contests, with more uncertain out-comes, are more attractive to fans. Empiricalstudies of fans’ demand for sport include a widerange of explanatory variables (Borland & Mac-donald, 2003), but uncertainty of outcome isusually regarded, on a priori grounds, as one of

262

ic Society of Australia-4932.2011.00778.x

the key factors. Moreover, the UOH is a centraltenet in the economic analysis of sports leagues.Concerns about lack of competitive balance andthe implications for fan interest via the UOHare often emphasised in sports antitrust cases tojustify restrictive practices (such as salary caps,player drafts and revenue sharing) that would beconsidered anti-competitive and unlawful inother industries. Consequently, there is a sub-stantial body of literature examining the UOHboth at the aggregate level (viewing each seasonas an individual observation) and at a moredisaggregated level (viewing each match as anobservation). However, although the UOH hasbeen around for over 50 years, it continues to bea focus for empirical testing. This is partlybecause of the mixed nature of the existing evi-dence on its relevance (Borland & Macdonald,2003; Szymanski, 2003; Downward et al., 2009)and partly because of the challenges of

1 The NRL was formed in 1907 as the New SouthWales Rugby League with the inaugural premiershipheld in 1908. It is now the most important rugbyleague championship in the Southern Hemispherewith, from 2007, ten teams from New South Wales,three from Queensland, one from Victoria, one fromthe Australian Capital Territory, and one from NewZealand.

2 Uncertainty of outcome is closely related to com-petitive balance, that is, how evenly teams arematched. Ignoring other factors, such as the extent ofhome advantage, a higher degree of competitivebalance tends to produce more closely contestedmatches and, hence, higher levels of match and sea-sonal uncertainty. However, an important difference isthat ex post measures (e.g. based on win percentages)are commonly used to track competitive balance,whereas uncertainty of outcome is inherently anex ante concept (Kringstad & Gerrard, 2007).

2012 PLAYOFF UNCERTAINTY, MATCH UNCERTAINTY AND ATTENDANCE 263

measuring the different unobservable ex antedimensions of uncertainty of outcome requiredto test the UOH (Sloane, 2006).

In this article, we investigate the effects ofuncertainty of outcome on match attendance inthe Australian National Rugby League (NRL).Given the span of the data examined, we focuson match uncertainty and ‘playoff uncertainty’,that is, uncertainty about which teams will finishin the top eight positions, which qualifies themfor post-regular-season playoffs that determinethe overall league winners. Playoff uncertaintyand other aspects of seasonal uncertainty havereceived less attention in the literature thanindividual match uncertainty, but seasonaluncertainty may have a more important effecton fan interest and attendance over the courseof a season as teams drop out of contention forthe top positions.

Measures of seasonal uncertainty in existingstudies are relatively crude, such as counting thenumber of games or points behind the leader.Our approach is to derive measures of bothplayoff and match uncertainty using a simula-tion model applied to data from the NRL. Simu-lation methods have previously been used topredict match and tournament outcomes (e.g.Clarke, 1993; Koning et al., 2003) and to inves-tigate the implications for attendance of differ-ent league structures or of equalising playingtalent across teams (Dobson et al., 2001; For-rest et al., 2005a). However, our study consti-tutes one of the first attempts, along with Bojke(2008), to use simulation methods specifically togenerate ex ante measures of different aspectsof uncertainty of outcome.

There are numerous previous studies of thedeterminants of attendance for different sports.However, relatively few consider rugby league,and these examine attendance at English rugbyleague matches (Baimbridge et al., 1995; Car-michael et al., 1999; Jones et al., 2000; Dobsonet al., 2001). Australian attendance demandstudies focus on the Australian Football League(e.g. Borland, 1987; Borland & Lye, 1992; Len-ten, 2009a), with analysis of the NRL concen-trating more on measurement of competitivebalance (e.g. Booth, 2004; Lenten, 2009b). Theunpublished paper by Alchin and Tranby (1995),which examines attendance demand for Austra-lian rugby league using season-level data for 35seasons (1960–1994), is an exception. Our arti-cle therefore contributes to a currently sparseliterature relating to attendance demand for

� 2011 The Economic Society of Australia

rugby league in general and for the NRL inparticular.1

In Section II, we provide an overview of thevarious measures used to quantify differentdimensions of uncertainty of outcome in theexisting literature testing the UOH. Section IIIoutlines a new approach to measuring bothmatch uncertainty and playoff uncertainty basedon simulating match and end-of-season out-comes. Section IV includes the simulation-baseduncertainty measures in an empirical model ofattendance demand for NRL matches. Resultsfrom fitting the model to five seasons of NRLdata are reported in Section V, including com-parisons of results for the simulation-based mea-sure of playoff uncertainty with measures usedin previous match attendance studies. SectionVI concludes.

II Measuring Uncertainty of OutcomeIt is usual to distinguish between (at least) three

different dimensions of uncertainty of outcomerelating to different relevant time spans: short-runmatch uncertainty, medium-term within-seasonuncertainty and long-run championship uncer-tainty (Cairns et al., 1986; Borland & Macdon-ald, 2003; Szymanski, 2003).2

Match uncertainty is concerned with the pre-dictability of individual matches. It is the mostfrequently examined dimension of outcomeuncertainty, although there is no clear consen-sus on the best way to measure it (Buraimoet al., 2008). Measures of match uncertaintyused in the literature are generally based on twomain sources of information: teams’ relative

264 ECONOMIC RECORD JUNE

performances prior to a match (as summarisedin relative league positions, points totals or winpercentages) or match betting odds.

Match uncertainty measures based on teams’league positions (e.g. Hart et al., 1975; Borland& Lye, 1992; Baimbridge et al., 1996; Falter &Perignon, 2000; Garcıa & Rodrıguez, 2002;Benz et al., 2009; Madalozzo & Villar, 2009),points totals (e.g. Wilson & Sim, 1995) or winpercentages (e.g. Welki & Zlatoper, 1999;Meehan et al., 2007) have drawbacks. They donot account for home advantage (Forrest &Simmons, 2002; Buraimo et al., 2008) or thedifficulty of the teams’ playing schedules up tothat point in the season, and do not necessarilyadequately capture current form (Sandy et al.,2004). Win percentages and league positions arelikely to display greater variability early in theseason when teams have played relatively fewgames, so the degree to which these measuresreflect teams’ relative abilities will vary overthe season. All these measures have also beencriticised for being ‘entirely backward-looking’and based on partial information (Downward &Dawson, 2000, p. 134).

In contrast, betting odds are regarded as incor-porating a wider range of relevant information,for example, on suspensions or injuries to play-ers. Odds-based measures of match uncertaintyare generally expressed in the form of the proba-bility of a home team win (Peel & Thomas, 1988,1992; Knowles et al., 1992; Czarnitzki & Stadt-mann, 2002; Benz et al., 2009; Lemke et al.,2010) or the ratio of the probability of a homewin to the probability of an away win (Forrest &Simmons, 2002). Although odds-based measuresaccord more closely with an ex ante notion ofoutcome uncertainty, concerns have been raisedabout biases in setting odds (Forrest & Simmons,2002; Dawson & Downward, 2005; Forrestet al., 2005b; Buraimo et al., 2008).3 Moreover,the historical record for such odds may notalways be available for use in empirical studies.

Despite the emphasis placed on the UOH inthe literature, empirical results on the signifi-cance of match uncertainty are mixed. Of 18studies reviewed by Borland and Macdonald

3 Dobson and Goddard (2008) provide a succinctbut comprehensive review of recent studies of theefficiency of fixed odds betting on football; most ofthe studies they review suggest that betting odds arenot efficient.

(2003), only 4 produced clear evidence of a sta-tistically significant positive effect of matchuncertainty on attendance. Difficulty in identify-ing significant match uncertainty effects may bepartly due to measurement problems, especiallyas measures are often based on ex post informa-tion and overlap with indicators of team qualityor success.4 In this study, as discussed inSection III, our measure of match uncertainty isneither determined purely by teams’ standingsnor reliant on betting odds, but is based on amatch’s predicted outcome and the distributionof observed errors.

Seasonal uncertainty is concerned with thedegree of within-season uncertainty surroundingteams finishing in some end-of-season position,for example, winning the championship or mak-ing the playoffs. From an overall league per-spective, fans are generally expected to preferhigher levels of uncertainty with many teams incontention throughout the season. Indeed, this isa primary motivation for playoffs as an elementof competition design. However, playoffs redis-tribute the probability of eventual success overmore teams, so there is a potential trade-offbetween increased attendance for teams kept incontention by the existence of playoffs anddecreased attendance for teams whose probabil-ity of eventual success has been consequentlyreduced (Bojke, 2008). Overall league atten-dance may therefore decrease, especially if thelatter are large market teams.

Measures of seasonal uncertainty used in theliterature are usually based on the number ofgames a team is required to win to make theplayoffs or to win the championship (e.g. Jen-nett, 1984; Borland & Lye, 1992), the numberof games (wins) or points behind the leadingteam (e.g. Borland, 1987; Whitney, 1988;Knowles et al., 1992; Garcıa & Rodrıguez,2002; Meehan et al., 2007; Benz et al., 2009;Lemke et al., 2010) or the significance of thematch for the championship, playoffs or relega-tion (e.g. Jones et al., 2000; Dobson et al.,2001; Madalozzo & Villar, 2009). Matchesbetween teams out of contention are expected to

4 Downward et al. (2009), in their review of stud-ies of short-run uncertainty of outcome, note thatleague standings, rather than differences in standingsor odds-based measures, tend to show up as more rel-evant in explaining attendance. However, actualstandings are more a reflection of team success orteam quality than of uncertainty of outcome.



attract less interest.5 The statistical significanceof such variables in empirical studies tends tobe stronger than for measures of match uncer-tainty; of 19 studies reviewed by Borland andMacdonald (2003), 12 reported a statisticallysignificant effect of seasonal uncertainty onattendance.6

Although useful in modelling match atten-dance, these variables have drawbacks as mea-sures of ex ante uncertainty. Any measure basedon the number of games a team needs to win tomake the playoffs, or to win the championship,requires information that is not available at thetime spectators decide whether to attend a match(Dawson & Downward, 2005). Counting thenumber of games behind provides a guide to thefeasibility of a team remaining in contention,but relies entirely on the current points table,does not consider the difficulty of remainingmatches in the schedule either for that team orfor others in contention and usually assesseshow teams rank relative only to the currentleader.7

Consecutive season uncertainty refers to theabsence of long-run domination by one team ora small number of teams According to the UOH,long-run domination by a few teams decreaseschampionship uncertainty and is expected tohave a negative effect on match attendance.There are relatively few empirical studies of thisdimension of uncertainty of outcome and resultsdo not provide clear conclusions (Borland &

5 An alternative approach is to examine the effectof playoff uncertainty on average attendance for theleague as a whole, rather than on attendance at indi-vidual matches. For example, Lee (2009) constructs ameasure of average league-wide playoff uncertainty,based on aggregating team-specific information ongames behind the leader.

6 Downward et al. (2009) review a selection ofstudies that overlaps with those considered by Borlandand Macdonald (2003). The results on seasonaluncertainty are again mixed. Overall, they conclude(p. 218) that ‘in the shorter run at least, a team’s suc-cess is at least as important as UO for determiningmatch attendances’.

7 In competitions with end-of-season playoffs, thenumber of games behind the current competition lea-der may not give an accurate reflection of a team’schance of making the playoffs. For example, the firstplaced team may be well ahead of all the other teams;what matters then is how tight the competition isamong the other teams vying for the remaining play-off positions.


Macdonald, 2003; Downward et al., 2009). Forattendance at the level of individual matches, asin the current study, consecutive season uncer-tainty has largely been ignored, primarilybecause of the restricted time span of suchstudies.

Although there are plausible links betweendifferent dimensions of uncertainty of outcomeand match attendance, existing evidence on therelevance of the relationships is surprisinglyambiguous. This may reflect the inadequate nat-ure of commonly used measures of the differentdimensions of uncertainty of outcome (Dawson& Downward, 2005; Sloane, 2006), motivatingfurther testing of the UOH. Uncertainty of out-come, by its very nature, is concerned with thedegree of predictability or unpredictability ofthe relevant outcome, and is therefore an ex anteconcept. In contrast, most measures of uncer-tainty of outcome, apart from those based onbetting odds, are backward-looking. In this arti-cle, we examine the relevance of measures ofmatch and season uncertainty obtained from aconsistent simulation framework that updatesprobability measures of match uncertainty andplayoff uncertainty (the most relevant aspect ofseasonal uncertainty in the NRL context) usinginformation available to spectators at the timeof their attendance decision. This correspondsmore closely to an ex ante formulation of uncer-tainty than used in many existing studies.

III Simulation-based Measures of PlayoffUncertainty and Match Uncertainty

Our proposed measures of playoff and matchuncertainty are derived by simulating the resultsof matches not yet played in the season. In par-ticular, the probability of each team making theplayoffs, at any point in the season, is measuredby the proportion of simulated end-of-seasonoutcomes for which that team finishes in theplayoff positions. A simulation-based measure ofplayoff uncertainty has several advantages com-pared with previous measures. It is not basedsolely on the current state of the league pointstable. It reflects a team’s likelihood of makingthe playoffs relative to all other teams in the lea-gue, not just the first-placed team. Moreover, theplayoff probabilities of the various teams areconsistent at every point because they arederived jointly. It takes into account the strengthof the schedule, that is, the difficulty of theremaining matches a team has to play in a sea-son. In addition, it utilises only information

9 By setting all initial values of team strength rat-ings equal to 0, the sum of all team strength ratings,and hence the average strength rating, are also 0 atany point in time. A team’s strength rating can there-fore be interpreted as the expected points marginresulting from a match against an average team at aneutral venue.

10 Clarke’s (2005) evidence suggests team-specific


available to spectators prior to the relevantmatch and evolves as the season progresses.

Predicted match outcomes are required tosimulate sequences of results through the sea-son. To predict match outcomes we use a frame-work similar to that of Stefani and Clarke(1992) and Clarke (1993, 2005). The outcome ofeach match is characterised by the home team’swinning margin (points scored by the hometeam less points scored by the away team). Thepredicted home team’s winning margin dependson the teams’ playing strengths and the extentof home advantage:

PMij;r;y ¼ kHHy þ Si;r�1;y � Sj;r�1;y; ð1Þ

where PMij,r,y is home team i’s predicted winningmargin against away team j, in round r of year y;kH is a dummy variable equal to 1 if the match isplayed at a non-neutral venue and 0 otherwise; Hy

is home advantage in year y, and Si,r)1,y is thestrength rating for team i based on information upto and including round r ) 1 of year y.8

To allow for evolution of current form, teamstrength ratings are adjusted as the season pro-gresses. For each match, the predicted outcomein Equation (1) is compared with the actualmatch outcome, and the prediction error is cal-culated as:

Eij;r;y ¼ AMij;r;y � PMij;r;y;

where Eij,r,y is the error in predicting the matchoutcome of home team i against away team j, inround r of year y and AMij,r,y is the correspond-ing actual winning margin. Team strength rat-ings are updated using a simple exponentialsmoothing scheme:

Home team: Si;r;y ¼ Si;r�1;y þ cEij;r;y;

Away team: Sj;r;y ¼ Sj;r�1;y � cEij;r;y;ð2Þ

where c is a positive constant. If the home teamwins a match by more than predicted, itsstrength rating increases, reflecting improvedform, and the away team’s strength ratingdecreases, reflecting worsened form.

Strength ratings of all teams are set equal to 0at the beginning of the 2003 season, the seasonprior to the first season of observations used infitting the attendance model in Section IV, andare updated as the season progresses using

8 PMij,r,y < 0 corresponds to a predicted win for theaway team with a points margin of |PMij,r,y|.

Equation (2).9 The parameters in the model(c and H) are determined by minimisingP

E2ij;r;2003; the sum of squared errors in predic-

tion for match outcomes in 2003. The end-of-2003 strength ratings are used as initial valuesfor the 2004 season. Strength ratings for 2004matches are then updated, day-by-day, usingEquation (2) and 2003 values for c and H; thesestrength ratings are then used in Equation (1) toobtain predicted winning margins. At the end ofeach season, the process is repeated; that is, thestrength ratings of all teams at the beginning ofseason y ) 1 are set equal to 0. The parametersc and H are obtained by minimising the sum ofsquared errors in prediction in season y ) 1. Theupdated strength ratings provide initial valuesfor season y. Strength ratings for season ymatches are then updated (using season y ) 1values for c and H), and are used to generatepredicted winning margins for matches inseason y.

This setup assumes a homogeneous homeadvantage across teams within each seasonalthough this is allowed to vary between sea-sons. Alternative assumptions are possible(Clarke, 2005), for example, home advantagemay be different for different teams.10 We adoptthe common home advantage formulationbecause the key motivation is to model specta-tors’ ex ante uncertainty of outcomes, not neces-sarily to maximise prediction accuracy. Themore variation in home advantage allowedacross teams and over time, the more explana-tory power can be loaded onto home advantage(with parameters Hi,y; i = 1, 2,…,16 reflect-ing home advantage), especially with only 24matches per team per season, but this is unlikelyto reflect fans’ ex ante expectations accurately.If we allow home advantage to vary by team,we find that the Hi terms vary considerably,for any i, from season to season; hence, last

home advantages are significant in the AustralianFootball League, but year effects are not significant.However, his tests are based on fitting all the data andtesting ex post for team and year effects.


13 For example, if there are five remaining roundsin a season containing 26 pre-playoff rounds, the 21completed rounds will give a points table reflectingactual standings at the end of 21 rounds. A simulatedend-of-season points table can be constructed by add-ing in simulated results for the final five pre-playoffrounds of matches. Repeating this process 1000 timesgives 1000 simulated end-of-season points tables. Theproportion of these points tables for which a teammakes the playoffs gives a predicted probability, eval-


season’s team-specific home advantage is notlikely to be a reliable guide to this season’steam-specific home advantage. We thereforeincorporate an average home advantage adjust-ment (based only on the previous season’sresults) rather than overfitting the model andreducing the apparent ex ante uncertainty facedby spectators.11 Despite this, the model esti-mates 59 per cent of match winners correctly.12

For the matches in our sample, actual hometeam scoring margins, AMij, range from )66 to+65; 45 per cent of the matches’ predicted scor-ing margins are within 10 points of the actualresult, 62 per cent are within 15 points, 75 percent are within 20 points and only 9 per cent ofthe prediction errors are more than 30 points.

Simulated match outcomes are generated byadding a random error to the predicted matchoutcome:

SMij;r;y ¼ kHHy þ Si;r�1;y � Sj;r�1;y þ GEij;r;y;

where SMij,r,y is home team i’s simulated win-ning margin against away team j, in round r ofyear y, and GEij,r,y is the corresponding gener-ated error. The errors are randomly drawn froma normal distribution with mean 0 and a stan-dard deviation equal to that observed in theactual errors in the fitted model. The distribu-tion of generated errors therefore approximatesthe distribution of observed errors.

The measure of playoff uncertainty is basedon the probability of the home team making theplayoffs. This varies as the season progressesand is constructed, for each round, by simulat-ing yet-to-be-played matches to give an end-of-season points table and repeating this process1000 times. Within each simulation, strengthratings are updated based on the previousrounds’ simulated results. The predicted proba-bility of the home team making the playoffs, atthat point in the season, is given by the propor-tion of simulated end-of-season points tables for

11 Year effects are maintained as the model is fittedto each season’s data separately. The optimised param-eter values vary across seasons (with c values rangingfrom 0.047 to 0.101 and Hy values from 1.961 to 5.620).

12 This compares favourably with the 61.4 per centsuccess rate in correctly predicting winning teamsattained by a sports prediction website for NRL overthe sample period (http://footyforecaster.com). Themean absolute value of the error in the predictedmatch outcome in our model is 14.37 compared withthe website’s 14.46.


which the home team makes the playoffs.13 Theprobability of the away team making the play-offs is constructed in the same way.14

Our measure of match uncertainty is based onthe probability of the home team winning thematch. In the context of our simulation, thisprobability can be constructed from the pre-dicted outcome of a match and the cumulativedistribution of the observed errors in the predic-tion of all match outcomes. For example, sup-pose that the home team is predicted to win agiven match by x points. Any error in predictionof less than x points will still result in the hometeam winning. Therefore, the proportion ofobserved errors greater than )x will give thepredicted probability of the home team winningthe match.15

The model used to predict match and playoffprobabilities was constructed using MicrosoftExcel 2007. Parameter values (c and H) weredetermined, on a season-by-season basis, usingthe Solver function to minimise the sum ofsquared errors in match outcome predictions.Matlab 10 was used to simulate the results foryet-to-be-played matches as each seasonevolves.

This simulation-based approach providesmeasures of playoff uncertainty and match uncer-tainty jointly derived from a consistent ex anteframework. The playoff uncertainty measure, inparticular, offers a potential improvement on

uated at the beginning of the 22nd round, of the teammaking the playoffs.

14 Bojke (2008) uses a similar simulation approachto obtain predictions of end-of-season finishing posi-tions and measures of game significance. However,his simulations are based on individual match bettingodds for which there are some time-matching prob-lems (Bojke, 2008, p.184).

15 This method assumes there is no correlationbetween the predicted match outcome and the error inthe predicted match outcome. Testing the correlationbetween these two variables reveals no significantcorrelation.


more ad hoc measures of playoff uncertainty usedin the past.

IV Modelling Match AttendanceTo assess the relevance of a measure of play-

off uncertainty based on simulated probabilities,and to compare its performance with alternativemeasures, we include these in a model of atten-dance at NRL matches.16 Comprehensivereviews of the literature on the determinants ofmatch attendance in different sports leagues areprovided by Borland and Macdonald (2003),Szymanski (2003) and Downward et al. (2009).Here we adopt a conventional single-equationframework, which allows us to focus on thevalue added of the new simulation-basedmeasures.

The empirical model for match attendancetakes the general form

lnðAttendanceÞ¼ f ðMatch Uncertainty;Playoff Uncertainty;

Interactions; WinStreak; PreviousYrWin;

Round; Round2; Sydney; Weather; Year;

Day of Week; Time of Day; Away Team;

Home TeamÞ þ u: ð3ÞThe dependent variable, ln(Attendance), is the

natural logarithm of match attendance. Thesemi-log functional form provides a partialresponse to heterogeneity in the variation inattendance levels across teams (discussed fur-ther later), although specifying the dependentvariable as Attendance does not qualitativelyalter the key results. u is a combined error termsuch that uit = ai + eit, where ai is a randomindividual-specific effect and eit is an idiosyn-cratic error for home team i at time t.

16 Most studies testing the UOH focus on matchattendance. Given the importance of television reve-nues for professional sports leagues, including theNRL, television viewers have become a much moreimportant group of consumers of professional sportingevents. It would therefore also be desirable to test theUOH for television viewers of NRL matches to add tothe few existing studies of television viewers of othersports (e.g. Forrest et al., 2005b; Buraimo, 2008;Buraimo & Simmons, 2009; Yang & Kumareswaran,2009; Alavy et al., 2010; Tainsky & McEvoy, 2011).However, television ratings data for NRL matches arenot readily available, so this is not feasible in the cur-rent study.

Match Uncertainty is modelled by includingthe simulated probability of a home team win,denoted as PHomeWin, as discussed in SectionIII. However, uncertainty is not a monotonicfunction of the home win probability, as low orhigh home win probabilities correspond toreduced uncertainty. We therefore also includethe squared value of PHomeWin. A quadraticrelationship between the simulated home winprobability and the log of attendance enables usto derive an estimate of the attendance-maximis-ing home win probability (e.g. Whitney, 1988;Knowles et al., 1992; Peel & Thomas, 1992;Czarnitzki & Stadtmann, 2002; Owen & Weath-erston, 2004a,b; Benz et al., 2009; Lemkeet al., 2010). If only the linear PHomeWin coef-ficient is statistically significant, then thisimplies a monotonic relationship between atten-dance and home win probability; this is morerepresentative of a ‘probability of success’effect than an uncertainty effect. Alternativeformulations of the match uncertainty variable,discussed in Section V, are also considered toassess the sensitivity of the results.

Playoff Uncertainty is the key variable ofinterest in this study. Our preferred measure isbased on the simulated probability of the hometeam making the playoffs at that stage of theseason, denoted as PHomePlayoff, as discussedin Section III. To allow for a quadratic rela-tionship between the playoff probability andattendance, we include the squared value ofPHomePlayoff. However, if there is a turningpoint, we expect it to be at a home team successprobability closer to unity than for individualmatches; that is, other things equal, home teamswith a high probability of making the playoffswill attract large crowds, unless fans are so sureof successful qualification that they hold offattending until the playoff matches. The corre-sponding probability for the away team, PAway-Playoff, and its squared term are also included.In addition, the relevance of match uncertaintymay depend on the probability of making theplayoffs (Sloane, 2006); the effect of matchuncertainty may be enhanced for teams in play-off contention, or match uncertainty may act asa substitute for a high playoff probability. Toallow for these possibilities, we include interac-tions between match and playoff uncertainty.

For comparison, we also examine variants ofplayoff uncertainty measures used in previousstudies (as discussed in Section II): the numberof points the home team is behind the current



leader, the average number of points the homeand away teams are behind the current leaderand the number of points the home team requiresto make the playoffs.17 These measures primar-ily reflect the likelihood of a team successfullymaking the playoffs; from this perspective, spec-tators are attracted to matches when the hometeam is closer to the current competition leaderor when fewer points are required to make theplayoffs. To allow for a possible quadraticuncertainty effect we also test for the relevanceof squared terms for these variables.

WinStreak is defined as the number of consec-utive wins (home and away) for the home team.Spectators like to see their team win; a signifi-cant positive effect of recent home team successon match attendance is a consistent finding ofprevious studies (Borland & Macdonald, 2003).

PreviousYrWin is a dummy variable equal to1 if the home team was the previous year’s pre-miership winner (or 0 otherwise). A positiverelationship between match attendance and Pre-viousYrWin is expected, reflecting increasedinterest in a team that has recently shown cham-pionship winning ability.18

Round, represents the number of rounds in theseason (1, 2,…,26) in which a match is played.Including Round and its squared value allowsthe stage of the season to affect attendance,after partialling out other factors such as teamsuccess and uncertainty measures. For example,fan interest may be high initially, decline as theseason progresses, but increase towards the endof the season.

Sydney is a dummy variable equal to 1 if bothplaying teams are from Sydney, and 0 other-wise. A positive relationship between matchattendance and Sydney is expected, because ofgreater support for the away team than usual.

Weather represents a set of six dummy vari-ables indicating if the weather at the match

17 Draws, in which each team receives half the avail-able points, are feasible although relatively rare in theNRL, so the number of points behind the current leaderis used instead of the number of games behind.

18 We also examined two other variants of this vari-able that allow the effect of recent success to dimin-ish as the season progresses. The first divides thePreviousYrWin dummy by the round in the season.The second multiplies PreviousYrWin by the numberof rounds left in the season. All three versions givestatistically significant effects, with no significantimplications for the other estimated coefficients.


location is classified as Hot, Overcast, Windy,Rain, Showers or Cold. Existing studies findpositive effects of warmer, sunnier weather onattendance and negative effects of rain (e.g.Czarnitzki & Stadtmann, 2002; Garcıa & Rodrı-guez, 2002; Owen & Weatherston, 2004a,b;Meehan et al., 2007; Lemke et al., 2010).

Year represents a set of 1–0 dummy variablesfor the year in which a match took place (with2004 as the base category). This controls forany season-specific factors influencing allteams’ average attendance but not captured bythe other explanatory variables (e.g. varyingaverage ticket prices across seasons). Day ofWeek represents a set of five 1–0 dummy vari-ables for the day of the week a match is played(Tues, Wed, Fri, Sat, Sun, with Monday as thebase category). This is motivated by the signifi-cance of day-of-the-week effects on attendancedemand in other sports (e.g. Garcıa & Rodrı-guez, 2002; Meehan et al., 2007; Lemke et al.,2010). Time of Day represents a set of 17dummy variables for different kick-off times(with 12 noon as the base category).

Away Team consists of a set of away-teamdummy variables to allow for the possibility thatsome visiting teams are intrinsically moreappealing to home fans than others, as Lemkeet al. (2010) find for baseball. Home Team rep-resents the home team-specific fixed effects.19

V ResultsThe data used to fit the model in Equation (3)

are individual match data from the NRL for sea-sons 2004–2008.20 The NRL currently hosts 16teams following the addition of the Gold CoastTitans in 2007. Each season contains 26 rounds(apart from 2007 when there were 25 rounds) ofregular season play followed by four rounds ofplayoffs for the eight highest-ranked teams.The empirical analysis focuses on the regularseason matches (924 matches in total). The datatherefore constitute an unbalanced panel com-prising 16 cross-sectional units (the home teams)with 60 ‘time-series’ observations (i.e. homematches) for each of the 15 teams, and 24

19 Fixed effects may capture factors such as teams’historical support base, different market size of catch-ment areas, ease of access to match venues, stadiumquality and alternative forms of entertainment avail-able to spectators.

20 The data were obtained from: http://stats.rleague.com and http://www.nrlstats.com.

TABLE 1Summary Statistics for Key Variables

Mean SD Minimum Maximum

ln(Attendance) 9.576 0.413 8.340 10.832PHomeWin 0.590 0.168 0.101 0.944PHomePlayoff 0.550 0.389 0 1PAwayPlayoff 0.535 0.392 0 1WinStreak 0.910 1.459 0 11PrevYrWin 0.065 0.247 0 1Round 13.451 7.535 1 26Sydney 0.207 0.405 0 1


observations for the remaining team, the Titans.21

Summary statistics for the key variables of inter-est are provided in Table 1.

The model in Equation (3) is treated as a sin-gle-equation demand function and the parametersare estimated using the fixed effects estimator,with home team fixed effects. For fixed effectsestimation, the regressors are assumed to be un-correlated with the time-varying component ofthe equation’s error term, eit, but they may becorrelated with the individual-specific ai compo-nents. The random effects estimator is a feasiblealternative estimator if the random effect, ai, isdistributed independently of all the explanatoryvariables for all t, but is inconsistent under theassumptions of the fixed effects model. A com-mon strategy to choose the estimator is to applya Hausman pre-test of the null hypothesis thatthe individual effects are random, and select thefixed or random effects estimator based on theresult of this pre-test. However, Guggenberger(2010) shows that such pre-testing can lead tosignificant size distortion in subsequent testingof parameter significance; directly using t-statis-tics based on the fixed effects estimator is there-fore recommended, rather than a two-stageprocess involving pre-testing.22

Exogeneity of the regressors (with respect toeit) would be an inappropriate assumption if, forexample, higher attendance enhanced a team’savailable resources sufficiently to attract betterplayers and improve the team’s relativestrength. However, any feedback from atten-dance to within-season performance and the

21 Unlike many panel datasets, the observations overtime are not equally spaced (because teams do not playat home every week, or even every other week) andthere is a gap between seasons. Moreover, the timingof the observations are not aligned for all teams, as ineach round some teams play at home and others playaway. Conventional methods for analysing the time-series aspects of the data are therefore not necessarilyappropriate; however, timing issues do not affect mostof our results, unless specifically indicated.

22 A Hausman test, derived as an F-statistic usingcluster-robust standard errors in an auxiliary regres-sion involving demeaned time-varying regressors(Wooldridge, 2002, p. 290) strongly rejects therandom effects specification (p = 0.000). Hence, inthis application, both Guggenberger’s (2010) pro-posed strategy and the conventional approach suggestfocusing on the fixed effects estimates. In any case,random effects estimates give qualitatively similarconclusions.

simulated uncertainty measures is likely to berelatively minor in the current context given thefocus on estimating the short-run effects ofuncertainty on individual match attendance.23 Inaddition, the operation of a salary cap, althoughsubject to breaches of varying degrees of sever-ity, has helped to dampen any link between rev-enue and on-field performance. If such feedbackeffects are of more significance in the longerrun, these may need to be considered in studiesusing longer time spans of data.24

Table 2 reports results for the fitted model,including diagnostic tests for normality, group-wise heteroskedasticity, serial correlation andcross-sectional dependence. The null of normal-ity of the errors is not rejected at the 5 per centsignificance level based on a chi-squared testexamining skewness and kurtosis. There is noobvious evidence of first-order autocorrelation,using Wooldridge’s (2002, pp. 282–3) test.25 Onthe basis of Pesaran’s (2004) CD test, there is

23 Admission price is not included in the set ofexplanatory variables. As Downward et al. (2009)note in their review of recent attendance demand stud-ies, this is not uncommon. Pricing in the NRL ishighly uniform and regulated; consequently, admis-sion prices within a regular season do not vary inresponse to match-specific factors affecting demand,such as match quality or uncertainty of outcome.

24 Match attendance reaches stadium capacity foronly 2 per cent of the regular season matches in thesample, so any bias or inconsistency because ofcensoring of the dependent variable (with attendanceat capacity, such that the number of spectators willingto pay to attend is not observable) is a minor issue.

25 The time counter for the autocorrelation testresults reported is based on the order of the homematches for each team. Owing to the irregular natureof the time dimension of the data, ‘time t’ observa-tions do not match exactly across different teams.Therefore, this result is only suggestive.



no evidence of cross-sectional dependence in theerrors. This is supported by the low averageabsolute value of the off-diagonal elements inthe matrix of residuals (denoted as AvAbsCross)and by the lack of statistical significance of theBreusch–Pagan (1980) Lagrange multiplier (LM)test applied to a balanced panel that omits thehome results for the Titans.26 The modified Waldtest for groupwise heteroskedasticity (Baum,2001) strongly suggests that error variances dif-fer across cross-sectional units, that is, hometeams. This is also apparent in Figure 1, whichplots values for ln(Attendance) and their meanvalues for each home team. Consequently, clus-ter-robust standard errors are reported; theseassume that errors are independent across teamsbut allow for varying error variances across 16clusters, that is, by home team.27 However, usingunadjusted standard errors, based on the assump-tion of i.i.d. errors, gives qualitatively similarconclusions for the key variables.

Initially, we included quadratic terms forPHomePlayoff and PAwayPlayoff, but theircoefficients were not statistically significant atthe 10 per cent level and, because of the highcorrelation between the linear and quadraticterms (0.970 for both variables), their inclusionreduced the precision of estimation of the coeffi-cients on the linear terms; the quadratic termswere therefore deleted.28

26 The Breusch–Pagan test is appropriate if thetime-series dimension of the panel, T, is greater thanthe number of cross-sectional units, N, as in our appli-cation. The Pesaran test is more appropriate for panelswith large N and T fixed (De Hoyos & Sarafidis,2006). The caveat about the irregular and unmatchedtiming of observations also applies to the results forboth these tests; in particular, they are unlikely tofully reflect common shocks and unobserved com-ponents that lead to dependence at relatively highfrequencies (e.g. less than a fortnight).

27 Using bootstrap standard errors, with resamplingover clusters, gives qualitatively similar results, apartfrom changes to the statistical significance of some ofthe time-of-match effects.

28 Similarly, an interaction between PHomeWin2,the squared value of PHomeWin, and PHomePlayoffwas initially included but this term is highly corre-lated with PHomeWin · PHomePlayoff (r = 0.969)and its effect is not statistically significant at the 10per cent level. To save space, results for modelsincluding the squared playoff probabilities and thePHomeWin2 · PHomePlayoff interaction are notreported, but are available upon request.


Our benchmark specification is reported inTable 2, column (1), with a variant containingthe interaction term PHomeWin · PHomePlayoffin column (2). The main focus of interest is thesize and statistical significance of the coefficientson the proxies for playoff and match uncertainty.The simulated probabilities of the home andaway teams making the playoffs both have esti-mated effects that are statistically significant atthe 0.1 per cent level. Based on the results inTable 2, column (1), other things equal, forevery increase of 0.1 in the probability that thehome team will make the playoffs, match atten-dance is estimated to increase by nearly 2 percent. Equivalently, this corresponds to a 20 percent higher attendance for a team certain of mak-ing the playoffs compared with a team having nochance of making the playoffs. An increase of0.1 in the probability that the away team willmake the playoffs, other things equal, boostsmatch attendance by about 1 per cent.

The simulated probability of a home win isentered in quadratic form and both terms are onthe margin of statistical significance at the 5 percent level. Based on the point estimates, the qua-dratic relationship between ln(Attendance) andPHomeWin has an attendance-maximising homewin probability of 0.605, a result in line withseveral previous studies for other sports (Borland& Macdonald, 2003). A quadratic relationshipwith significant coefficients, indicative of aninverted U-shaped relationship between homewin probability and attendance, is conventionallyinterpreted as supportive of the UOH at the levelof match uncertainty; however, previous studiesdo not usually examine whether the marginaleffect of the home win probability is significantthroughout its range of values. The 95 per centsymmetric confidence interval for the marginaleffect of PHomeWin can be obtained as:

ðb1 þ 2b2PHomeWinÞ� 1:96½varðb1Þ þ 4PHomeWin2 varðb2Þþ 4PHomeWin covðb1; b2Þ�1=2

in which b1 and b2 are the point estimates onPHomeWin and PHomeWin2, respectively, andvar(b1), var(b2) and cov(b1,b2) are the esti-mated cluster-robust variances and covarianceof the relevant estimated parameters (Aiken &West, 1991). The point estimates and confi-dence intervals for the marginal effect for themodel in Table 2, column (1), are represented

TABLE 2Fixed Effects Estimation Results with Alternative Match Uncertainty Measures

(1) (2) (3) (4) (5)

PHomeWin 0.753* (2.18) 0.586 (2.03)PHomeWin2 )0.622 (2.03) )0.352 (1.41)PHomePlayoff 0.194*** (8.53) 0.366*** (4.21) 0.204*** (9.46) 0.196*** (9.51) 0.205*** (9.34)PAwayPlayoff 0.106*** (5.01) 0.103*** (4.88) 0.0962** (3.87) 0.103*** (4.35) 0.0947** (3.87)PHomeWin ·PHomePlayoff

)0.290 (1.97)

WinStreak 0.0381*** (4.48) 0.0385*** (4.54) 0.0387*** (4.25) 0.0383*** (4.32) 0.0390*** (4.35)PreviousYrWin 0.168*** (4.35) 0.164** (4.05) 0.173*** (4.47) 0.169*** (4.38) 0.174*** (4.47)Excite50 0.120 (1.32)Excite60 0.208 (1.82)MatchUnbal )0.0291 (1.56)Round )0.0512*** (9.33) )0.0501*** (8.98) )0.0511*** (9.49) )0.0513*** (9.45) )0.0511*** (9.41)Round2 0.00176*** (8.00) 0.00172*** (7.85) 0.00175*** (8.10) 0.00176*** (8.09) 0.00175*** (8.05)Sydney 0.121* (2.23) 0.120* (2.27) 0.120* (2.23) 0.121* (2.24) 0.120* (2.24)Hot 0.0216 (0.18) 0.0212 (0.18) 0.0182 (0.16) 0.0229 (0.19) 0.0173 (0.15)Overcast )0.0150 (0.25) )0.0116 (0.19) )0.0147 (0.24) )0.0147 (0.24) )0.0144 (0.24)Windy )0.109** (3.29) )0.105** (3.33) )0.109** (3.32) )0.108** (3.32) )0.109** (3.30)Rain )0.242*** (4.27) )0.241*** (4.32) )0.242*** (4.27) )0.241*** (4.27) )0.242*** (4.27)Showers )0.188*** (6.27) )0.184*** (6.22) )0.191*** (6.54) )0.189*** (6.30) )0.191*** (6.56)Cold )0.0559 (1.21) )0.0550 (1.15) )0.0582 (1.24) )0.0552 (1.19) )0.0577 (1.24)2005 0.0944** (3.59) 0.0933** (3.49) 0.100** (3.68) 0.0960** (3.45) 0.101** (3.74)2006 0.00890 (0.27) 0.00777 (0.23) 0.0170 (0.54) 0.0111 (0.33) 0.0172 (0.54)2007 0.00630 (0.17) 0.00659 (0.18) 0.0106 (0.29) 0.00768 (0.21) 0.00919 (0.25)2008 0.0772* (2.49) 0.0771* (2.51) 0.0863* (2.65) 0.0790* (2.47) 0.0860* (2.64)Tues 0.873*** (6.27) 0.868*** (6.32) 0.862*** (6.22) 0.870*** (6.30) 0.863*** (6.23)Wed 0.516** (3.94) 0.525*** (4.13) 0.494** (3.76) 0.517** (4.00) 0.495** (3.77)Fri )0.160 (0.68) )0.151 (0.63) )0.145 (0.62) )0.165 (0.69) )0.147 (0.63)Sat )0.285 (1.20) )0.277 (1.15) )0.273 (1.16) )0.291 (1.22) )0.274 (1.16)Sun )0.0666 (0.72) )0.0684 (0.74) )0.0774 (0.83) )0.0670 (0.72) )0.0755 (0.81)

R2 0.697 0.699 0.696 0.697 0.696Normality-p 0.186 0.152 0.225 0.207 0.233Hetero-p 0.000 0.000 0.000 0.000 0.000BP-LM-p 0.128 0.154 0.113 0.134 0.112Pesaran CD-p 0.504 0.532 0.442 0.447 0.478AvAbsCross 0.128 0.126 0.127 0.128 0.127Auto-p 0.239 0.277 0.301 0.344 0.268

Notes: The dependent variable is ln(Attendance). Absolute t-statistics, based on cluster-robust standard errors, are reportedwithin parentheses. *, ** and *** denote significances at the 5 per cent, 1 per cent and 0.1 per cent levels, respectively. Dummyvariables for away teams and time of kick-off are included in the models but estimates are not reported; full results areavailable on request. N = 924 for all models. R2 values are obtained from equivalent least-squares dummy variable regressionsthat include the home team fixed effects. Suffix p denotes p-values reported for diagnostic tests. Normality is a chi-squared testfor normality, Hetero is a modified Wald test for groupwise heteroskedasticity, BP-LM is the Breusch and Pagan (1980) LM testfor cross-sectional independence of the errors, Pesaran CD is Pesaran’s (2004) cross-sectional dependence test, Auto isWooldridge’s (2002) test for first-order autocorrelation and AvAbsCross is the average absolute value of the off-diagonalelements in the matrix of residuals.


graphically in Figure 2. Increasing the home winprobability has a statistically significant positivemarginal effect on match attendance up toapproximately a value of PHomeWin of 0.5.Thereafter, the marginal effect, includingbeyond the turning point in the relation-ship between ln(Attendance) and PHomeWin, is

not statistically significantly different from 0.The results obtained therefore provide onlyrelatively modest support for the UOH withrespect to match uncertainty.

The interaction term PHomeWin · PHome-Playoff is included in Table 2, column (2); itscoefficient is negative, implying some degree of


8.5

9

9.5

10

10.5

11

0 5 10 15Home number

ln Attendance ln Attendance_mean

FIGURE 1Heterogeneity in ln(Attendance) Across Home Teams

–1–0.75

–0.5

0

0.50.75

11.25

Mar

gina

l effe

ct o

f PH

omeW

in

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9PHomeWin

Marginal effect of PHomeWin95% confidence interval

FIGURE 2Marginal Effect of Simulated PHomeWin on

ln(Attendance)


substitutability between the home team’s matchand playoff success probabilities; that is, otherthings equal, increases in PHomeWin have asmaller attendance-enhancing effect at high val-ues of PHomePlayoff. However, the estimatedcoefficient on the interaction term is statisticallysignificant only at the 10 per cent but not the 5per cent level.29

The statistical and quantitative significance ofthe other coefficient estimates are robust across

29 With the interaction term included, the playoffprobabilities are still highly statistically significantand the quantitative significance of the effect ofPHomePlayoff on attendance is enhanced. However,the coefficient on the quadratic term PHomeWin2 isno longer statistically significant at even the 10 percent level, further dampening support for the UOHapplied to match uncertainty. However, the highdegree of intercorrelation between the various proba-bilities, their squares and interactions makes it diffi-cult to estimate some of these effects precisely.


columns (1) and (2), so we focus on results forthe former. The estimated coefficient on hometeam success is positive and statistically signifi-cant at the 0.1 per cent level. The point estimatesuggests that a three-match increase in Win-Streak increases attendance by 11.4 per cent.The estimated average effect of winning the pre-miership in the previous season is an increase inattendance of approximately 17 per cent. Eachof these estimated effects assumes other thingsare equal; however, for a team with a success-ful run of wins, consequent improvements instrength ratings and league standing alsoenhance the probabilities of winning matchesand of making the playoffs.

The coefficients on Round and its squaredvalue are both statistically significant at the 0.01per cent level and imply initially decliningattendance as the season progresses, with a turn-ing point after 14 rounds, other things equal.This pattern is consistent with heightened earlyseason interest in matches, followed by a fall-off in interest and then a revival towards theend of the season.

Matches involving two Sydney-based teamshave statistically and quantitatively significantlyhigher attendance, whereas rain, showers orwindy weather, on average, have negativeeffects on attendance. Attendance in 2005 and2008 (the NRL’s centenary year) was on aver-age higher than in the base year of 2004. Mid-week matches (Tuesday and Wednesday) attractstatistically significantly higher attendance (com-pared with Monday matches). The identity ofthe away team also has statistically significanteffects on attendance (not reported in Table 2)with several away teams, for example, the Drag-ons and the Broncos, drawing significantlyhigher crowds than others.30 Some significanttime-of-day effects are also found (primarilynegative effects from later kick-off times in theafternoon compared with noon, other thingsequal).

Given the marginal significance of the terms inthe quadratic formulation involving the PHome-Win in Table 2, column (1), we experimentedwith alternative measures of match uncertainty.Columns (3)–(5) report results using Excite50(defined as 0.5 – Œ0.5 ) PHomeWinŒ), Excite60

30 The null hypothesis of zero coefficients on allthe away team dummy variables is decisively rejectedwith a p-value of 0.0000.

TABLE 3Fixed Effects Estimation Results with Alternative Playoff Uncertainty Measures

(1) (2) (3) (4)

PHomeWin 0.699 (1.95) 0.771 (2.12) 0.863* (2.20) 0.607 (1.73)PHomeWin2 )0.665* (2.18) )0.655 (2.05) )0.656 (1.96) )0.604 (2.03)HomePtsBack )0.0156*** (6.53) )0.0142*** (5.55)AwayPtsBack )0.00592* (2.77)AvPtsBack )0.0198*** (7.58)PtsRequired )0.0224*** (6.50)WinStreak 0.0358** (3.85) 0.0356** (3.91) 0.0383*** (4.21) 0.0339** (3.77)PreviousYrWin 0.158** (3.27) 0.154** (3.11) 0.147* (2.94) 0.152** (3.21)Round )0.0423*** (7.78) )0.0401*** (7.69) )0.0408*** (8.01) )0.0782*** (9.61)Round2 0.00169*** (7.91) 0.00170***(7.96) 0.00172*** (8.10) 0.00190*** (7.87)

R2 0.685 0.687 0.685 0.691Normality-p 0.075 0.044 0.035 0.074Hetero-p 0.000 0.000 0.000 0.000BP-LM-p 0.177 0.225 0.331 0.035Pesaran CD-p 0.185 0.077 0.097 0.482AvAbsCross 0.122 0.120 0.118 0.127Auto-p 0.228 0.122 0.117 0.293

Notes: See notes to Table 2. Dummy variables for weather characteristics, Sydney teams, year and day effects, away teams andtime of kick-off are included in the models, but estimates are not reported; full results are available upon request.


(defined as 0.6 – Œ0.6 ) PHomeWin)Œ) and Match-Unbal (defined as Œln(PHomeWin ⁄ (1 ) PHome-Win))Œ). None of these alternative formulationshas a statistically significant effect at the 5 percent level, although the coefficient on Excite60 issignificant at the 10 per cent level.31

In Table 3, we report results using alternativemeasures of playoff uncertainty: the number ofpoints the home team is behind the current lea-der (HomePtsBack) in column (1), HomePtsBackand the number of points the away team isbehind the current leader (AwayPtsBack) in col-umn (2), the average of the number of pointsthe home and away teams are behind the currentleader (AvPtsBack) in column (3) and the num-ber of points the home team requires to makethe playoffs (PtsRequired) in column (4). Eachof the four measures of playoff uncertainty hasthe expected coefficient sign and each is highlystatistically significant.32 Varying the definitionof the playoff uncertainty measure has littleeffect on the size and significance of the coeffi-

31 Excite50 and Excite60 have maximum values athome win probabilities of 0.5 and 0.6, respectively,the latter closely corresponding to the turning point ofthe quadratic relationship in Table 2, column (1).

32 If quadratic terms are included in the model foreach of these measures, none is statistically significantat the 5 per cent level.

cients on other variables, except for changes inthe marginal significance level of PHomeWin.These results suggest that all the measuresexamined are capturing, in different ways, theeffects of the playoff probabilities on matchattendance.

VI ConclusionsThe simulation-based approach adopted in this

study to generate measures of uncertainty ofoutcome in modelling sports attendance pro-duces promising results. It has several appealingfeatures compared with existing ad hoc methodsof characterising seasonal or playoff uncer-tainty; in particular, it provides a consistent setof playoff probabilities across all teams reflect-ing the strength of the past and future schedulesand uses a wider set of relevant ex ante infor-mation than just current league standings. Itwould be feasible to apply this approach in arange of different league settings to evaluate theattendance implications of different aspects ofcompetition design, such as different playoffstructures or multiple prizes (e.g. avoiding rele-gation and ⁄ or qualification for other competi-tions, such as in European football).

The results obtained for the NRL suggestthat playoff uncertainty, or more specifically ateam’s probability of qualifying for the playoffs,is a more significant driver of attendance than



individual match uncertainty. Although we havecharacterised existing points-behind-based mea-sures of playoff uncertainty as relatively crude,and their marginal levels of statistical signifi-cance are not quite as impressive as the simula-tion-based measures, they do appear to capturebroadly similar effects as compared with theplayoff probabilities. Hence, to the extent thatthe NRL experience is representative, the use ofsuch measures in other attendance demand stud-ies may not have seriously misrepresented therole of teams’ chances of end-of-season success.However, given the highly intercorrelated natureof the various relevant probabilities, separatingthe effects of uncertainty from the effects of theprobability of success is difficult, especially foranalysis at the level of match attendance. Inkeeping with existing results for other sports,consistent winning performances have a quanti-tatively greater effect on attendance than uncer-tainty measures.

Overall, NRL fans are attracted to winningteams; the various estimated effects reflectingthe home team’s past win performances andenhanced probabilities of match and playoffsuccess combine to produce a virtuous cyclethat improves match attendance.

REFERENCES

Aiken, L.S. and West, S.G. (1991), Multiple Regres-sion: Testing and Interpreting Interactions. Sage,London.

Alavy, K., Gaskell, A., Leach, S. and Szymanski, S.(2010), ‘On the Edge of Your Seat: Demand forFootball on Television and the Uncertainty of Out-come Hypothesis’, International Journal of SportFinance, 5, 75–95.

Alchin, T.M. and Tranby, H.W. (1995), ‘Does theLouis-Schmelling Paradox Exist in Rugby LeagueMatch Attendances in Australia?’, Working Papersin Economics, No. WP95 ⁄ 09, University of Wes-tern Sydney, Nepean.

Baimbridge, M., Cameron, S. and Dawson, P. (1995),‘Satellite Broadcasting and Match Attendance: TheCase of Rugby League’, Applied Economics Letters,2, 343–6.

Baimbridge, M., Cameron, S. and Dawson, P. (1996),‘Satellite Television and the Demand for Football:A Whole New Ball Game’, Scottish Journal of Politi-cal Economy, 43, 317–33.

Baum, C.F. (2001), ‘Residual Diagnostics for Cross-Section Time Series Regression Models’, StataJournal, 1, 101–4.

Benz, M.-A., Brandes, L. and Franck, E. (2009), ‘DoSoccer Associations Really Spend on a Good Thing?


Empirical Evidence on Heterogeneity in the Con-sumer Response to Match Uncertainty of Outcome’,Contemporary Economic Policy, 27, 216–35.

Bojke, C. (2008), ‘The Impact of Post-Season Play-Off Systems on the Attendance at Regular SeasonGames’, in Albert, J. and Koning, R.H. (eds), Sta-tistical Thinking in Sports. Chapman & Hall ⁄ CRCPress, Boca Raton, FL; 179–202.

Booth, R. (2004), ‘The Economics of Achieving Com-petitive Balance in the Australian Football League,1897–2004’, Economic Papers, 23, 325–44.

Borland, J. (1987), ‘The Demand for Australian RulesFootball’, Economic Record, 63, 220–30.

Borland, J. and Lye, J. (1992), ‘Attendance at Austra-lian Rules Football: A Panel Study’, Applied Eco-nomics, 24, 1053–8.

Borland, J. and Macdonald, R. (2003), ‘Demand forSport’, Oxford Review of Economic Policy, 19, 478–502.

Breusch, T.S. and Pagan, A.R. (1980), ‘The LagrangeMultiplier Test and its Applications to ModelSpecification in Econometrics’, Review of EconomicStudies, 47, 239–53.

Buraimo, B. (2008), ‘Stadium Attendance and Televi-sion Audience Demand in English League Football’,Managerial and Decision Economics, 29, 513–23.

Buraimo, B. and Simmons, R. (2009), ‘A Tale of TwoAudiences: Spectators, Television Viewers andOutcome Uncertainty in Spanish Football’, Journalof Economics and Business, 61, 326–38.

Buraimo, B., Forrest, D. and Simmons, R. (2008),‘Outcome Uncertainty Measures: How Closely dothey Predict a Close Game?’ in Albert, J. and Kon-ing, R.H. (eds), Statistical Thinking in Sports. Chap-man & Hall ⁄ CRC Press, Boca Raton, FL; 167–78.

Cairns, J.A., Jennett, N. and Sloane, P.J. (1986), ‘TheEconomics of Professional Team Sports: A Sur-vey of Theory and Evidence’, Journal of EconomicStudies, 13, 3–80.

Carmichael, F., Millington, J. and Simmons, R.(1999), ‘Elasticity of Demand for Rugby LeagueAttendance and the Impact of BSkyB’, Applied Eco-nomics Letters, 6, 797–800.

Clarke, S.R. (1993), ‘Computer Forecasting of Austra-lian Rules Football for a Daily Newspaper’, Journalof the Operational Research Society, 44, 753–9.

Clarke, S.R. (2005), ‘Home Advantage in the Austra-lian Football League’, Journal of Sports Sciences, 23,375–85.

Czarnitzki, D. and Stadtmann, G. (2002), ‘Uncertaintyof Outcome versus Reputation: Empirical Evidencefor the First German Football Division’, EmpiricalEconomics, 27, 101–12.

Dawson, A. and Downward, P. (2005), ‘MeasuringShort-Run Uncertainty of Outcome in Sporting Lea-gues: A Comment’, Journal of Sports Economics, 6,303–13.

De Hoyos, R.E. and Sarafidis, V. (2006), ‘Testing forCross-Sectional Dependence in Panel-Data Models’,Stata Journal, 6, 482–96.


Dobson, S. and Goddard, J. (2008), ‘ForecastingScores and Results and Testing the Efficiency ofthe Fixed-Odds Betting Market in Scottish LeagueFootball’, in Albert, J. and Koning, R.H. (eds),Statistical Thinking in Sports. Chapman & Hall ⁄CRC Press, Boca Raton, FL; 91–109.

Dobson, S., Goddard, J. and Wilson, J.O.S. (2001),‘League Structure and Match Attendances in Eng-lish Rugby League’, International Review of AppliedEconomics, 15, 335–51.

Downward, P. and Dawson, A. (2000), The Economicsof Professional Team Sports. Routledge, London.

Downward, P., Dawson, A. and Dejonghe, T. (2009),Sports Economics: Theory, Evidence and Policy.Butterworth-Heinemann ⁄ Elsevier, Oxford.

Falter, J.-M. and Perignon, C. (2000), ‘Demand forFootball and Intramatch Winning Probability: AnEssay on the Glorious Uncertainty of Sports’,Applied Economics, 32, 1757–65.

Forrest, D. and Simmons, R. (2002), ‘Outcome Uncer-tainty and Attendance Demand in Sport: The Caseof English Soccer’, Journal of the Royal StatisticalSociety, Series D (The Statistician), 51, 229–41.

Forrest, D., Beaumont, J., Goddard, J. and Simmons,R. (2005a), ‘Home Advantage and the Debate aboutCompetitive Balance in Professional Sports Leagues’,Journal of Sports Sciences, 23, 439–45.

Forrest, D., Simmons, R. and Buraimo, B. (2005b),‘Outcome Uncertainty and the Couch PotatoAudience’, Scottish Journal of Political Economy, 52,641–61.

Garcıa, J. and Rodrıguez, P. (2002), ‘The Determi-nants of Football Match Attendance Revisited:Empirical Evidence from the Spanish Football League’,Journal of Sports Economics, 3, 18–38.

Guggenberger, P. (2010), ‘The Impact of a HausmanPretest on the Size of a Hypothesis Test: The PanelData Case’, Journal of Econometrics, 156, 337–43.

Hart, R.A., Hutton, J. and Sharot, T. (1975), ‘A Sta-tistical Analysis of Association Football Atten-dances’, Journal of the Royal Statistical Society,Series C (Applied Statistics), 24, 17–27.

Jennett, N. (1984), ‘Attendances, Uncertainty of Out-come and Policy in Scottish League Football’, Scot-tish Journal of Political Economy, 31, 176–98.

Jones, J.C.H., Schofield, J.A. and Giles, D.E.A. (2000),‘Our Fans in the North: The Demand for BritishRugby League’, Applied Economics, 32, 1877–87.

Knowles, G., Sherony, K. and Haupert, M. (1992),‘The Demand for Major League Baseball: A Test ofthe Uncertainty of Outcome Hypothesis’, The Amer-ican Economist, 36, 72–80.

Koning, R.H., Koolhaas, M., Renes, G. and Ridder, G.(2003), ‘A Simulation Model for Football Champi-onships’, European Journal of Operational Research,148, 268–76.

Kringstad, M. and Gerrard, B. (2007), ‘Beyond Com-petitive Balance’, in Parent, M.M. and Slack, T.(eds), International Perspectives on the Manage-

ment of Sport. Butterworth-Heinemann, Burlington,MA; 149–72.

Lee, Y.H. (2009), ‘The Impact of Postseason Restruc-turing on the Competitive Balance and Fan Demandin Major League Baseball’, Journal of Sports Eco-nomics, 10, 219–35.

Lemke, R.J., Leonard, M. and Tlhokwane, K. (2010),‘Estimating Attendance at Major League BaseballGames for the 2007 Season’, Journal of Sports Eco-nomics, 11, 316–48.

Lenten, L.J.A. (2009a), ‘Unobserved Components inCompetitive Balance and Match Attendances in theAustralian Football League, 1945–2005: Where is allthe Action Happening?’ Economic Record, 85, 181–96.

Lenten, L.J.A. (2009b), ‘Towards a New DynamicMeasure of Competitive Balance: A Study Appliedto Australia’s Two Major Professional ‘‘Football’’Leagues’, Economic Analysis and Policy, 39, 407–28.

Madalozzo, R. and Villar, R.B. (2009), ‘BrazilianFootball: What Brings Fans to the Game?’ Journalof Sports Economics, 10, 639–50.

Meehan, J.W., Jr, Nelson, R.A. and Richardson, T.V.(2007), ‘Competitive Balance and Game Atten-dance in Major League Baseball’, Journal of SportsEconomics, 8, 563–80.

Owen, P.D. and Weatherston, C.R. (2004a), ‘Uncer-tainty of Outcome and Super 12 Rugby Union Atten-dance: Application of a General-to-Specific ModelingStrategy’, Journal of Sports Economics, 5, 347–70.

Owen, P.D. and Weatherston, C.R. (2004b), ‘Uncer-tainty of Outcome, Player Quality and Attendanceat National Provincial Championship Rugby UnionMatches: An Evaluation in Light of the Competi-tions Review’, Economic Papers, 23, 301–24.

Peel, D. and Thomas, D. (1988), ‘Outcome Uncer-tainty and the Demand for Football: An Analysis ofMatch Attendances in the English Football League’,Scottish Journal of Political Economy, 35, 242–9.

Peel, D.A. and Thomas, D.A. (1992), ‘The Demandfor Football: Some Evidence on Outcome Uncer-tainty’, Empirical Economics, 17, 323–31.

Pesaran, M.H. (2004), ‘General Diagnostic Tests forCross Section Dependence in Panels’, CESifoWorking Paper No. 1229.

Rottenberg, S. (1956), ‘The Baseball Players’ LaborMarket’, Journal of Political Economy, 64, 242–58.

Sandy, R., Sloane, P.J. and Rosentraub, M.S. (2004),The Economics of Sport: An International Perspec-tive. Palgrave Macmillan, Basingstoke.

Sloane, P.J. (2006), ‘Rottenberg and the Economics ofSport after 50 Years: An Evaluation’, IZA Discus-sion Paper No. 2175, Institute for the Study ofLabor, Bonn.

Stefani, R. and Clarke, S. (1992), ‘Predictions andHome Advantage for Australian Rules Football’,Journal of Applied Statistics, 19, 251–61.

Szymanski, S. (2003), ‘The Economic Design ofSporting Contests’, Journal of Economic Literature,41, 1137–87.



Tainsky, S. and McEvoy, C.D. (2011), ‘TelevisionBroadcast Demand in Markets without LocalTeams’, Journal of Sports Economics, doi: 10.1177/1527002511406129.

Welki, A.M. and Zlatoper, T.J. (1999), ‘U.S. Profes-sional Football Game-Day Attendance’, AtlanticEconomic Journal, 27, 285–98.

Whitney, J.D. (1988), ‘Winning Games versus WinningChampionships: The Economics of Fan Interest andTeam Performance’, Economic Inquiry, 26, 703–24.


Wilson, P. and Sim, B. (1995), ‘The Demand for Semi-Pro League Football in Malaysia 1989–91: A PanelData Approach’, Applied Economics, 27, 131–8.

Wooldridge, J.M. (2002), Econometric Analysis ofCross Section and Panel Data. MIT Press, Cam-bridge, MA.

Yang, Q.C. and Kumareswaran, D. (2009), ‘Uncer-tainty of Outcome, Match Quality and TelevisionViewership of NPC Rugby Matches’, New ZealandCommerce Commission, mimeograph.

Playoff Uncertainty, Match Uncertainty and Attendance at Australian National Rugby League Matches

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