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Home advantage in the Australian football league. Stephen R. Clarke. Journal of sports sciences 23(4): pp. 375-385

© 2005 Taylor & Francis Group Ltd.

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HOME ADVANTAGE IN THE AUSTRALIAN FOOTBALL LEAGUE

Stephen R. Clarke

Swinburne University of Technology, PO Box 218, Hawthorn, Vic. 3122,

This paper investigates home advantage (HA) in Australian rules football, and demonstrates that individual clubs have different HAs. Traditional measures of HA as applied to whole competitions, such as percentage of games won, and alternative measures such as average margin of victory for the home team, are calculated. Problems with these measures are discussed. Individual HAs for each team are obtained via a linear model fitted to individual match margins, the resultant HAs analyzed, and variations and possible causes or groupings of HA are proposed. It is shown that some models allowing different HAs for different clubs are a significant improvement over previous models assuming a common HA. The results show a strong isolation effect, with non-Victorian teams having large HAs, and lend support to the conclusion that crowd effects and ground familiarity are a major determinant of HA.

Keywords: Home advantage, sport, football, linear models

Introduction

The major winter sport of the southern states of Australia is Australian rules football. The game is played on grounds with a rugby shaped ball between teams of 18 players plus reserves. A match consists of four quarters, each of about 30 minutes. Scores consists of goals worth six points and behinds worth one point, and usually range from 50 to 150 points. Winning margins average about 30 points but can be over 100 points. Draws are rare, occurring about once every 125 games. The major competition in Australian rules, organized by the Victorian Football League (VFL), began in 1897 with 14 rounds between eight Victorian based clubs. By 1925 the competition consisted of 12 Victorian clubs, and it was still in that form in 1980 when the data for this study begins. All clubs were based in metropolitan , with the exception of Geelong situated only 90 km distant. In 1982, with the relocation of the Sth Melbourne club to , the VFL began to transform into a national competition. In 1990 the administration of the competition was transferred to the Australian Football League (AFL), and by 1998 the competition had grown to 16 teams, including at least one from each of the five mainland states. An unusual feature of the AFL competition is the lack of both opponent and ground balance in the home and away draw. With the exception of a few years, the length of the playing season has not allowed each team to play each other team twice. Furthermore, while non-Victorian teams currently play half their matches on their home ground, the Victorian sides do not. In the AFL draw, irrespective of where the match is played, the first named team is nominated as the home team. However teams do not necessarily play home matches on their training grounds. To maximize crowds it has become common to share grounds and move some matches to large capacity grounds. In 1970, the League built their own ground, , and in some later seasons required all clubs to play some home matches there. The League has also attempted to maximize the use of the (MCG), and by 1994 this ground was used by five teams for home matches. Because of the large capacity and the practice of selling ground memberships, the crowds at these two grounds contain a larger proportion of disinterested spectators than other grounds. For example, the MCG, commonly called the “people’s ground”, with a capacity of about 100,000 is rarely full, and would always contain a significant proportion of seats allocated to MCG and AFL members. Since many clubs play on the MCG, other teams will also be familiar with the ground. For many teams, these effects have meant steady erosion of the traditional meaning of home ground as where a team plays, trains and has majority crowd support.

Home advantage

The phenomenon of home advantage (HA) has been the basis of considerable study since the seventies. Three explanations for HA are usually advanced: learning factors (ground familiarity), travel factors (fatigue, disruption to routine) and crowd factors (home crowd support and possible referee bias). Early studies looked at the importance of these factors, but generally via the percentage of home wins in whole competitions. Courneya and Carron (1992) give a comprehensive review of this early work. In the section where they survey the relationship between game location and outcome, all but one of the 16 studies listed quote the home win percentage. Other measures such as points per game are not investigated. Pollard (1986) is typical of the approach in that HA is measured as the number of games won by teams playing at home expressed as a percentage of all games played. However the percentage of wins by the home team depends as much on the closeness of the competition and the variability of results as on HA. For example, if teams are all equal in ability, then a small HA will result in most home teams winning. If teams are wide apart in ability, the HA will not often overcome the large ability differences. Thus the percentage of home wins in a competition depends on the range of performance levels in the group as well as the HA. Furthermore, even if the weaker team does not win, the HA effect may still make the match closer than it would otherwise have been. Because the quality of teams varies, differences in ability must be allowed for when measuring HA. Neville & Holder, (1999) recognize this in their review of more recent work in HA “...there is a need to adjust the tournament results for the quality or the standard of the competitors prior to the competition before any home advantage can be assessed”. Holder & Nevill (1997) and Neville et al (1997) use innovative methods to do this when investigating HA in unbalanced competitions such as golf and tennis tournaments. The early holistic approach is also inefficient. Within a competition some teams would travel a lot, others little. Some clubs play in front of large partisan crowds, others to smaller or more balanced audiences. If the individual HAs of teams are calculated, these might be related to the specific travel requirements or crowd factors of those individual teams. HAs, particularly of individual clubs, are better investigated through the use of models that incorporate the performance level of the teams as well as a HA. This has been the approach taken by researchers whose primary interest was in forecasting sporting contests. To do this successfully they had to measure HA and team ability, and found linear models a suitable vehicle. While early models used a common HA, some progress has been made with models assuming individual HAs.

Linear Models

There are several models that can be used in analysing results of games between two teams. Some that are common in the literature are given here. Let wij be the (signed) winning margin when the nominal home team i plays away team j. Let ui be a rating for team i. This summarizes a team's level of performance, their ability or form. Let eij be a random error, usually assumed to be zero mean.

Model 1. No HA wij = ui - uj + eij (1)

Clarke, S. R. (2005). Home advantage in the Australian football league. J. of Sports Sciences 23 (4): 375-385. This model allows for no HA. Stefani (1977) used such a model to predict American football and basketball.

Model 2. Common HA wij = ui - uj + h + eij (2) where h is a common HA and includes all that is advantageous for a team playing at home and disadvantageous for a team playing away. The team rating ui now is interpreted as a measure of the performance of team i on a neutral ground. Where all matches are not played on the home ground of team i, h is replaced by 0, +h or -h depending on whether the match is played on a neutral ground, or the home ground of team i or team j. Harville (1980) used such a common HA model to give estimates of just over two points per game for the HA in NFL for each year from 1971 to 1977, and Stefani (1980) quotes a three point HA for college and a two point HA for pro football.

Model 3. Distinct HA for each team wij = ui - uj + hij + eij (3) where hij is interpreted as hi if team i is the only team at home, -hj if team j is the only team at home, 0 if neither team is at home, and hi-hj if both teams are at home. The hi-hj term is necessary as in Australian rules teams can share a home ground. In many competitions this is not the case, and this term is unnecessary. hi includes all that is advantageous for team i playing at home and disadvantageous for any other team playing at i's home ground. Stefani and Clarke (1992) used this model to investigate individual HAs in Australian rules by using pairs of matches to extract individual HAs. However this proves wasteful of data. Clarke and Norman (1995) used this model to find individual HAs for all English soccer teams, and found some evidence for their significant difference. Harville and Smith (1994) calculated HAs for individual teams by fitting Models 1, 2 and 3 to college basketball. They defined home court advantage as the expected difference in score in a game played by a team on its home court minus the expected difference in the score played by the same team on a neutral court against the same opponent. In Model 1 this is zero, in Model 2 this is h and in Model 3 this is hi. By looking at the marginal difference in the sums of squares between the models, they found strong evidence for a common HA, and some evidence for different HAs, but also that the practical difference was not great. This approach is taken here. By fitting models of increasing complexity it is shown that individual HAs in AFL football are both significant and large enough to be of practical importance.

Method

While Australian rules football followers recognize that some teams have larger HAs than others, rarely is the actual advantage of individual teams in points calculated. Because the draw is not balanced, result tables and ladders are not split up into home and away results as in association football. This paper investigates first the HA of the competition as a whole using traditional measures. The HA of individual clubs is then modeled, and the justification for these more complicated models is tested. Data have been collected on an on going basis for all AFL football matches from 1980 onwards. The data consist of year, round, (nominal) home team, away team, ground and home team winning margin in points. The data were originally collected on a weekly basis from daily newspapers and football records for the purpose of forecasting match results. All 2889 home and away matches from 1980 to 1998 inclusive was used for the analysis in this paper. In the AFL, it is arguable which is the home ground of some teams. Teams play their

Clarke, S. R. (2005). Home advantage in the Australian football league. J. of Sports Sciences 23 (4): 375-385. designated home matches on a variety of grounds. For this study, the home ground of a team for a particular year was defined as the ground on which the team played the most home matches. In all cases this resulted in the same ground as that officially recognized by the AFL. Table 1 gives the list of teams and their home grounds each year. Most clubs have been very stable, only moving to the MCG or Waverley. Fitzroy is the exception, with five home grounds in the period of study.

Table 1. Home grounds of AFL teams for the period 1980 to 1998

Team State Home ground

Adelaide South Australia , 91-98

Brisbane Queensland Carrara Gold Coast 87-92, CG 93-98

Carlton 80-98

Collingwood Victoria Victoria Park 80-93, MCG 94-98

Essendon Victoria Windy Hill 80-91, MCG 92-98

Fitzroy Victoria 80-84, Victoria Park 85-86, Princes Park 87-93, , 94-95, Princes Park 96 Fremantle , 95-98

Footscray Victoria Whitten Oval 80-97, Princes Park 98

Geelong Victoria 80-98

Hawthorn Victoria Princes Park 80-91, Waverley Park 92-98

Melbourne Victoria MCG 80-98

Nth Melbourne Victoria Arden St 80-84, MCG 85-98

Port South Australia Football Park, 97-98

Richmond Victoria MCG 80-98

StKilda Victoria Moorabbin, 80-92 Waverley Park 93-98

SthMelbourne/ Victoria 80-81, Lakeside Oval 80-81 Sydney NSW 82-98 Sydney CG 82-98

West Coast Western Australia Subiaco Oval, 87-98

Clarke, S. R. (2005). Home advantage in the Australian football league. J. of Sports Sciences 23 (4): 375-385.

The above definition does mean that some games, which may carry a large HA, are not classified as played on a home ground. For example, for several years West Coast played about four home matches each year at the WACA, a ground a few miles from their normal home ground, but still 3000km travel for visiting teams and supporters. These matches, played on neither team’s home ground nevertheless may give one side a significant HA. Such a team was categorized as having a perceived HA. Similarly, many matches are actually played on neutral grounds, so neither team would have a perceived HA. The traditional measure of HA (the percentage of games won by the home team), and an alternative (the average margin of victory by the home team) are calculated for those matches in which one of the teams had a perceived HA. HAs between seasons are compared. To make comparisons across competitions and sports the latter measure is standardized by comparing it to the total number of points scored in a match. An alternative approach is to fit a model with team and HA effects to the original match results for each year separately. Any of the Models 1, 2 or 3, or variations could be used. The most complicated model 3 is fitted first to obtain individual HAs for each year. These HAs are then analyzed separately to investigate if various groups such as MCG teams, or teams playing for the first time on a new home ground have different HAs. An alternative method for testing if HAs can be grouped is to test for significance of adding complication to the model. For example, only one HA for non-Victorian teams, one for MCG teams and one for other teams may be needed. Harville and Smith (1994) tested the significance of Models 1 to 3 in basketball by successively fitting the models and testing if the incremental improvement is significant. They found that while including a common HA in Model 2 is highly significant, the gains made by the extra complication of including individual HAs in Model 3 were not significant. One of the improvements they suggested was to group teams. This approach is adopted here, and two incremental models between Models 2 and 3 are tested. The first of these extra models (Model 2a) allows a different but common HA for all non-Victorian teams (hi) to the Victorian teams (hv), while the second (Model 2b) allows a common HA for the MCG teams (hm). When fitting Models 1-3 to an N team competition, there will be N team ratings, and 0, 1 or N HAs respectively. Since the uis are clearly only solvable to within an additive constant, an extra condition such as the average rating is 100 or zero is necessary. The models are fitted with a regression procedure of a statistical package using a matrix of indicator variables. When applied to Australian rules football, the residuals can be shown to be normally distributed, and significant tests can be applied.

Results

In 19 years of Australian rules football, 2299 or 80% of matches carried a perceived HA. Of these the advantaged team won 1371.5 matches, counting a draw as half a win. This amounts to just on 60%, a figure consistent with that found in many other sports. Table 2 gives the percentage of games won each year by the team with the perceived HA. Table 2 also gives the average winning margin of the home team (HA in points), the average total points scored in a match and the ratio (the average number or points scored for every point attributable to HA). The table shows that HA is quite variable from year to year, but that over 19 years it averaged 10.4 points a game or about one point in every 19. The percentage of games won by the home teams has generally increased. This is probably due to the introduction of non-Victorian teams. For example, in the seven years prior to the introduction of two more non-Victorian teams in 1987 the win percentage for home teams averaged 57.6%. The 12 years following averaged 61.7%. This difference was significant at the 1% level (p=0.006). The drop in points scored at the end of 1993 is partly

Clarke, S. R. (2005). Home advantage in the Australian football league. J. of Sports Sciences 23 (4): 375-385. attributable to a change in the length of the quarters and time off definitions, which reduced the effective playing time. While this would presumably also cause a slight decrease in the average home winning margins, this effect has been ignored in this analysis.

Table 2. Match results and HA in points ratio for the team with the perceived HA for each year 1980 - 1998

Year Total Win % HA - Average Total Ratio of games winning points total points margin of to HA home team

1980 107 58.4 3.4 210.5 62.2

1981 102 54.9 10.3 199.4 19.4

1982 104 57.2 12.9 226.6 17.5

1983 106 55.7 8.9 214.7 24.1

1984 103 59.2 10.5 205.3 19.6

1985 100 52.5 5.6 212.7 38.1

1986 100 58.0 11.7 205.5 17.6

1987 119 63.0 13.7 212 15.5

1988 116 61.6 11.1 193.8 17.4

1989 121 64.9 14.4 187.9 13.0

1990 118 60.2 9.6 201.6 21.1

1991 130 60.0 12.0 204.7 17.1

1992 134 53.7 5.3 208.6 39.4

1993 131 60.7 10.9 208.5 19.1

1994 135 62.6 11.4 189.6 16.6

1995 142 57.7 4.8 187.7 39.1

1996 142 67.3 19.2 188.5 9.8

1997 148 64.5 14.5 182 12.6

1998 141 60.6 6.6 184 27.7

ALL 2299 59.9 10.4 200.2 19.2

Clarke, S. R. (2005). Home advantage in the Australian football league. J. of Sports Sciences 23 (4): 375-385. Using linear regression analysis on individual match results

The HAs for each club obtained by fitting Model 3 separately to each year are given in Table 3. In this case all the data are used, as even matches on neutral grounds assist in determining the uis. The HAs are consistent with those given in Stefani and Clarke (1992) which covered the years 1980-89, and their comments on the relative mix of travel, especially across time zones, crowd intimidation, and lack of familiarity with the playing conditions in regard to international comparisons apply here. There is clearly an isolation effect. The five biggest HAs all belong to non-Victorian clubs. The similarity between the average HA given in the last row of Table 3, and the average home win in points in Table 2, demonstrate that the latter simpler method gives adequate results even though it does not allow for strength of opposition. Do different teams have different HAs or are the above differences due to random variation? Table 3 provides data that can be analyzed by normal statistical methods. The year- to-year variation in HA for individual teams is very large, and little faith could be placed on individual values. Nevertheless, some may be of interest to administrators and supporters. For example, why did Footscray, after a decade of consistently high positive HAs, have a huge -50 in 1990? St. Kilda, after its move to Waverley in 1993, had three consecutive HAs all less than they had enjoyed in any of the preceding nine years. Some aspects have been investigated in more detail below.

Team and year effects. The data were analyzed in various ways using general linear models. With HA as the dependant variable a model for all the data with a year and team effect was highly significant (p=0.03). The year effect was not significant (p=0.57) but the team effect was highly significant (p=0.002). This is clear evidence that in Australian rules the HAs of all teams are not the same. Non-Victorian teams. Much of the cause of this difference can be traced to the non- Victorian clubs. If the same model is fitted to the years 1980 to 1986 (before the introduction of Brisbane and West Coast) the model as a whole is not significant (p = 0.74), and the team effect has a p value of 0.56. However when fitted to the years 1987 to 1998, the overall model was significant at p = 0.04 and the team effects at p=0.01. When the HAs from 1987 to 1998 were split into two groups, Victorian and non-Victorian, the 209 Victorian values had a mean HA of 7.4 with standard deviation of 17.6. The 55 non-Victorian values had a mean of 18.0 with a standard deviation of 19.3. The difference in standard deviation was not significant, allowing an equal variances t test which showed the difference in the means for the two groups was significant with p=0.0001. Note that the differences are not just statistically significant, but of practical significance. The average HA of the non-Victorian teams is more than double the Victorian clubs. MCG teams. For reasons outlined previously it might expected that clubs using the MCG have a lower HA than other grounds. To investigate if teams sharing the MCG had a different HA than other teams, the non-Victorian teams were removed. Since they have a higher HA than average, and none use the MCG, their inclusion would confound the new ground effect with an interstate effect. This analysis was therefore restricted to the Victorian clubs only. The 64 HA values for clubs in the seasons when they used the MCG as a home had a mean of 2.8, the other 145 values for Victorian clubs had mean of 9.5. The difference was significant at p=0.01. New ground effect. When clubs change ground, they would be less familiar with their new ground and hence should have a lower HA. Pollard (2002) found a reduction in HA for baseball, basketball and ice hockey teams moving to a new stadium in the same city. During the period 1980 to 1998, Victorian clubs changed grounds to another Victorian venue nine times. The nine HAs for the first season at the new grounds had a mean of -5.7. The other 200

Clarke, S. R. (2005). Home advantage in the Australian football league. J. of Sports Sciences 23 (4): 375-385. seasons by Victorian clubs had a mean of 8.0. This difference is significant (p=0.02). This effect could be confounded with the effect shown in the previous section, as three of the moves were to the MCG. However a combined model still showed both effects significant.

Table 3. HAs for all clubs in the AFL 1980-1998 Team Year 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 80-98 Adel 46 34 44 29 29 53 36 14 36 Bris -11 33 39 43 -5 45 48 30 20 21 20 20 25 Frem -15 31 33 28 19 WC 42 21 38 -2 17 17 12 -15 27 19 16 7 17 Port 36-2 17 Foot 15 17 12 34 28 25 26 10 12 19 -50 29 7 20 33 -6 21 -24 15 13 Car 13 5 39 33 -11 -3 12 17 32 -6 -6 20 16 -2 48 5 11 -6 -2 11 StK -2 7 15 -16 8 6 20 38 17 33 25 13 11 8 -10 -7 25 10 1 11 Coll -11 29 11 32 11 -33 6 -9 21 17 25 32 -2 8 13 6 -12 19 19 10 Syd 36 5 17 9 5 15 6 28 -18 10 2 -4 4 34 -18 8 18 24 1 10 Ess 5 11 10 15 7 32 -2 31 8 17 -13 23 -19 -14 29 -8 -1 0 12 8 Fitz 9 12 -3 35 6 -10 28 28 29 -8 15 9 -5 2 -10 -13 9 8 Geel -3 28 27 -40 20 -5 22 17 -28 25 15 3 14 24 7 -5 -9 23 -29 6 Melb -10 15 -9 12 -4 18 20 3 5 -15 21 -18 7 37 1 -7 0 0 -3 4 Haw 25 -12 19 -28 9 30 -9 8 20 24 -24 10 -12 -12 1 9 3 26 9 5 Rich -5 -4 -6 -10 14 -9 8 -0 14 12 17 -17 -13 -12 28 7 5 24 38 5 NthM -17 2 21 28 23 -23 2 -10 12 -3 53 -3 -31 -35 18 -22 30 -11 -6 1 All 4 10 13 9 10 4 12 14 13 14 9 10 5 11 12 2 14 14 8 9.9

Significance of various models

Because the primary interest is in the non-Victorian effect, in this section only the years 1991 to 1998 are considered. The process is explained in detail for 1995, and then summary results are given for all years 1991-1998. In keeping with Harville and Smith (1994), the notation Si|j represents the difference between the residual sum of squares obtained by fitting Model i and j respectively - i.e. the extra sum of squares explained by fitting Model j over that obtained by fitting Model i. Table 4 shows the marginal sums of squares explained by progressively fitting the models. An F ratio can be formed to test if the model is a significant improvement over the previous model using the final residual mean square (these are the values given in the table). More correctly, the marginal sums of squares can be totalled to test any required hypothesis. Suppose we wish to test whether Model 2 is a significant improvement over Model 1. The improvement in the sum of squares gained by fitting the extra parameter in Model 2 is 2634.1. The residual sum of squares is 10547.8+11.2+10794.9+ 223567.5 = 244921.4 with 1+1+13+145 = 160 degrees of freedom. This gives an F statistic of 1.7, in this case not significant. To test if Model 3 is an improvement over Model 2, the extra 15 parameters of Model 3 contribute 10547.8+11.2+10794.9=21353.9 for a mean square of 1423.6. Compared to the error mean square of 1541.8 this gives an F value of 0.92, clearly not significant. On the basis of 1995 only, there is strong evidence for Model 1 and 2a, somewhat marginal evidence for Model 2 and no evidence for the other models. While it is surprising that Model 2 is not significant, note from Table 3 that 1995 had one of the lowest HAs in terms of points for all years. Other years yield a different result. The results of the analysis for each model for the years 91 to 98 follow.

Clarke, S. R. (2005). Home advantage in the Australian football league. J. of Sports Sciences 23 (4): 375-385. Table 4. Marginal significance of various models for the year 1995

Source df Marginal Sum of Mean F p squares square Model 1 15 SS1 = 131217.4 8747.8 5.7 .00

Model 2| 1 SS2|1 = 2634.1 2634.1 1.7 .19 Model 1

Model 2a| 1 SS2a|2 = 10547.8 10547.8 6.8 .01 Model 2

Model 2b| 1 SS2b|2a = 11.2 11.2 .01 .92 Model 2a

Model 3| 13 SS3|2b = 10794.9 830.4 .5 .92 Model 2b

Residual 145 223567.5 1541.8

Total 176 378773.0

Model 1: Model 1 alone is highly significant, with a p value < 0.01 each year. There is little doubt there are differences in the mean level of team performances. Model 2: Model 2 proved to be significant in most years. Table 5 gives the significance of the improvement for Model 2 over Model 1 (i.e. for the hypothesis test h=0), the R-square value and the estimated value of the common HA for each year and its standard error. Clearly Model 2 is significant and its place as the standard model is justified by these results. Note the estimated values for the common HA are all within one standard error of those given in Table 2, which suggests that the simple methods used there do give a reasonable estimate of a common HA. The model generally explains only about 40% of the variation in results, which illustrates the large unexplained variation present in Australian rules.

Table 5. Model 2 results for the years 1991-98

p for Year H0: h=0 R2 h se(h) 1991 .002 .44 11.2 3.6 1992 .07 .42 6.5 3.6 1993 .001 .41 11.8 3.4 1994 .004 .37 12.2 3.6 1995 .19 .35 4.4 3.4 1996 .0001 .47 15.5 3.4 1997 .0001 .31 15.1 3.2 1998 .04 .20 6.7 3.3

Model 2a: The inclusion of a different HA for non-Victorian teams is generally significant. Table 6 gives the significance of the improvement for Model 2a over Model 2 (i.e. for the hypothesis test hi = hv), the R-square value and the estimated value of the common HAs for non-Victorian and Victorian teams. With five of the eight years significant

Clarke, S. R. (2005). Home advantage in the Australian football league. J. of Sports Sciences 23 (4): 375-385. there is strong evidence for the non-Victorian teams having a different HA to Victorian clubs. However there are still large residuals in the estimates and averages over several years need to be taken to obtain more stable estimates. 1994 is atypical with the estimate for Victorian clubs slightly higher than non-Victorian clubs. Nevertheless the table as a whole is evidence that some clubs do have higher HAs than others, and that a more complicated model than a common HA is justified.

Table 6. Model 2a results for the years 1991-98

p for Year H0: hi=hv R2 hi se(hi) hv se(hv) 1991 0.30 0.45 19.4 8.6 7.2 5.1 1992 0.01 0.45 27.4 8.2 -3.6 5.0 1993 0.02 0.44 31.1 8.6 3.6 4.8 1994 0.76 0.37 10.0 8.0 13.2 4.9 1995 0.01 0.38 21.2 7.1 -5.3 4.9 1996 0.04 0.48 28.3 7.0 8.1 4.9 1997 0.04 0.33 27.2 6.6 6.6 5.1 1998 0.43 0.20 11.2 6.6 3.6 5.1

Model 2b: The evidence for a different HA for the MCG and other Victorian clubs is somewhat inconclusive. The p values for 1991 to 1998 for the improvement in Model 2b over Model 2a were 0.05, 0.11, 0.50, 0.77, 0.93, 0.74, 0.98, and 0.97, which suggests that while a difference may have previously existed in the past it has disappeared in later years. Model 3: There is little evidence for an improvement in Model 3 over Model 2. The respective p values are 0.51, 0.29, 0.11, 0.25, 0.54, 0.53, 0.56 and 0.75. While these average slightly less than 0.5, any improvement can be put down to the gains made by the simpler Model 2a. The p values for the improvement of Model 3 over 2a are 0.52, 0.77, 0.30, 0.20, 0.93, 0.73, 0.81, and 0.73, which show no tendency towards significance. However not a great deal is lost by using Model 3 in place of Model 2. The adjusted R2 value, which adjusts R2 making allowances for the number of parameters in the model, is generally slightly higher for Model 3.

Fitting several years simultaneously

In the previous section, Model 3 was fitted to each year’s data separately. Although teams have large differences in their HAs, significance is difficult to obtain because of the large variation in Australian rules and the limited sample size. Thus in Table 6, the difference in the HAs of the non-Victorian and Victorian clubs was not significant in 1998. However as the seventh time in eight years the non-Victorian HA was higher than the Victorian HA, it supports the premise of higher HAs for non-Victorian clubs. The separate year results have a cumulative effect. Similarly in Table 3, Adelaide, Brisbane and West Coast consistently have large HAs, while North Melbourne is usually low. Yet fitting the model separately to each year loses this effect. One would expect most of the causes of HA to be reasonably constant from year to year. While crowd support may alter depending on a team's success, unless a team changes grounds, the effects of travel, ground familiarity and climatic conditions would remain the same. Clarke and Norman (1995) found a significant year effect in HA for English soccer, but could give no reason. Here, Table 3 showed no significant year effect, so it seems reasonable to fit Model 3 to several years data, allowing for team ratings to change from year to year, but for constant team HAs. The period 1994 to 1998 was chosen as the only changes

Clarke, S. R. (2005). Home advantage in the Australian football league. J. of Sports Sciences 23 (4): 375-385. in home ground in this period were by two Victorian clubs from the Whitten Oval to Princes Park, a distance of about 5 km. Thus the HAs of all clubs could be considered reasonably stable during this period. This gave a model with 81 team-year ratings and 17 HAs. The results were in line with those obtained previously. The individual HAs obtained were approximately equal to the average of the relevant years from Table 3. Model 2 gave a common h of 10.6 which was significant with p= 0.0001. Model 3 just failed to be a significant improvement over Model 1, with p = 0.06. However Model 2a, with a non- Victorian HA of 20 and a Victorian HA of 5, was a significant improvement over Model 2 (p = 0.001). Model 2b failed to show any improvement over Model 2a.

Discussion

Clearly there is evidence for non-Victorian clubs having a higher HA than Victorian clubs, but it is difficult to disentangle the possible causes. Since interstate travel causes problems for fans as well as teams, it is difficult to apportion the positive effects of home crowd bias and the negative effects of away team travel. While the hotter climate may be a factor in the HA of the WA teams and Brisbane, the Adelaide teams have similar HAs. Similarly the more arduous travel to West Coast and Brisbane does not result in larger HAs for these clubs than the Adelaide sides. A comparison of Sydney (the only non-Victorian club without a large HA) and Adelaide (at the top of the HA table) indicates crowd support is an important factor. Team travel between Melbourne and either Sydney or Adelaide is comparable - only a one- hour plane flight. Climatic conditions are not widely different. However South Australia is a traditional Australian rules state, and matches are played in front of one-sided capacity crowds. Sydney is the one non-Victorian team that was actually formed by relocating a Melbourne club to a traditionally non-Australian rules city. Consequently the crowd support at matches in which Sydney plays is much less one sided than for Adelaide. There is also some evidence that teams sharing the MCG, with its more neutral crowds, have a lower than normal HA. Melbourne, Richmond and North Melbourne are all at the bottom of the table, and Essendon has averaged a negative HA since its move to the MCG in 1992. However this could also be due to ground familiarity. There is evidence that teams have a lower HA when they move to a new ground. Since most teams play on the MCG a few times a year, that is the ground apart from their home ground with which they are most familiar. Footscray is the only Victorian club with a HA approaching that of the non-Victorian clubs, but this appears to have been built up in the eighties (average 20) and eroded in the nineties (average 6). The above observations suggest that based on the results in 1991 to 1998, while a common HA or separate HAs for non-Victorian and Victorian teams is justified, further increasing the number of distinct HAs is not. Other groupings may be possible. For example it may be advantageous to remove Sydney from the group of non-Victorian teams, as they are much less isolated than the others in the group. There may also be justification for singling out Victorian sides who have a reputation for a large HA. Of course, one way of deciding possible candidates for groupings is to fit a model with unique HAs for each team and further investigate their similarities and differences. For this reason alone it is worth persevering with Model 3.

Current home advantages

Between 1998 and 2003, ground management has continued to develop. The League ground at Waverley has been replaced with a new roofed stadium at Docklands in the centre of Melbourne. The comments made about the MCG in terms of crowd density and neutrality would apply equally to the Docklands. In 2003, four clubs used Docklands for their home

Clarke, S. R. (2005). Home advantage in the Australian football league. J. of Sports Sciences 23 (4): 375-385. matches, and another four clubs shared the MCG. This leaves only Carlton and Geelong of the Victorian clubs to play on their own unshared training ground. The data on which this study is based was originally collected for a football prediction model, Clarke (1993), which has been published in the press for over 20 years. The program bases its predictions on a team rating and a ground effect. Thus the program has a team- ground interaction – a measure of the extra points a team can expect if the match is played on any ground. This measure is updated after every game, via an exponential smoothing technique, and for a team’s home ground is equivalent to the hi in Model 3. The values at the end of the 2003 season (October) for each team on their home ground are shown in Table 7. This demonstrates that the trends outlined in the paper continue. The non-Victorian teams take six of the top seven places; the bottom six teams are all Melbourne clubs on home grounds shared by several teams. Following their move to The Docklands, Footscray’s fall from near the top of the HA table in the 1980s to the bottom is complete. Clearly HAs for the non-Victorian teams are as strong as ever, and the evidence is that teams playing on the MCG and the Docklands have very low HAs.

Table 7. Home ground effects as at 1 Oct 2003.

Team HA Type of home ground Port Adelaide 25.0 Non-Victorian Brisbane 23.7 Non-Victorian WestCoast 23.7 Non-Victorian Fremantle 23.3 Non-Victorian Adelaide 18.2 Non-Victorian St.Kilda 9.2 Docklands Sydney 8.4 Non-Victorian Geelong 8.3 Traditional Essendon 8.3 Docklands Carlton 5.8 Traditional Hawthorn 4.6 MCG Richmond 4.2 MCG Collingwood 2.0 MCG Nth Melbourne -0.8 Docklands Melbourne -0.9 MCG Footscray -4.4 Docklands

This analysis appears to support the conclusion of Nevill and Holder (1999) that a major cause of HA is due to crowd effects. If the negative effect of travel was a major contributor to HA, the HA of non-Victorian teams should be decreasing as clubs become used to travel with the introduction of more non-Victorian sides, and as travel generally becomes easier. With six non-Victorian teams, one would also expect Victorian clubs to be building up HAs comparable to the non-Victorian sides. Neither of these is occurring. Clubs such as Collingwood, Footscray and StKilda have seen traditionally strong HAs reduce as they have moved to shared grounds with lower crowd density and a high proportion of neutral spectators. The two Victorian clubs to retain their own ground have also retained reasonable HAs. The only non-Victorian team with a single figure HA is the one formed in the state where Australian rules football is not the traditional game, and crowds have not been strong. However an argument could also be made that such effects are due to ground familiarity. Shared grounds are also the most familiar to away teams. Interstate matches in Brisbane and

Clarke, S. R. (2005). Home advantage in the Australian football league. J. of Sports Sciences 23 (4): 375-385. West coast often experience hot conditions, and it is probably true that away sides have more difficulty coping with this than non-Victorian teams have with Victorian weather.

Conclusions

The AFL competition is not balanced with respect to quality of opposition nor home and away matches. The added complication of ground sharing makes it difficult to calculate team ratings and HA. Over the period 1980 to 1998 the teams with a perceived HA won approximately 60% of the matches. This is made up of two distinct periods. Prior to 1987 the home win percentage was 57%, but this increased to 62% after the introduction of new non- Victorian teams in 1987. However a better measure is the average winning margin of the home team, which was about 10 points. Although this is not adjusted for ability of opposition, it gives similar yearly values to fitting a regression model with a common HA. Regression analysis was used for each year to calculate individual HAs for each club. When this is done an ordering of the clubs by HA clearly shows an isolation effect. Non-Victorian teams head the table while inner city Melbourne clubs which share the MCG bring up the rear. Detailed analysis of these showed that the team effect was highly significant. There is strong evidence that this is due to the non-Victorian teams having a different HA to the others, and fitting a single model to the years 1994 to 1998 supported this conclusion. There was also evidence for MCG teams and teams playing for the first season on a new ground having a lower than average HA. It should also be noted that HAs of non-Victorian clubs are not only significant, but also large enough to be of huge importance to a team’s chances. Most non-Victorian clubs have HAs over 20 points, in a competition where the average margin of victory is about 30 points. Nor do these HAs appear to be waning. In 2002, the two Western Australian teams between them won 16 of 20 matches played at home against other opponents, but won only 2 of their 20 away matches. By investigating models of varying complexity, it is shown that the use of models more detailed than those incorporating only a common HA is justified. While unique HAs for all clubs may not be necessary, in the AFL competition they are at least as accurate as using a common HA. The optimum appears to be somewhere in between, with perhaps a different HA for non-Victorian teams from the others. While evidence is often ambivalent, this study appears to support the conclusion that a major cause of HA is due to crowd effects. Further analysis is needed to support the conclusion of Nevill and Holder (1999) that crowd effects are produced through the mechanism of biasing referees. With a high scoring game such as Australian rules football, this would require more than the odd decision in favour of the home team. The paper also supports the findings of Pollard (2002) that moving to a new stadium results in a reduced HA. The analysis has clearly shown that different clubs have different HAs. This allows an investigation of the effects of differences in travel, crowd and familiarity factors of clubs. This was previously done by comparing competitions between different seasons, grades or sports.

References

Clarke, S. R. (1993). Computer forecasting of Australian rules football for a daily newspaper. Journal of the Operational Research Society, 44, 753-759 Clarke, S. R., and Norman, J. M. (1995). Home ground advantage of individual clubs in English soccer. The Statistician, 44, 509-521. Courneya, K. S., and Carron, A. V. (1992). The home advantage in sport competitions: A literature review. Journal of Sport and Exercise Psychology, 14, 13-27.

Clarke, S. R. (2005). Home advantage in the Australian football league. J. of Sports Sciences 23 (4): 375-385. Harville, D. A. (1980). Predictions for National Football League games via linear-model methodology. Journal of the American Statistical Association, 75, 516-524. Harville, D. A., and Smith, M. H. (1994). The home-court advantage: How large is it, and does it vary from team to team? The American Statistician, 48, 22-28. Holder, R. L. and Nevill, A. M. (1997). Modelling performance at international tennis and golf tournaments: is there a home advantage? The Statistician, 46, 551-559. Nevill, A. M. and Holder, R. L. (1999). Home advantages in sport: an overview of studies on the advantage of playing at home. Sports medicine 28, 221-236. Nevill, A. M., Holder, R.L., Bardsley, A., Calvert, H. and Jones, S. (1997). Identifying home advantage in international tennis and golf tournaments. Journal of Sports Sciences 15, 437-443. Pollard, R. (2002). Evidence of a reduced home advantage when a team moves to a new stadium. Journal of Sport Sciences, 20, 969-973. Pollard, R. (1986). Home advantage in soccer: A retrospective analysis. Journal of Sport Sciences, 4, 237-248. Stefani, R. T. (1977). Football and basketball predictions using least squares. IEEE Transactions on systems, man, and cybernetics, 7, 117-121. Stefani, R. T. (1980). Improved least squares football, basketball and soccer predictions. IEEE Transactions on Systems, Man and Cybernetics, SMC -10 (2), 116-123. Stefani, R. T., and Clarke, S. R. (1992). Predictions and home advantage for Australian rules football. Journal of Applied Statistics, 19, 251-261.

Clarke, S. R. (2005). Home advantage in the Australian football league. J. of Sports Sciences 23 (4): 375-385.