The Extent to Which Unbalanced Schedules Cause Distortions in Sports League Tables # Liam J. A. Lenten * School of Economics and Finance

Transcription

1 The Extent to Whch Unbaanced Schedues Cause Dstortons n Sports League Tabes # Lam J. A. Lenten * Schoo of Economcs and Fnance La Trobe Unverst Abstract The Austraan Footba League (AFL) has operated ts fxture on the bass of an unbaanced schedue snce the eague expanded from 2 to 4 teams n 987. Ths sstem contans a number of factors (some random) determnng the set of batera combnatons of teams that pa each other on an extra occason durng the course of the season not east of a maxmsng attendances. Whe the status quo ma be unavodabe to some extent (t s aso a bone of contenton to man fans) ts mpcatons for wthn-season measures of compettve baance are nonetheess obvous. Ths s because bases are created n the end-of-season eague tabe as a resut of the unbaanced schedue. Ths paper uses a modfed mode to correct for ths nherent bas over the seasons and the resuts are dscussed n ntrcate deta. The mode s aso generasabe to man unbaanced schedue desgns observed n professona sports eagues wordwde. JEL Cassfcaton umber: C4 L83 Kewords: Compettve Baance Measurement Methods # Current verson prepared for the Research Semnar Seres Department of Economcs Maquare Unverst 20 March Research assstance on ths paper was provded b Lan guen. The author woud aso e to than Damen Edrdge for some usefu comments. * Contact detas: Department of Economcs and Fnance La Trobe Unverst Vctora 3086 AUSTRALIA. Te: Fax: E-ma:.enten@atrobe.edu.au

2 . Introducton An unbaanced schedue s the practce n some professona sports eagues whereb not a batera parngs of teams pa each other on an equa number of occasons n a season. Hstorca unbaanced schedues are extreme rare n the maor footba eagues of Europe where the common practce has awas been to have each team pa each other once home and awa. However the have ong been commonpace n the maor professona sports eagues n orth Amerca such as the atona Basetba Assocaton (BA) atona Footba League (FL) Maor League Baseba (MLB) and atona Hoce League (HL). In these eagues the bass of the unbaancedness of the fxture s determned wthn the conference and dvsona sstem whch vares hgh n terms of specfc deta n each of these eagues. In the ast two decades or so the same has apped aso n Austraa s two bggest eagues Austraan Rues Footba s AFL and Rugb League s atona Rugb League (RL) as these eagues expanded durng the 980s n ther drve towards becomng natona compettons. In dong so the number of teams ncreased whereas the ength of the season remaned constant (tradng off economc factors wth concerns over paer fatgue) creatng unbaanced schedues n both compettons. In the AFL ths status quo s unpopuar wth man fans especa snce there are a number of hgh-drawng fxtures that are guaranteed to be schedued twce n ever reguar season (as opposed to baancng the schedue out over a number of ears) for the purposes of maxmsng attendances rather than on the bass of team-quat equasaton. Tabe dspas the number of tmes each batera parng of teams has paed each other over the perod As s shown there are a number of batera parngs that have been fxtured the maxmum 24 tmes over the perod such 2

3 as the two Perth teams the two Adeade teams and the trumvrate of arge-maret Mebourne teams: Carton Congwood and Essendon. Meanwhe combnatons such as Congwood-Geeong and West Coast-Carton have paed each other on 3 tmes - cose to the possbe mnmum. In spte of the practcates of ths sstem the probem t creates for sports economsts s that t renders team standngs from the end-of-season eague tabe based due to the raw pacngs not tang the strength of schedue nto account. Thus standard metrcs of compettve baance used b sports economsts are potenta nvad. Whe ths resut was found b Lenten (2008) wth respect to Scottsh Premer League (SPL) data the correcton technque proposed was tsef based on a based estmator. Therefore the purpose of ths stud s to app a modfed verson of that adustment procedure to nvestgate to what extent accountng for the strength of schedue affects reported compettve baance measures for AFL data. Ths exercse has ntutve appea for numerous reasons reatng man to the dfferences n the bass on whch the schedue s unbaanced. For AFL data t s more uncertan than the SPL case whether the adusted eague tabe w produce reported compettve baance outcomes sgnfcant dfferent to the unadusted tabe. Addtona of more concern s whether some teams are sstematca better or worse off than others mere because of the fxture. Aso of nterest here s the extent to whch (f an) the eague uses the fxture for team-quat equasaton from one season to the next. These ssues are dscussed n deta. Fna ths w be a cruca poc ssue n the future of It s the atter case that s somewhat controversa snce the other (smaer-maret) Mebourne teams woud prefer to pa these teams more often themseves. 3

4 tournament desgn from as the AFL expands towards an 8-team competton. The foowng sectons of the paper are structured hence: secton 2 outnes some of the terature on unbaanced schedues and tournament desgn. Secton 3 summarses the methodoog used to account for the strength of schedue probem nherent n unbaanced schedues. The resuts are then presented and dscussed n deta n secton 4 aong wth some (eague) poc mpcatons. Fna a bref summar and concuson s presented n secton Lterature Revew Snce unbaanced schedues are common n orth Amercan pro-sports eagues much of the terature acnowedgng ther dosncrases has centred on the mpcatons for these eagues. Wess (986) noted the bases that are created b ths tpe of tournament desgn whe Jech (983) provded a forma representaton of such ncompete tournaments. Other wor centred on team ratngs most wth an appcaton to the FL or CAA Coege Footba where there s the perenna probem of awardng the natona champon. Varous statstca methods have been apped to ths probem ncudng mnmsaton of (absoute) errors (Bassett 997); the anatca herarch approach (Snuan-Stern 988); and maxmum ehood (Thompson 975; Mease 2003). It s the atter stud that most resembes what s beng done here snce Mease s methodoog proposed ndependence from wnnng margns. An addtona maor reason that admnstrators utse unbaanced schedues s ther beef that t ncreases aggregate attendances. In ths ght Pau (2003) and Pau Wenbach and Mevn (2004) fnd supportve emprca HL and MLB 4

5 evdence for ths respectve fndng that the roe of oca derbes s an mportant determnant of demand. The exstence of unbaanced schedues has mpcatons for tournament desgn whch s a cruca theoretca aspect of economcs genera especa abour economcs (see Sutter 2006; or Harbrng and Irenbusch 2003 as recent exampes). Szmans (2003) provdes a thorough exposton on the roe and consequences of tournament desgn on professona sport genera wth varous emphases such as comparatve anases between sports revenue-sharng rues optma eague sze and even cub versus countr ssues. Meanwhe Ehenberg and Bognanno (990) provdes a specfc mode of tournament desgn that of ran-order tournaments on the ncentves of professona gofers to exert effort on the PGA Tour. Of utmate nterest to sports economsts and statstcans s the measurement of compettve baance the noton of whch goes bac to Rottenberg (956). Compettve baance refers to the degree of part or otherwse n sports eagues and s cruca because of the n to the demand for sport va the uncertant of outcome effect. See Sanderson and Segfred (2003) for a genera commentar on these ssues. To ths end there s a desre to mae comparsons between eagues e those of Qur and Fort (992) and Vrooman (995) for the purpose of comparng the reatve effectveness of varous abour maret and revenue-sharng eague poces that are used to enhance compettve baance. Therefore one of the prmar motvatng factors behnd nvestgatng whether adustng for unbaanced schedues affects compettve baance measures s that n the affrmatve case t then begs the queston of whether the resuts of such comparatve studes woud themseves be dfferent. For 5

6 exampe woud Booth s (2005) fndngs comparng AFL compettve baance wth the RL and Austraan atona Basetba League (BL) be dfferent snce the atter has a baanced schedue? 3. Methodoog As a smpe ustratve exampe magne a eague ( I ) comprsed of a set of four teams I { p 2 p 3 p 4 } ordered compete refexve and transtve n terms of team quat (and maret sze) ths orderng observabe ex-ante. Suppose eague offcas face an mposed four-game season ength n whch there s one fu roundrobn of matches pus one extra round of matches - n whch s ptted purpose aganst because t s consdered a premum fxture (n whch case pas n the 2 same round). Whe ths woud arguab maxmse eague-wde aggregate fan nterest the paoffs from the fna eague tabe ma be perverse sewed. Specfca assumng ever game produces the expected outcome both and fnsh on two wns from four games eavng the possbt that 3 coud unust fnsh n second pace (dependng on the secondar crteron for separatng teams ted on wns). Furthermore ths probem s accentuated f a snge paoff match foows nvovng the top two-paced teams from the reguar season to determne the offca champon. For a generasaton of the prevous exampe we use a modfed verson of the unbaanced schedue mode proposed b Lenten (2008) that taes a eague wth a set of teams henceforth denoted as I. The eague has an unbaanced schedue n whch ever team n the eague pas other teams (an non-negatve nteger) 6

7 tmes durng the course of a gven season and the other teams tmes (a ver smpe unbaanced schedue format qute common outsde orth Amerca). From ths nformaton the nta ( ) resut matrx for a gven season (wth competed baanced schedue) S s constructed as x S M x L O L x x L ( ) ( ) ( ) ( ) ( )( ) M M O M M O M L z L z z L z () where { 00.5 x } s the resut n terms of wn vaue for team n game {... ( ) } the porton of the season n whch the schedue s baanced. 2 Aso {0 0.5} refers to the anaogous resut for the porton of the season that s unbaanced between the soft and hard parttons ( { ( )...( ) } ). Fna 0 z s a notona (contnuous) wn vaue for an extra games for each team ( { ( )... ( )( ) }) requred to baance out the schedue on the rght-hand sde of the hard partton but based pure from nformaton contaned on the eft-hand sde of the hard partton. 3 Ths s the e feature that dstngushes ths pure adustment factor approach from usng one of the exstng pethora of predctve-ste procedures to estmate z and arguab the e mprovement of ths methodoog as there s no precse consensus on whch predctve mode s best. It s presumed that the orderng of the teams n equaton () corresponds to the actua ran-order from the eague tabe after ( ) games. 4 2 Whe the ncdence of draws s ver ow n the AFL (0.9 per cent of a matches n ths sampe) the occurrence of draws s of mnma concern snce the tota assgnment of competton ponts s equa (four two each) for a draw compared to a wn for ether team. 3 In other words we want to remove a other exogenous factors (such as nures home-ground advantage boge teams etc.) from the anass. 4 An casua orderng of teams n S s permssbe however. 7

8 In order to correct the bas n the end-of-season eague tabe due to the unbaanced schedue one needs to cacuate mped wn-vaues for each of the unpaed matches for each team requred to baance out the schedue. To do ths one can begn b cacuatng an overa season performance vector (actua) whch ndcates the wn ratos of a of the teams n the eague from the V games paed as thus x x x 2 2 M M V (2) The am s to estmate the theoretca wn-rato that woud have apped for each team had the schedue been baanced but b usng a of the nformaton contaned n the fu season even n the unbaanced porton. Conceptua one wa to do ths woud be to estmate the vaues aowng the competon of the vector z Rˆ the best estmate of the fna standngs (wn-ratos) n the event that each team had actua paed each other tmes hence baancng the schedue ˆ ˆ ˆ ˆ z z z x x x M M M R (3) For each row n the wn rato s smp the arthmetc mean vaue of a eements on the eft-hand sde of the hard partton. The nformaton contaned n V s what s beng used to cacuate the mped wn-vaues for a hpothetca matches for S 8

9 ( { )} K. As a method of estmatng for a batera combnatons of team pang aganst an unspecfed opponent Lenten (2008) maes use of the ogstc reaton b z ' b β x x α z z b b b b ' ' ˆ n (4) Ths smpe ogt-ste rue produced a souton to the SPL unbaanced schedue probem that contaned a number of attractve numerca propertes such as 2 ˆ z x (5) whch s to sa that the adustment procedure shoud not affect the sum of wn ratos across a teams and a seasons. However n addton to ths the foowng propert s hgh desrabe 2 2 ˆ ˆ ˆ z z z M M (6) Ths propert ensures that once the season s scaed up to games Rˆ s nvarant f nstead scaed to an other postve mutpe of games. However equaton (4) does not produce ths propert n Rˆ thus an aternatve approach shoud contan ths propert. Fgure demonstrates ths probem wth the scaebac bas for Lenten s SPL data potted aganst the orgna wn-ratos on the horzonta axs. Ths bas s cacuated as the dfference between the adusted wnratos from scang the orgna 38-game wn-ratos up to 44 games on 9

10 one hand and bac to 33 (( ) ) games on the other hand. Fgure shows that the ogt-adustment procedure (b mere vrtue of ts statstca propertes) unfar rewards medocre teams at the expense of rea bad or good teams (abet to a sma degree) an dosncras that was not evdent n the SPL data whch dd not contan extreme outers but nevertheess woud be obvous wth AFL data. To adust the raw wn-ratos (for team ) approprate n accordance wth the desred propertes outned prevous the procedure shoud begn b cacuatng the dfference between the mean wn-rato of a other teams and the mean wnrato of a other teams that team paed on occasons. To scae up to ( )( ) games ths dfference shoud then be weghted b the proporton of one fu round-robn of further matches requred to baance the schedue forward. Appng ths rue w produce a reaton for the adusted wn-rato for team denoted at ths stage as the th eement of Rˆ as rˆ rˆ w ( ) 2 w ( ) ( ) I w ( )( ( ) ) (7) where I I s a set contanng eements correspondng to the teams that team paed on tmes durng the course of the season. For Rˆ to be unbased n an wa t must be aso possbe to scae bac to ( ) games and obtan the precse same vaue that s 0

11 rˆ w 2 w ( ) ( ) I w (( ) ) (8) where ths tme I I s the set of teams that team paed tmes contanng eements such that I I. Furthermore ettng I { I U I } aows the I consderaton of an team I \ I. To compete the pcture t s aso possbe to soate the adustment vector arsng from the procedure for a teams determned as the foowng ( R V) E A ˆ (9) where E s a vector of estmate error terms. The sampe perod s an annua one extendng from the 997 season foowng the merger of Brsbane Bears and Ftzro and the ntroducton of Port Adeade to the tme of wrtng consttutng a tota of tweve vector observatons wth I dentca throughout. The dstnctve feature of 2008 s that the eague oosened the restrcton that each team had to pa ever other team once n the frst 5 games resutng n a scrambng n the order of x and terms n equaton () f the chronoog of matches s mportant n estmaton due to tme-varng team strength effects. 5 However ths s not the case wthn ths modeng framewor; therefore ths ssue s not of specfc concern. Over the sampe perod the tournament desgn condtons of the AFL produces the foowng vaues: 6 and 7 whch s smar to the tournament desgn n the RL snce 2007 except that 9 n a 24-game competton. 5 See Care (993) for a predctve mode that s specfed wth tme-varng team ratngs.

12 4. Resuts The startng pont s the raw wn-ratos (defned as the number of games won b team dvded b the number paed w g ) for each of the 6 teams whch are dspaed n tabe 2. As can be seen there s consderabe turnover of teams over the sampe perod wth each team havng at east one season where the won ess than 40 per cent of ther matches and at east one other season where the won at east 60 per cent. Ths s due to the consderabe success of the between-season equasng effect of the sute of abour maret devces and revenue-sharng rues used b the eague to enhance compettve baance - see Booth (2004) for more detas. There are aso a few extreme vaues (cose to zero or one) present n the data these are vaues that are partcuar susceptbe to bases created b the non-neart present n the ogstc adustment procedure. As a wa of descrbng the eve of compettve baance n the AFL a range of varous measures are used n an attempt to gan an overa mpresson. Frst the benchmar ASD/ISD rato measure popuar attrbuted to o (988) and Scu (989) s consdered based on the rato of the standard devaton of wn-ratos to that from a eague n whch the resut of each match were pure random thus ASD/ISD t w 0.5 t g t (0) 0.5 g t 2 where t refers smp to the current season. It can be noted that for an team : w g ( ) x ( ) ( ) ( ). Second the Herfndah Index of compettve baance 2

13 (HICB) s reported based on the orgna ndex from IO but adusted to aow for changes n over tme hence 2 4 w HICB t () t g Aso ncuded s a concentraton ndex of compettve baance C4ICB. It measures the proporton of wns accounted for b the top teams n an gven season seected to be four n ths case snce the top four teams quaf for the doube chance n the t fnas seres. 6 Ths s cacuated as C4ICB t w 4 2g t (2) where w are now assumed to be ordered specfca n terms of end-of-season ran as stated on p. 7. Fna the Gn coeffcent s aso reported specfed as GII t 4 h h 2 t w g t t (3) Ths measure s not tota nvarant to changes n and g however ths s not of t t concern n ths sampe anwa snce both varabes were constant. 7 The unadusted measures of compettve baance are shown for a seasons (aong wth ther sampe means) n tabe 3. It s observed that the frst two seasons of the sampe (997 and 998) were unusua compettve baanced even b hstorca standards whereas the fna ear of the sampe (2008) was the most uneven season snce the ntroducton of the natona paer draft and saar cap n the md-980s. A other seasons produced a smar eve of compettve baance accordng to these measures. 6 Ths means that a team can ose n the frst wee of the fnas seres and st be n contenton to wn the tte. Ths s not the case for teams that fnsh ower (ffth through to eghth). 7 GII coud be adusted va the methodoog of Utt and Fort (2002) to overcome senstvt to t and g t. Such a procedure s outned b Larsen Fenn and Spenner (2006). However the denomnator term s varabe to the a pror ran-orderng of teams used to construct the term when the unbaanced schedue s hgh randomsed n nature as s the case wth the AFL tournament desgn. 3

14 Of prmar nterest s the adustment procedure and the effect that the procedure has on the wn-ratos where now wˆ g ( ) x ( ) ( ) ( )( ) ( )( ) ( ) zˆ. The adusted wn-ratos are shown n tabe 4 sted b actua ran-order fnsh. Of most concern s the frequenc wth whch nta pacngs from the orgna eague tabe woud change under the hpothetca adusted pacngs. From a tota of 92 pacngs (6 teams mutped b 2 seasons) where percentage s used as the secondar crteron to determne nta ran-order a tota of 68 teams fnsh n a dfferent notona spot. 8 In some cases teams fnsh up to three paces awa from ther orgna ran. Of the 30 mutatera cases where teams swap ranng 23 nvove mere two teams whereas 4 cases nvove 3 teams and 3 cases nvove 4 teams. In most cases order-swappng nvoves teams that had an dentca wn-rato however n 9 cases; ran-order changes overcome the wn vaue of a draw (0.0227). In the case of 2008 St Kda drops from fourth to seventh swappng order wth orth Mebourne despte fnshng wth an extra haf-a-wn. In two cases the adustment factor even overcomes one entre wn (Port Adeade overtaes Hawthorn from thrteenth to twefth n 2006; and Adeade rses from eghth to sxth at the drect expense of Congwood n 2007). In varous seasons these ran-order changes affect a maor end-of-season outcomes ncudng fnshng n the fnas doube-chance home-ground advantage n frst wee of fnas and the wooden spoon (and b mpcaton the number one draft pc). The adustment vectors for a seasons are aso shown n tabe 5. Over a observatons the mean absoute adustment s wth a standard devaton of 8 Percentage s cacuated smp as tota ponts for dvded b ponts aganst mutped b 00. 4

15 o snge adustment s greater than the magntude vaue of a wn (0.0455) wth the most extreme vaues beng (Hawthorn n 999) and (Adeade n 2003). Most mportant the adustments are seemng not sstematca correated wth the orgna wn-ratos as can be seen graphca from a casua gance of fgure 3. 9 Tabe 6 dspas the adustments at an aggregate eve hepng to dentf f there s an sstematc favourtsm n the fxture. B team t s seen that the 2-season means are a ower n magntude than the mean absoute adustment however the absoute mean dfference between the most favoured team (Hawthorn) and east favoured team (Adeade) s near haf of a wn vaue at a worrng hgh magntude for a 2-ear sampe. Furthermore from the sx non-vctoran teams fve have mean adustment vaues n postve terrtor. Much of ths phenomenon ma be expaned b the non-vctoran teams (average wn-rato of 0.533) havng outperformed the Vctoran teams (average wn-rato of 0.483) on an aggregate eve durng the sampe perod couped wth the fxturng of a-vctoran and a-non- Vctoran matches ( batera average of 7.9 and 8.53 respectve) more often than nterstate-parng matches (batera average of 7.3). Ths resut sounds a warnng of the rs of these sorts of structura effects budng n season-toseason nequtes n the fxture. It aso strengthens the case for dscardng the current sstem for somethng that more resembes a rotatona sstem or even a powermatchng form of unbaanced schedue the es of whch s used n the SPL. 9 In comparson to Lenten s (2008) SPL resuts the mean absoute adustment s ower (compared wth 0.022) athough the extreme vaue s greater n magntude (compared wth on ). These resuts are not surprsng gven the maxmum-bas tournament desgn of the SPL couped wth the fact mn{ } that the vaue of ndcatng the abt for the adustment procedure to ater the wnrato s over 2.4 tmes the vaue of the correspondng vaue for the ( ) SPL. 5

16 One possbe wa to do ths woud be to abandon the guaranteed schedung of fxtures nvovng the arge-maret Mebourne teams twce as ths woud essen the bas auded to n the prevous paragraph. Whe there s tte doubt that schedung the Perth and Adeade derb matches twce maes perfect sense the optmsng (n terms of attendance) effects of the Mebourne bocbusters s ess cear. One wonders whether the so-caed bocbuster premum s overvaued - see Buter (2002) whose resuts from Maor League Baseba suggests that fans are een to see ther team aganst other teams that the have not paed aganst as often n past seasons. Snce the arge Mebourne teams woud presumab draw arge crowds rrespectve of whch (Vctoran) team the pa the net effect ma actua be neggbe overa. In terms of fnsh pace the 2-season means are smar n magntude to the b-team means. More concernng s that most of the postve (negatve) means appear n the top (bottom) part of the tabe ths s confrmed b the correaton coeffcent of between mean adustment and fnsh pace. Ths provdes some support for the contenton that teams that woud have fnshed hgher on the adder anwa end up recevng a net (ex-post) beneft from the strength aocaton contaned n the fxture. Whe of concern the eague obvous cannot observe team quat ex-ante. Of more poc mportance are expectatons of team quat when the fxture s fnased. To ths end the exercse s repeated assumng that the prevous season s standngs had been repcated. 0 Tabe 6 shows that the dstrbuton of postve and negatve mean adustment vaues b fnsh pace s more even dstrbuted wth a 0 The correaton coeffcent between the 6 teams standngs n seasons t and t has a mean vaue of 0.40 over the reevant one-season changes. 6

17 correaton coeffcent between mean adustment and fnsh pace of meanng the fxture (as ntended) fas on the equasng sde of random. Fna we woud e to use the adusted wn-ratos to re-cacuate the four common compettve baance measures for to see f there s a sgnfcant dfference to the unadusted measures. Tabe 7 shows the outcome of ths whe tabe 8 dspas the arthmetc changes of a resut of the adustment. In a star contrast to Lenten s SPL data there s seemng no sstematc drectona effect of the adustment on the compettve baance measures. Begnnng wth the ASD/ISD rato the resuts of whch are shown graphca n fgure 2 there are more negatve adustments (that s adustment nfers the eague to be more even than based on the raw measure) than postve adustments and the 2-season mean s aso negatve but ver sma n magntude. The same s true for each of the other three measures. Furthermore wth the excepton of seasons the four measures produce a consstent drectona change arsng from the adustment procedure n an gven season. To formase the sgnfcance or otherwse n the magntudna change from the adustment procedure the nonparametrc Wcoxon ran-sum test s used snce a casua oo at the data casts doubt over the normat of the dstrbuton of these measures (and hence the dfferences) over the sampe. For the record the test statstc s T L 0 ndcatng that the ran-sums of the two dstrbutons are precse equa. evertheess despte ths fndng t coud be argued that the use of the adusted seres s more approprate that the unadusted seres for use n an tme-seres stud of the reaton between attendances and compettve baance. Such an asserton Over the fu hstor of the eague from the dstrbuton of unadusted ASD/ISD s hgh negatve sewed (-0.682) athough t s cose to perfect mesourtc (0.035). 7

18 woud be on the bass that fans are not fooed b the dstortons created b unbaanced schedues and base ther udgements on the reatve quat of teams n a batera contest accordng. 5. Concuson Ths paper has presented a modfed verson of the Lenten (2008) unbaanced schedue mode that s generasabe to an eague n whch teams pa a other teams ether or tmes. The mode was then apped to end-of-season data from the AFL over the perod The maor fndngs ncude that whe the magntudna effects of the adustment procedure were sma the number of notona postona changes n the eague tabe arsng from the adustment over ths perod was ndeed consderabe. Furthermore at an aggregate eve n terms of both b team and b ran-order n the eague tabe the 2-season means were arge enough to be a cause for concern promptng questons about optma schedung procedures. Utmate however the adustment of wn-ratos dd not cause a sgnfcant change to an of the four common measures of reported compettve baance. The fndngs presented theren have cruca mpcatons for the game s governng bod as t oos ahead to further expanson to 8 teams n One of man cruca ssues that w surface wth the entr of the two new proposed teams s that of tournament desgn. The eague s consttuent cubs ma agree coectve that an ateraton to the status quo of schedung s n order. Whe far beond the scope of the mode presented here the mode coud be extended further to orth-amercan pro-sports eagues where there s a far greater varet of unbaanced schedue tournament desgn formats. 8

19 Tabe : umber of Matches between Each Batera Parng of AFL Teams over the Perod ADL BE CT CWD ESS FRM GEE HAW MEL MB PAD RCH STK SYD WCT WBL ADL BE CT CWD ESS FRM GEE HAW MEL MB PAD RCH STK SYD WCT WBL

20 Tabe 2: Fna (22-Game) Wn Ratos of A Teams n the AFL ( ) Team Adeade Brsbane Carton Congwood Essendon Fremante Geeong Hawthorn orth Mebourne Mebourne Port Adeade Rchmond St Kda Sdne West Coast Western Budogs Adeade Brsbane Carton Congwood Essendon Fremante Geeong Hawthorn orth Mebourne Mebourne Port Adeade Rchmond St Kda Sdne West Coast Western Budogs

21 Tabe 3: Orgna Compettve Baance Measures and Summar Statstcs ( ) Season ASD/ISD HICB C4ICB GII Mean ( )

22 Tabe 4: Cacuated Adusted Wn Ratos Accordng to Actua Ran-Order Fnsh from Tabe 2 Fnsh Pace *Percentage was used as the secondar crteron to determne ran-order as s used n the AFL. 22

23 Tabe 5: Dfference between Adusted and Orgna Wn Ratos b Ran-Order for Each Season Fnsh Pace *Percentage was used as the secondar crteron to determne ran-order as s used n the AFL. 23

24 Tabe 6: Average Dfference between Adusted and Orgna Wn Ratos ( ) b Team and Fnsh Pace and Based on Prevous Season Fnsh Team Fnsh Pace Season Lag Adeade Brsbane Carton Congwood Essendon Fremante Geeong Hawthorn orth Mebourne Mebourne Port Adeade Rchmond St Kda Sdne West Coast Western Budogs Tabe 7: Adusted Compettve Baance Measures ( ) Season ASD/ISD HICB C4ICB GII Mean ( ) *Orderng for C4ICB was determned b pre-adustment ranngs. Ths made a dfference n on 3 ears out of 2 n the sampe and the dfference was sma n each case. 24

25 Tabe 8: Arthmetc Change Arsng from the Adustment Procedure for Each of the Compettve Baance Measures Season ASD/ISD HICB C4ICB GII Mean ( ) Fgure : SPL 'Scae-Bac' Bas from 44 to 33 Games n Lenten (2008)

26 Fgure 2: Orgna (Thc Lne) and Adusted (Dashed Lne) ASD/ISD Rato Fgure 3: Adustment Factor Aganst Orgna Wn-Rato

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