Is he Decline in he Frequency of Draws in Tes Mach Cricke Derimenal o he Long Form of he Game? # Liam J. A. Lenen * Deparmen of Economics and Finance La Trobe Universiy Absrac The frequency of draws in es cricke has declined noiceably in he las 15 years. This has been brough abou by changes in he syle of he 5-day game, coupled wih several rule changes designed o exend ime played. While many cricke fans (and adminisraors) believe his o be good for he game, he conradicory argumen is forwarded here o balance he debae, based on he premise ha oo many Tess are finishing excessively early, and hence are predicable. Regression resuls indicae ha rising run raes and rising average wickes per Tes have some explanaory power over he frequency of draws, bu he rule changes have also played a big par. This is one issue (of several) ha adminisraors mus address in order o ensure ha he oldes and pures form of he game is able o coninue o compee for consumer ineres wih shorer forms of he game in he fuure. JEL Classificaion Number: L83 Keywords: Compeiive Balance, Cricke, Demand for Spor # The auhor would like o hank Wayne Geerling and Glyn Wiwer for heir commens on an earlier draf. This paper is a developed version of a shor opinion piece by he same auhor ha appears in he non-refereed biannual magazine, EcoNZ@Oago, Universiy of Oago, New Zealand, no. 21, July 2008. * Conac deails: Deparmen of Economics and Finance, La Trobe Universiy, Vicoria, 3086, AUSTRALIA. Tel: + 61 3 9479 3607, Fax: + 61 3 9479 1654. E-mail: l.lenen@larobe.edu.au 1
1. Inroducion and Previous Lieraure When I was growing up waching cricke in he 1980s, while I was ineresed by Tes Cricke, One-Day Inernaionals (ODIs) seemed o be a far more glamorous elevision opion for a youngser who was also playing he game a junior level. In hindsigh, maybe i was he hen revoluionary Tri-Naions ournamen forma (which lased righ up unil he summer of 2008 before is evenual demise) ha also allowed Ausralian viewers o wach neural games, ha was responsible for much of is appeal o me. Alernaively, perhaps i was he day/nigh mach forma, or he coloured uniforms along wih whie mach balls, or even he disincive rules, such as he 30-mere circle and 15-over field-seing rules. Above all, one furher alernaive has o be considered for why ODIs appealed o me more so han Tes Maches ha i was simply a shorer form of he game. 1 Whaever i was, here was subsanial evidence o sugges ha Kerry Packer had developed an exremely successful business model for inernaional cricke in Ausralia, which laer flowed on o domesic-level and oher counries. However, here is no doub a he ime ha he game s puriss were dismayed a he proliferaion of ODIs a he relaive expense of Tess a worrying rend ha hey had possibly foreseen as early as he World Series War of he mid-o-lae-1970s. This proliferaion was brough abou mainly because he limied-overs forma produced higher aendances and raings, and hus (evenually) higher players salaries, allowing he evenual ransformaion of cricke from a semi-professional spor o a fullyprofessional one. 1 Maybe i was merely a percepion a he ime ha Tes Cricke was he form of he game associaed wih old men and he upper-class. 2
This rend has coninued unabaed since, as can be seen in able 1 and visually in figure 1 wih he aid of a sylised dashed rendline, righ up o (he World Cup year of) 2007. More recenly, he invenion and subsequen meeoric rise in populariy of he even shorer (so-called) Tweny20 form of he game will be even much more worrying for he puriss going forward, especially wih he huge amouns of money on offer. As my own have ases maured since my childhood, I now find myself firmly in ha camp, and proudly so, along wih he elie players who hemselves have always regard Tes Maches as he ulimae form of he game. One of he many (arguably endearing) disincions of Tes Maches specifically is he possibiliy of a draw, whereby he mach is no compleed a he conclusion of he five days of scheduled play, hough in ODIs and Tweny20 maches, here is he possibiliy of a no resul in rain-affeced maches. The primary purpose of his paper is o analyse he apparen decline of he frequency of draws in Tes Mach cricke over he las 15 years, and explore some possible reasons for i, some anecdoal, ohers empirical. This is an ineresing problem in iself, alhough here are a few oher appealing reasons for such a sudy. Firsly, given he exraordinary recen and projeced fuure prosecs of India, a counry in which cricke is he bigges spor, cricke is experiencing a relaive surge in is worldwide financial clou, relaive o oher spors. Secondly, cricke is a spor wih arguably more idiosyncrasies involved (in erms of is rules, power srucures, ec.) han any oher fully-professional spor. Thirdly, and mos imporanly, he curren and pas volume of academic work on inernaional cricke is disappoiningly hin wihin he spors economics fraerniy, a deficiency ha his paper hopes o play a role in overcoming. 3
Despie he dearh of economics lieraure on cricke, a very nice general commenary regarding recen economic influences on cricke can be found in Preson (2006). Meanwhile, Bhaacharya and Smyh (2003) underake a classic-syle esimaion of demand for spor exercise for cricke maches in Ausralia, finding in favour of he prevalence of mach-specific facors (such as uncerainy of oucome) over more general economic facors (such as price and income) in deermining demand. Much of he remaining work on cricke cenres on eam raings and predicion, such as Allsop and Clarke (2004), as well as Brooks, Faff and Sokulsky (2002), whose ordered response model correcly prediced over 70 per cen of all wihin-sample Tes Mach resuls from 1994-1999 a mos impressive resul considering he riumvirae of possible resuls. 2 Oher cricke conribuions have ended o be quie specific and limied in scope. One such example includes Ringrose s (2006) invesigaion ino he effeciveness of he move owards neural umpires in recen years by way of analysing leg before wicke (LBW) decisions. Anoher such example is Blackman and Chapman (2004), who esimae he addiional revenue o he game from he supersar effecs arising from he presence of Donald Bradman in he Ausralian line-up. The srucure of he remainder of his paper is as follows: secion 2 ensues by relaing he changes ha have been observed in cricke o changes in rends in he now highlycompeiive spors indusry, and how cricke s decision-makers have responded. Secion 3 hen applies hese ideas o he specific case of draws in Tes Cricke, and he 2 Ignoring, for pracical reasons, he possibiliy of a ied mach. 4
major facors surrounding he decline in he frequency of draws since he early 1990s. Following ha, secion 4 examines changes in he rends of he mechanics of he game (boh a Tes and ODI-level), o ry and explain he sory behind hese broad rends, some of which have been noed previously by cricke commenaors and wriers. Ulimaely, here is a link made back o he demand for spor via he uncerainy of oucome hypohesis in secion 5, as well as some houghs on possible policy changes. Secion 6 concludes wih a brief summary. 2. Background on Compeiion beween Spors As an unapologeic puris, I have recenly found myself osracising Tweny20 as cricke for people who do no really like cricke, and referring o is supporers as hose wih shor aenion spans. However, one has o analyse he reasons for Tweny20 s populariy o undersand why here is an explosive growh in he number of inernaional maches being scheduled (see able 1 again). Once upon a ime, spors adminisraors ended o view heir own spor as having a subsanial amoun of monopoly power, owing o heir belief ha heir spor was highly differeniaed compared o oher spors. However, wih he passage of ime, as elie spo has become increasingly hough of as an enerainmen produc, hese adminisraors have realised ha hey are, in essence, compeing wih oher spors for much of he same marke. Hence, hey have done heir umos o reform heir spors coninually o recrui new and reain exising 5
paying cusomers and he revenues ha hey produce, wheher a-he-gae or hrough oher forms, such as elevision raings and even merchandise sales. 3 Now, his is all compleely raional behaviour, bu changes in cricke have been made very rarely wih puriss in mind, since hey are already a capive marke, and i is herefore harder o exrac exra marginal revenues from his cohor. Raher, hese changes are made wih he inenion of aracing new people o he game from nonradiional cricke loving demographic groups hese are mainly he groups o which Tweny20 is argeed. Adminisraors and players canno be blamed for riding he wave of his surge in demand ha he shores form of he game has brough. However, i may be ime o consider some possibiliies o make Tes Cricke more aracive and compeiive (wihou compromising is inegriy), so ha his 130-year old insiuion can coninue o survive well ino he fuure. Such a shif in he demand curve for Tes Cricke need no necessarily occur a he expense of ODIs. 3. Sexy Tes Cricke In he 1980s, Tes Cricke was seen by a lo of people who were no really ino i as being on he nose, owing o a few characerisics, one of which was he relaively high proporion of maches ha finished in draws. Draws were ofen associaed wih negaive, defensive play a he ime, as acics were ofen aimed a no losing he Tes (especially away from home), as opposed o rying o win i. An annual ime-series 3 As an aside, I believe ha he phenomenon of his growing compeiion also goes a long way owards explaining he proliferaion of oher mach-enerainmen and shameless gimmicks. These iems include grauious general promoion, fireworks displays, cheerleaders, celebriy naional-anhem singers, domesic and naional eam nicknames, bonus poin sysems and bilaeral-eam pairing rophies (of which here are now 11 in Tes Cricke, wih he mos recenly insiued being he Warne- Muraliharan Trophy for Ausralia v Sri Lanka Tes Series). 6
represenaion of he percenage of Tes maches by calendar year ha finished in draws over he period 1978-2007 is shown in figure 2. 4 The second (bold) line is a rend esimaed by applying he HP (Hodrick and Presco, 1997) filer, which for any ime series daa can be obained by solving he following opimisaion problem min z T = 1 T 1 2 ( X Z ) + λ [ ( Z + 1 Z ) ( Z Z 1 )] = 2 2 (1) where X is he acual value of he series; Z is he rend componen; X Z is he resuling cyclical componen; and λ is he smoohing parameer. In accordance wih he suggesion of Presco (1986), a value of 100 is used here for he smoohing parameer, λ, which is sandard for annual daa. Provided ha he error erms are relaively small, he HP filer is an empirically opimal valid of esimaing a smoohly varying rend componen of a ime series, and is a mos popular rending procedure in empirical economics. However, he purpose of applying a HP filer for his annual series is no so much on echnical grounds. Raher, he HP filer is applied and displayed in figure 2 merely o provide some idea of he underlying rend of he series for visual purposes. From his figure, as can be seen, roughly 45 per cen of all Tess played during he 1980s finished in draws a level ha even he puriss would have admied a he ime required redressing. 4 The Tes beween Ausralia and India in Adelaide, 28 January-3 February 1978 did no produce a resul a he end of he fifh day; raher i wen ino a sixh day and produced a resul. For he purposes of comparabiliy in definiion, i is couned as a draw here. Also, he 1986 ied es beween India and Ausralia in Chennai (hen Madras), is no couned as a draw, as a ie consiues a compleed mach and hence a resul. 7
The response by cricke s adminisraors, he Inernaional Cricke Council (ICC) in conjuncion wih he various naional governing bodies of he small number of Tes playing naions, was caegorical. Rule changes were inroduced progressively, designed o exend he oal number of overs played in ess, including minimum over (per day) rules, making up for ime los due o rain or bad ligh, and even allowing he use of he available ligh owers a relevan grounds. However, oher forces were also a work simulaneously hrough he 1990s: he growing volume of ODIs was finally beginning o have a maerial effec on he way ha Tes Cricke was being played, insofar ha acics were becoming more aacking. This effec gahered even more pace from around 1995 when ODIs hemselves became more aacking, wih rising run raes in ha form, evenually filering hrough o Tess, a poin ha will be revisied laer in secion 4. However, admiedly here is a large number of oher (albei minor individually) minor facors ha collecively play a role in deermining he incidence of Tes draws no considered here, such as he now sandardised use of boundary ropes, improvemens in grounds-keeping echnology and maybe even climae change. A any rae, hese changes have, in essence slowly evolved Tes cricke ino somehing ha slighly more resembles ODIs han used o be he case, in order o make i sexier. Ausralia have been a he fronier of his rend, a one poin having an incredible run of 48 consecuive ess beween 1999 and 2003 wihou a draw, excluding 3 (consecuive) draws in a single Tes Series agains New Zealand in Ausralia (November-December 2001). As an aside, he sexy movemen has no los pace, as recenly here has even been alk abou he possibiliy of nigh ess, a concep 8
ha would mos cerainy have been implemened by now had i no been for players concerns over he peculiariies of he colour and movemen in he air of he ball a nigh. In any even, he HP rendline in figure 2 suggess ha he decline in Tes draws may have finally plaeaud, a jus under 24 per cen. Such a change in he proporion of maches ending in draws has also alered he menaliy of he cricke-following public and he spors media ha repors on he game. One such manifesaion of his change was he apparen hype surrounding he Ausralian eam ha won 16 consecuive Tess (2005-2008). The final vicory in ha sreak (v India in Sydney, January 2008) equalled he previous record (also se by Ausralia in 1999-2001), hough wih his vicory, here was far less aenion a he ime given o heir mosly conemporaneous unbeaen sreak, which had exended o 22 maches wih ha win. However, when one considers ha a successive winning sreak can be broken by pure virue of bad luck if inclemen weaher prevails during a Tes (ofen he case in Tes venues such as Dunedin or Mancheser), arguably far more imporance should be placed on unbeaen sreaks, as used o be he case, and is sill mos ofen he case in associaion fooball (soccer). Incidenally, while his unbeaen sreak was Ausralia s longes in heir Tes hisory, i sill fell shor of he all-ime record of 27, se by he mighy Wes Indies eam of 1982-1984. 5 5 This fac seems o be ignored rouinely in analyss dialogues, when hey aemp o compare and conras hese wo grea eams ineremporally. 9
4. Game Trends and Resuls As a firs sep owards a formal ime-series regression analysis, he approach aken here is o break he mechanics of he game of cricke down ino is principal componens: runs, balls and wickes. The purpose of his approach is o idenify hose facors ha are more closely inerwined wih he occurrence of draws, and also o ell he general sory abou changes o he syle of cricke in he las generaion. A descripion of he resuls arising from he formal regression analysis hen follows. For he purposes of he following analysis, he sample begins slighly laer han (ha used in figures 1 and 2) in 1981, since he daa on ODIs is somewha hin unil ha poin. All of he daa was obained or consruced from mach daa available from he CricInfo websie a: hp://www.cricinfo.com/ Since scoring raes have been menioned in his paper hihero, le us begin by examining figure 3, which plos run raes (per over) in boh Tess and ODIs by calendar year. Saring wih ODIs, here appears o have been a seady growh in run raes over ime, as baers began o play an increasing volume of ODIs, evenually coming o erms wih he limied-overs forma. However, he greaes surge during he sample is he period from 1994-1998, since which here has been lile furher growh, implying ha eams baing firs now have o score beer han 250 o give hemselves a beer han even-money chance of winning, whereas ha figure was once more like 220. I aribue rising run raes in ODIs a ha ime much o he success of he acics of he 1996 World Champion Sri Lankan eam (especially hiing over he infield during he firs 15 overs of heir innings), and he prompness wih which oher eams adoped heir syle. 10
Analogously, run raes in Tess appears more o have cycled during he 1980s and 1990s, alhough from 2000, here is a clear srucural break, as run raes have acceleraed, which leads naurally o he quesion of he degree o which ODIs are responsible for his. The logic of higher ODI run raes causing Tes run raes o increase makes perfec inuiive sense, and he correlaion coefficien beween conemporaneous run raes in he wo forms of he game over he period from 1981-2007 is 0.70. However, a simple Granger-causaliy es (resuls no repored) shows ha even wih varying lags of 1-5 years, he null hypohesis ha ODI run raes do no Granger-cause Tes run raes could no be rejeced under any circumsances, even a he 10 per cen level of significance. Neverheless, if here is some real influence of some forms of cricke on ohers, hen we would expec o see even higher run raes sill in boh Tess and ODIs in he fuure, as Tweny20 cricke becomes much more common. 6 Observing higher run raes, he nex logical sep is o address he issue of wheher his more expediious scoring is associaed wih beer baing over ime, or raher if wickes are falling more ofen. To deal wih his issue, figure 4 exhibis baing averages in boh forms of he game. 7 When one ignores he seemingly saisical oulier of 1989, i is difficul o idenify a clear overall rend in Tes averages over ime, hough here is a very small decline hroughou mos of he 1990s. However, wheher beer fielding or he hen growing prevalence of reverse-swing pioneered by he Pakisanis (or even somehing else) was responsible for his is unclear. Wha is clear is ha baing has improved noiceably during he curren decade, a resul ha is 6 In he firs 50 official Tweny20 inernaional maches (up unil end of 2007), he average run rae was 7.94 per over. 7 This measure is calculaed simply as oal runs divided by oal wickes in a calendar year. Therefore, his also couns exras or sundries, which would ypically no be couned when calculaing an individual baer s average. 11
consisen wih figure 3. The rend in improved baing averages in ODIs, however, is reasonably obvious, nowihsanding he overall flucuaion of he series, bu he change is more modes compared o ha implied in figure 3. The oher side o he sory described hus far is he frequency wih which wickes fall. To his end, srike raes (average balls per wicke) are shown in figure 5. Here he sory is very similar for boh Tess and ODIs (he correlaion coefficien is 0.56), insofar ha here is a lo of noise in he series wih no clear rend unil abou 1994, when in boh forms of he game, srike raes fall immediaely and significanly, and remain a he lower levels hereafer. Given he srucural naure of he change and ha i has occurred in boh forms of he game, one is inclined o forward he inroducion of he hird (video) umpire as a primary reason for he increase in frequency of dismissals (especially in he case of run ous and sumpings). This is paricularly so in ligh of he previous umpiring edic of giving any benefi of doub o he baer. However, i is difficul o ell o wha exen his fall in srike raes is also aribuable o possible growing impaience of faser-scoring baers over ime. While he figures discussed hus far reveal much, we have no ye addressed he overall-game dimension. Figure 6 chars he average number of balls bowled in a mach. The more ineresing sory here is for ODIs, however, i mus be noed iniially ha he figures produced for ODIs in figure 6 are unreliable unil 1987. 8 Neverheless, from ha poin onward, we see a seady decline in he number of balls bowled. This resul is acually consisen wih he riskier baing in recen years ha 8 The reason for his is ha numerous ODIs early in he sample were no he now-sandard 50 over perside maches unil hen. For example, he maches in he 1983 World Cup (60) as well as maches in Pakisan (40) and Sri Lanka (45) were no changed o 50 over-maches unil abou 1986. Even hereafer, maches in England were 55 overs per side righ up unil 1995. 12
has come wih faser run raes. We now observe more eams going for broke, especially in he second session of a mach, meaning ha irrespecive of wheher or no he risky sraegy works, more maches (sadly in my opinion) are finishing earlier on in erms of overs bowled. 9 One facor behind his is ha eams have become increasingly asue over ime acically a uilising all heir wickes (when viewed as resources in he spiri of he run-rae adjusmen mehodology of Duckworh and Lewis, 1998). This resul may also be being driven by anecdoal evidence ha piches have become seadily quicker. For Tess, once he oulier of 1989 is ignored, i is oherwise challenging o idenify a clear long-erm rend, hough i is arguable ha here has been a sligh decline owards he end of he sample, perhaps due in par o he increase in he number of Tess involving Bangladesh and Zimbabwe. Finally, in erms of average number of wickes falling per mach, i is seen in figure 7 ha for ODIs, he long-erm rend has indeed been upward hroughou mos of he sample, despie ailing-off in recen years. This sory is consisen wih he Duckworh-Lewis resources-syle sory menioned previously. For Tess, he rend has also been upwards generally, wih some variabiliy in he series, alhough here, he role of declaraions is also imporan, which have (again anecdoally) become more aacking in recen years. 10 Thus, here may be some downward bias in his series in he laer years. 9 The inroducion of bonus poins in ODI ournamens has accenuaed his apparen problem. 10 The radiional acics were hose whereby he (aacking) eam baing hird, for insance, would ake heir opponens ou of he game oally prior o declaring, and hen se aacking fields. This involved declaring laer in he mach and (ceeris paribus) less wickes down. In recen years, he rend has been owards capains backing hemselves in by declaring earlier, hereby giving heir opponens a small chance of vicory, bu wih more overs remaining in he mach o bowl hem ou. 13
The following descripion oulines he modelling process for he ime-series ordinary leas squares regression analysis of he daa described already. For he purposes of he narraive of he resuls, we examine individual coefficien esimaes and he F-es for join significance, as well as goodness-of-fi, diagnosic and model evaluaion resuls. In erms of goodness-of-fi, he unadjused coefficien of deerminaion, 2 R and is adjused counerpar 2 R ; as well as he sandard error of he equaion, ~ σ, are repored. In associaion wih hese ess, he following diagnosic ess are also saed: he residual ess are he Breusch and Godfrey (1981) es for firs- and second-order serial correlaion, which is an F-saisic, SC; he Jarque and Bera (1980) es for normaliy, which follows a 2 χ (2) disribuion, NO; and he Breusch and Pagan (1979) and Godfrey (1978) es for heeroscedasiciy, which is an F-saisic as well, HE. Srucural sabiliy of he model is accouned for by he Ramsey (1970) RESET es for funcional form wih one fied erm, which is also an F-saisic, FF. Finally, a comparison of overall model validiy can be aained by looking a he Akaike (1973 and 1977) informaion crierion, AIC; and he Schwarz (1978) Bayesian crierion, BIC. All of hese ess are sandard in Economeric Views 6. In deermining he opimal model for he daa, a general-o-specific mehodology is employed, as here is no real way of knowing a priori precisely which variables have he mos explanaory power. The precise version of he model ha is esimaed o begin wih is a mos general version ha conains all variables in he form TD = α + βrr + γav + δsr + θbm + κwm + ε (2) where TD is he proporion of Tes Maches finishing in a draw in year, while AV is he baing average in Tess, SR is he corresponding bowling srike rae, BM is 14
he average balls per mach, WM is he average wickes per mach, and ε is a whie noise error erm. The model is esimaed over he full sample from 1978-2007. The resuls of he regression corresponding o equaion (2) are repored in able 2. The model is valid, insofar ha i passes all of he residual ess, meaning ha i is no misspecified, furher, i is also srucurally sable. However, neiher he inercep nor any of he regressors are significan, ye he F-es for join significance of he variables is easily significan, even a he 1 per cen level. From his is i obvious ha mulicollineariy is a problem. This resul is unsurprising, as hese variables are linear combinaions of merics ha are overlapping in some of hese variables. Since quie high, some explanaory variables can be eliminaed easily. 2 R is To decide exacly which variables o exclude, a correlaion coefficien marix is consruced in he form of able 3. In dealing wih mulicollineariy, we look for explanaory variables ha are no very highly correlaed wih TD, hough highly correlaed wih he oher explanaory variables. A quick glance a able 3 reveals ha AV paricularly fis his descripion, while BM also fails o jusify is presence. Hence, he regression is re-esimaed wihou hese wo variables, leaving he represenaion as follows TD = α + βrr + δsr + κwm + ν (3) The esimaes of his model are also displayed in able 2. The resuls are quie pleasing overall, wih saisfying goodness-of-fi, as well as passing all of he diagnosic ess, and he model evaluaion ess indicaing a noiceable improvemen on equaion (2). All of he coefficien esimaes are now significan apar from κ, 15
however, δ is no he sign ha we would expec lower bowling srike raes should mean less draws. To improve he model furher WM is dropped from he regression. This leaves he following model TD = α + βrr + δsr + ω (4) On his occasion, alhough he inercep is insignifican, boh of he remaining coefficiens are significan, and κ is now posiive as expeced. However, he fi of he model has declined, and he model evaluaion resuls demonsrae an overall deerioraion of he model compared o equaion (3). As an alernaive o equaion (4), we resore WM o he model, his ime excluding SR insead. There is also an inuiive appeal for his aleraion RR is a funcion of runs and balls whereas WM is a funcion of wickes and maches, hereby circumvening any overlap beween he linear combinaions of he remaining variables (whereas RR and SR have balls a common denominaor). A his poin, we are lef wih a model aking he following form TD = α + βrr + κwm + ξ (5) By referring once again o able 2, we see ha boh coefficien esimaes are significanly negaive (he inercep erm is also significan), as would be expeced. Tha is o say ha he rends of increasing Tes run raes and an increasing number of wickes falling in a mach have boh had a significan influence on Tes draws becoming less frequen. 16
As a final variaion of he baseline model we now have, we replace RR in equaion (5) wih is ODI counerpar, ODIRR, over he period 1978-2007. This is implemened as a furher way of esing he possible impac of he increasing volume of he one-day game (and is own propensiy o have become more aacking in recen years) on he way Tes Maches are being played. From his, we have TD = α + κwm + τodirr + ζ (6) The resuls in he righ-hand column of able 2 reveal ha he model surpasses even equaion (5). This is according o he model evaluaion saisics, as well as he improved fi, reduced sandard errors on he coefficien esimaes, consisen wih ODIRR being more srongly (negaively) wih TD han RR, as seen in able 3. One has o be cauious abou making any srong inferences abou his resul, however. While equaion (6) also passes he FF es, he possibiliy of a srucural break in 1994 was also considered, for he possibiliy ha higher srike raes arising from he inroducion of he hird umpire had a significan impac as a sand-alone even. However, a simple Chow (1960) breakpoin es reveals ha for equaions (4), (5) and (6), he es saisic esimaes are 1.71, 2.01 and 0.74 respecively, all of which are insignifican a he 5 per cen level. One final varian on he models discussed here was considered ha of he inclusion of a (one-period) lagged dependen variable as an independen variable, o allow for he possibiliy of persisence in TD. The variable proved o be insignifican wherever i was included, however, and in some cases dragged oher coefficien esimaes ino insignifican erriory. In summary, cauion mus be exercised a he OLS figures oulined in able 2 ha seem o sugges ha run raes and he numbers of falling wickes are alone driving he 17
resuls. As cricke followers are well aware, dozens of facors (many of hem negligible individually) are a work in deermining he incidence of Tes draws, hough such a mach-by-mach model accouning for all hese facors would be prohibiively complex. Raher, he chosen approach here has been a parsimonious model ha acually looked a broad, aggregae and longer-run facors. 5. Uncerainy of Oucome and Possible Policy Changes The implicaions of hese resuls have a maerial effec on he demand for Tes Cricke. In spors economics, he much discussed uncerainy of oucome hypohesis, which can be raced back as far as Roenberg (1956), suggess ha fans wan o see an even cones. No ha hey wan o see heir eam lose, raher hey wan o know ha here is some chance ha heir eam will lose. Hence, we should observe higher levels of demand for Tes Cricke when here is some uncerainy as o he resul. Unforunaely, in recen years, he underperformance of Tes minnows Bangladesh and he once-reasonably compeiive Zimbabwe, along wih he serial dominance of Ausralia, have produced a higher number of one-sided coness. The spors economics lieraure is abundan wih research papers esing he uncerainy of oucome hypohesis, mainly in reference o eam league spors, wih he majoriy of work finding favourable evidence of is exisence. Wih cricke s many endearing idiosyncrasies, i is a piy ha such work on cricke is so scarce, hough Hyndes and Smih (1994) is a noable excepion, looking a uncerainy of oucome in he framework of wihin a Tes mach on one hand versus wihin he Tes series on he oher hand. 18
Wih lile change o average oal innings scores in Tess, bu wih more overs in each day and faser run-raes, he consequence has been a larger number of ess being compleed wihin four days, and a larger proporional increase sill in hose finishing wihin hree days. The obviousness of his problem can be seen by looking a figure 8, which displays he percenage of all Tes maches ha finish early. The rising frequency of Tess finishing wihin four days and wihin hree days is easily discernable from a quick eyeball. 11 Furhermore, he HP rend (no shown in figure 8) of he frequency of Tess finishing wihin four days rises over he 1981-2007 sample from 19.0 per cen o 40.8 per cen, while he analogous figure for Tess finishing wihin hree days is even much more dramaic, rising from 2.5 from 15.3 per cen. The problem wih his rend is wo-fold: firsly, in business erms here is he obvious significan los aendance and elevision revenues from he Tes no going five days as scheduled. Secondly, in purely crickeing erms, he vas majoriy of Tess ha finish so early are inherenly highly predicable ha is o say, he cones is onesided from early on in he game. In fac, you have o go back o he 2005 Ashes Series (England v Ausralia) o find he mos recen (as a February 2008, he ime of wriing) Tes ha finished wihin four days wih a winning margin of less han four wickes or 40 runs. In fac, ha series produced wo such Tess (he 2 nd and 4 h, boh won by England), he former of which concluded before lunch on he fourh day, however such insances are far oo rare. Meanwhile, ou of 18 innings-plus vicories in he 109 Tess since he beginning of he same series, 10 were concluded wihin hree days. Furhermore, in Tess ha go well ino he fifh day where one eam is 11 The number of days couned in a Tes does no include res days, once common in Tess a generaion ago, bu phased ou over ime unil he las occasion, Wes Indies v India, Bridgeown, 28 March 1997. 19
dominaing, here is sill an uncerainy of oucome prevailing by virue of he oher eam aemping o hang on for he draw. Unlike he 1980s, very few draws look o be cerain draws a he end of he fourh day (i.e. boring coness). While i is no being suggesed ha he opimal probabiliy of a draw should be close o 0.5, as i was hroughou much of he 1980s, perhaps i would be nice o see a figure somewha higher han wha we observe oday. One school of hough suggess ha he ideal scenario is one in which boh eams (ignoring home advanage) each have a one-hird chance of winning he mach, while here is a one-hird chance of a draw. Neverheless, one opion available o he ICC ha I would favour personally is o adjus he exising 15-over rule, inroduced in he 1990s, exending he six hours of play by up o an exra 30 minues if 90 overs have no been bowled. 12 The rule was inroduced iniially o preven eams from bowling slow over raes deliberaely. However, he rule has acually done more o merely exend he day s play (essenially compressing he imeline of he mach) raher han lifing over raes, as drinks breaks, injuries, ec., mean ha a eam can easily fall below 15-overs an hour even when rying o mainain he over rae (hird-umpire decision delays do no help, eiher). Furhermore, he rule exacerbaes he endency of wickes falling more ofen jus prior o sumps, as ligh deerioraes and baers ofen become overly cauious. To es his asserion, I looked a over raes in he 97 Tess played beween Ocober 2005 and February 2008, and seleced only hose Tess wih no rain or bad ligh 12 Oher rule changes have played a more suble role, such as alering he new-ball rule from 85 o 80 overs. 20
delays, nor an innings change on he firs day (in heory, 90 overs should be bowled on hese days according o he rules). A oal of 39 Tess me his crieria, bu 90 overs were bowled on jus 20 (virually half) of hese (firs day) occasions, even wih he exra 30 minues, and on only one occasion was more overs (91 on ha occasion) bowled wihin six hours. The average overs bowled on he firs day in he oher 19 Tess was 86.4, providing some evidence ha he 15-over rule is far less effecive han would be oher possible rules o preven eams from slowing he game down deliberaely. Such rules could alernaively ake he form of some financial penaly, he likes of which have been used previously in ODIs, hough he ICC has saed repeaedly ha hey are loahe o inroducing such penalies. 13 In essence, perhaps 14 overs (84 per day) would be a more realisic minimum arge over rae. This is especially he case when one considers he viewer, wheher a he ground or a home, who has been waching cricke all day and has really had enough, ye hey feel incapable of ceasing o wach unil sumps is called officially. 14 6. Conclusion This sudy has sough o provide an insigh ino changing rends in Tes Cricke, looking from numerous angles. These angles include he raionalisaion ha occurred following he game s mos umuluous period (he World Series War ), as well as growing compeiion beween spors, he proliferaion of differen formas of he same 13 The overall average overs bowled for he whole sample of 39 Tess was 88.3. When a wicke fell during he final over, resuling in he immediae conclusion of play on ha day, he number of overs was rounded up o he nex ineger in calculaing hese averages, since in heory he over would have been compleed in he absence of he fall of ha wicke. 14 A second (and admiedly less radical) rule change I would recommend is o award sixes only for shos ha clear he acual fence, raher han merely he boundary rope. This would circumven he diminishing value of sixes, since hey are now much easier o score (if Adam Gilchris had o clear he fence, would his career ally of 100 sixes sill be greaer han Vivian Richards ally of 84)? In any even, since boundary ropes were supposedly made sandard purely for reasons of player safey (no jus o increase run raes), hen here should be no reason for cricke adminisraors o disagree. 21
spor, and he effec ha all his has had on he original form of he game of cricke, boh in erms of scheduling and playing syle. One of he major already-esablished observaions ha his sudy reinforces is he reforms made (rule changes and oherwise) o Tes Cricke o reduce he incidence of draws which are frequenly associaed wih unaracive cricke in order o broaden is appeal o spors consumers. This analysis leads o one playing he role of devil s advocae in arguing ha he frequency of Tes Mach draws has fallen oo far in he las 15 years, ironically aking a fair degree of ineres ou of Tes Cricke. The basis for his argumen is ha many Tess ha finish subsanially early are oo one-sided and ha he opion of one eam playing for a draw during he fifh and final day can mainain ineres in he Tes for longer. I is no being suggesed ha he ideal Tes Cricke mach is one in which a draw is he resul, bu mos Tess ha finish wih a resul in he final session of he fifh day are highly absorbing Tes maches, and under he curren saus quo, here are no enough Tess going ino he fifh day. As an example, my all-ime favourie memory of Tes Cricke from an Ausralian perspecive is acually jus managing o hold ou for a draw agains New Zealand a home, December 1987 in Melbourne. Given he recen developmen of compeiive forces o he game s orhodoxy arising from he Indian Champions League (ICL) consorium, and he official response by he Cricke Conrol Board of India of he formaion of he Indian Premier League (IPL), he issues of he relaive decline of Tess are criical o he ICC. This is especially he case as Tes Cricke will find i coninually more difficul o figh for survival in he increasingly crowded mach calendar agains shorer forms of he game. 22
Table 1: Number of ICC-Sancioned Cricke Maches by Type, 1978-2007 (No Couning Cancelled or Abandoned Maches) Calendar Year Tess ODIs Tweny20 1978 27 10 1979 28 26 1980 25 21 1981 23 28 1982 28 33 1983 30 66 1984 34 51 1985 26 65 1986 30 62 1987 25 74 1988 24 61 1989 21 55 1990 26 61 1991 21 39 1992 26 89 1993 36 82 1994 38 98 1995 40 60 1996 28 127 1997 44 115 1998 45 108 1999 43 154 2000 46 131 2001 55 120 2002 54 145 2003 44 147 2004 51 128 2005 49 107 3 2006 46 160 9 2007 31 191 38 Source: hp://www.cricinfo.com/ 23
Table 2: OLS Regression Resuls Equaion (2) Equaion (3) Equaion (4) Equaion (5) Equaion (6) α -243.31 (538.20) 201.38* (80.65) 31.08 (42.22) 253.86* (35.12) 255.18* (32.11) β 32.17 (133.04) -19.95* (7.8814) -16.36* (5.3578) -22.01* (7.2817) γ -5.0187 (12.27) δ 7.1962 (8.1880) -4.3224* (1.5077) 1.1980* (0.3881) θ -0.1527 (0.0654) κ 5.8268 (16.84) τ 0.3642 (0.5028) -5.0568* (1.1059) -4.6500* (1.0480) -17.30* (4.5131) F 7.45* 12.83* 16.13* 19.32* 24.37* 2 R 0.6083 0.5968 0.5444 0.5887 0.6435 2 R 0.5266 0.5503 0.5106 0.5582 0.6171 ~ σ 8.22 8.01 8.36 7.94 7.39 SC 1.80 2.35 0.43 1.93 0.48 NO 0.04 0.20 2.98 0.83 0.48 HE 1.29 2.21 0.17 0.57 2.62 FF 1.99 1.07 0.10 1.30 0.04 AIC 7.23 7.12 7.18 7.08 6.93 BIC 7.51 7.31 7.32 7.22 7.07 *Significan a he five per cen level. Figures in parenheses are sandard errors. Table 3: Correlaion Marix of Time-Series Variables TD RR AV SR BM WM ODIRR TD 1.0000-0.5065 0.1917 0.7330 0.3063-0.7065-0.5861 RR -0.5065 1.0000 0.5531-0.4047-0.3284 0.2673 0.6974 AV 0.1917 0.5531 1.0000 0.5366 0.3063-0.4304 0.2234 SR 0.7330-0.4047 0.5366 1.0000 0.6610-0.7498-0.4504 BM 0.3063-0.3284 0.3063 0.6610 1.0000-0.0018-0.2788 WM -0.7065 0.2673-0.4304-0.7498-0.0018 1.0000 0.3781 ODIRR -0.5861 0.6974 0.2234-0.4504-0.2788 0.3781 1.0000 24
Figure 1: All Maches Played by Type (100% Sacked) 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 Tess ODIs T20 Figure 2: Percenage of All Tes Maches Played Finishing in a Draw (Thin Line) and HP Trend (Bold Line) 70 60 50 40 30 20 10 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 25
Figure 3: Run Raes Per Over in All Tes (Bold Line, LHS) and ODI (Thin Line, RHS) Maches by Calendar Year, 1981-2007 3.4 5.2 3.3 5.0 3.2 3.1 4.8 3.0 4.6 2.9 4.4 2.8 2.7 4.2 2.6 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 4.0 Figure 4: Baing Averages in All Tes (Bold Line, LHS) and ODI (Thin Line, RHS) Maches by Calendar Year, 1981-2007 40 32 38 31 36 30 34 29 32 28 30 27 28 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 26 26
Figure 5: Srike Raes in All Tes (Bold Line, LHS) and ODI (Thin Line, RHS) Maches by Calendar Year, 1981-2007 82 42 78 41 74 40 70 39 66 38 62 37 58 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 36 Figure 6: Average Balls Bowled in All Tes (Bold Line, LHS) and ODI (Thin Line, RHS) Maches by Calendar Year, 1981-2007 2250 580 2200 570 2150 560 2100 550 2050 540 2000 530 1950 520 1900 510 1850 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 500 27
Figure 7: Average Wickes Fallen in All Tes (Bold Line, LHS) and ODI (Thin Line, RHS) Maches by Calendar Year, 1981-2007 33 15.5 32 15.0 31 14.5 30 14.0 29 13.5 28 13.0 27 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 12.5 Figure 8: Percenage of All Tes Maches Played Finishing Inside x Days 60 50 40 30 20 10 0 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2 Days 3 Days 4 Days 28
References Akaike, H. (1973), Informaion Theory and an Exension of he Maximum Likelihood Principle, in 2nd Inernaional Symposium on Informaion Theory, eds Perov, B. N. and Csaki, F., Akadémiai Kiadó, Budapes. Akaike, H. (1977), On Enropy Maximizaion Principle, in Applicaions of Saisics, ed. Krishniah, P. R., Norh Holland, Amserdam. Allsop, P. E. and Clarke, S. R. (2004) Raing Teams and Analysing Oucomes in One-Day and Tes Cricke, Journal of he Royal Saisical Sociey (Series A), 167 (4), 657-667. Bhaacharya, M. and Smyh, R. (2003), The Game is No he Same: The Demand for Tes Mach Cricke in Ausralia, Ausralian Economic Papers, 42 (1), 77-90. Blackham, J. and Chapman, B. J. (2004), The Value of Don Bradman: Addiional Revenue in Ausralian Ashes Tess, Economics Papers, 23 (4), 369-385. Breusch, T. S. and Godfrey, L. G. (1981), A Review of Recen Work on Tesing for Auocorrelaion in Dynamic Simulaneous Models, in Currie, D. A., Nobay, A. R. and Peel, D. A. (eds.), Macroeconomic Analysis, Croom Helm, London, 63-105. Breusch, T. S. and Pagan, A. R. (1979), A Simple Tes for Heeroscedasiciy and Random Coefficien Variaion, Economerica, 47 (5), 1287 1294 Brooks, R. D., Faff, R. W. and Sokulsky, D. (2002) An Ordered Response Model of Tes Cricke Performance, Applied Economics, 34 (18), 2353-2365. Chow, G. C. (1960), "Tess of Equaliy beween Ses of Coefficiens in Two Linear Regressions", Economerica, 28 (3), 591-605. Duckworh, F. C. and Lewis, A. J. (1998) A Fair Mehod for Reseing he Targe in Inerruped One-Day Cricke Maches, Journal of he Operaional Research Sociey, 49 (3), 220-227. Godfrey, L. G. (1978), Tesing agains General Auoregressive and Moving Average Error Models When Regressors Include Lagged Dependen Variables, Economerica, 46 (6), 1293-1301. Hodrick, R. J. and Presco, E. C. (1997), Poswar U.S. Business Cycles: An Empirical Invesigaion, Journal of Money, Credi and Banking, 29 (1), 1-16. Hyndes, M. and Smih, I. (1994), The Demand for Tes Mach Cricke, Applied Economics Leers, 1 (7), 103-106. 29
Jarque, C. M. and Bera, A. K. (1980), Efficien Tes for Normaliy, Heeroscedasiciy and Serial Independence of Regression Residuals, Economics Leers, 6 (3), 255-259. Presco, E. C. (1986), Theory Ahead of Business Cycle Measuremen, Federal Reserve Bank of Minneapolis, Quarerly Review, 10, 9-22. Preson, I. (2006), The Economics of Cricke, in Handbook on he Economics of Spor, eds Andreff, W. and Szymanski, S., Edward Elgar, Chelenham and Norhampon, pp. 585-593. Ramsey, J. B. (1969), Tess for Specificaion Errors in Classical Leas-Squares Regression Analysis, Journal of he Royal Saisical Sociey (Series B), 31 (2), 350-371. Ringrose, T. J. (2006), Neural Umpires and Leg Before Wicke Decisions in Tes Cricke, Journal of he Royal Saisical Sociey (Series A), 169 (4), 903-911. Roenberg, S. (1956), The Baseball Players Labor Marke, Journal of Poliical Economy, 64 (3), 242-258. Schwarz, G. (1978), Esimaing he Dimension of a Model, Annals of Saisics, 6 (2), 461-464. 30