EXPLAINING INTERNATIONAL SOCCER RANKINGS. Peter Macmillan and Ian Smith

Transcription

1 EXPLAINING INTERNATIONAL SOCCER RANKINGS Peter Macmllan and Ian Smth School of Economcs and Fnance Unversty of St Andrews St Andrews Ffe, KY16 9AL Unted Kngdom Tel: (Smth), (Macmllan) Fax: e-mal: s@st-and.ac.uk, pdm1@st-and.ac.uk 1

2 Abstract Exstng research on the determnants of FIFA s nternatonal soccer rankngs suffers from serous statstcal problems, partcularly sample selecton bas and non normal errors. We correct for ths by extendng the data set by an addtonal 100 countres. Furthermore, we fnd mportant roles for new varables n the form of the sze of populaton and a long hstory of nternatonal soccer n explanng world football rankngs. We also nvestgate the determnants of an alternatve rankng measure to that constructed by FIFA. JEL classfcaton codes: F0, L83, H50, Z10. Keywords: nternatonal football rankngs, hstory.

3 I. Introducton There can be lttle doubt that the team sport of soccer boasts both the greatest number of partcpants and spectators worldwde. But despte the evdent global popularty of soccer and ts sgnfcance as a lesure pursut and busness, studes of natonal team performance are scarce. There are only two emprcal contrbutons of whch we are aware. Frst, Torgler (004) recently nvestgated the factors that affected the outcomes of matches n the FIFA World Cup 00 hosted by Japan and South Korea. 1 Second, Hoffman, Lee and Ramasamy (00a) (henceforth HLR) estmated the determnants of the varaton n FIFA soccer rankngs dated January 001 for a cross-secton of 76 countres. These rankngs receve consderable publc attenton prmarly for reasons of natonal prestge and esteem, and also as a vsble ndcator of relatve performance and progress. As they measure the average level of success over a number of years, the FIFA rankngs are not ntended for use as a devce for forecastng the results of ether ndvdual matches or major tournaments. Indeed, unless the dfference n rankngs s suffcently large, they would not be expected to be partcularly useful for predctng the results of ndvdual games gven the sgnfcant role n outcomes played by essentally random factors such as player njures, motvaton, ftness and team sprt. The focus of our research, therefore, s on what determnes longer term nternatonal soccer strength, as measured by the FIFA rankng scores, rather than the predctve accuracy of those rankngs n nternatonal competton. The same objectve of explanng the varaton n nternatonal soccer rankngs was adopted n the study conducted by HLR. However, the method they use to select the sample of 76 countres s non-random. Snce an overwhelmng majorty of ther chosen countres are located above the medan of the rankng dstrbuton, the authors 3

4 unntentonally sample on the dependent varable. As a result, ther estmates exhbt both sample selecton bas and also non-normal errors. Our contrbuton remedes these problems by augmentng ther sample wth data on 100 addtonal countres. We also nclude new varables to capture the mportance of populaton and country-specfc football hstory for nternatonal performance. Furthermore, gven doubts about the utlty of FIFA s rankng algorthm, the robustness of the results s evaluated usng an alternatve rankng system. II. The Sample, Varables and Data The 76 countres chosen by HLR are the medal wnners at the Sydney 000 Olympc games used n a companon study of Olympc success (Hoffman et al, 00b). Ths smple samplng devce was ntended to avod bas. However, HLR (pp.56-57) earler state that: These studes have found that the number of medals won by a country at the Olympc Games s partally explaned by factors such as ts per-capta GNP, populaton sze as well as certan geographcal, poltcal and cultural nfluences. It would seem reasonable to suspect that varables explanng performance over a range of sports should partally explan the success of countres n nternatonal football. In other words, HLR expect that both Olympc medal wnnng and nternatonal soccer success are correlated wth the same or smlar set of explanatory varables. If ths s so, then confnng the sample of countres used to nvestgate football performance to Olympc wnners s unlkely to generate a random selecton. Rather, the lkelhood s that a dsproportonate number of countres wll be chosen from the upper end of the 4

5 nternatonal soccer rankng dstrbuton. The descrptve statstcs lsted n the upper part of Table 1 document ths outcome. Of the 76 countres selected by HLR, 66 are above the medan FIFA rankng of 41 ponts and only 10 are below. < Table 1 near here > As the selecton process s related to the value of the dependent varable (FIFA rankng ponts, denoted Y ), t can ntroduce correlaton between the error term and the regressors, leadng to bas and nconsstency n the OLS estmators. Ths wll arse n so far as there are omtted varables that are correlated wth the regressors and whch jontly determne Olympc success and nternatonal football performance. The magntude of the bas s, of course, an emprcal matter. To address the sample selecton bas ssue, we collected data on 100 excluded countres. Ths omts 7 teams n the full FIFA lst for whch GNP per capta data were unavalable for 001 or a nearby year n the World Bank database. Typcally, these non-reportng countres are small sland states (such as Montserrat and Angulla) or poltcal outlers (such as Iraq, Lbya and North Korea). Snce ther rankng s generally below the FIFA medan, ths stll mposes some resdual selecton on the value of the dependent varable. Table 1 ndcates that the extended sample of 176 countres has a rankng ponts mean of 405.7, margnally hgher than that for the 03 FIFA teams of The z statstc for the null hypothess that the mean µ of the extended sample s drawn from a populaton wth µ = s 1.36, ndcatng non-rejecton at conventonal levels of statstcal sgnfcance. However, ths concluson does not hold for the 76 country sample of HLR where the z statstc s 6.87, easly rejectng the null hypothess of an unbased sample. 5

6 The algorthm adopted by FIFA for calculatng ts world rankng ponts by country has been crtcsed for generatng apparently counter-ntutve orderngs. 3 For example, just pror to the 1998 World Cup, FIFA ranked Egypt n equal 17 th place wth the same ponts as France, despte the fact that the French team was clearly superor n the eyes of most experts at the tme. One possble explanaton for such anomales s the fact that the FIFA rankngs nclude the results of frendly matches. Ths s a cause for concern snce these games lack the performance ncentves of compettve matches. Ther outcomes, therefore, are more lkely to be msleadng as a measure of footballng strength. Indeed, Torgler (004) reports that FIFA world rankng dd not play an mportant role n predctng the outcome of matches n the 00 World Cup. But snce he dd not test alternatve rankng measures, t s not possble to assert a pror whether ths reflects a falure of the rankng system tself, a problem wth hs equaton specfcaton or smply the vagares of one-off compettve matches at the hghest level. Alternatve unoffcal ndces to FIFA s measure are calculated by enthusasts and publshed on the world wde web. One of the most carefully constructed s the Elephant rankng whch s based on results n the World Cup and contnental champonshps, ncludng qualfers, and specfcally excludes frendly games. 4 In what follows, results are presented usng both FIFA s rankng ponts and the Elephant alternatve as the dependent varable. Note that all of the regressons are estmated usng (FIFA or Elephant) calculated rankng ponts rather than the actual ranks themselves as the dependent varable. Ths s because the use of pure ranks would result n the loss of nformaton regardng the dstance between countres n terms of relatve strength. Notwthstandng some sgnfcant dscrepances wth respect to the poston of ndvdual countres, the FIFA and Elephant measures are hghly correlated; r = 0.91 for the 76 countres n HLR s sample. 5 6

7 Gven the paucty of readly avalable soccer-specfc nputs by country such as expendture on football or numbers of players or teams or leagues, HLR s study was constraned to use explanatory varables unrelated to football. There are four explanatory varables n ther preferred equaton. The frst s gross natonal product per capta, GNP, collected from the World Bank database. The varable s a proxy for the mpact of prvate and publc football fundng. Hgher levels of GNP per capta are antcpated to have a postve but decreasng effect on nternatonal football success across countres below a threshold ncome level, above whch the relatonshp becomes negatve due to the relatvely low ncome elastcty of demand for partcpaton n football. A quadratc specfcaton n GNP per capta s employed to capture ths postulated nverted U-shaped relatonshp wth rankng ponts. 6 Ths s consstent wth the approach of Johnson and Al (000, 00) who adopted the same non-lnear specfcaton n per capta ncome for ther Olympc medal count equaton. 7 A temperature varable ( 14) TEMP s ntroduced to capture the effect of clmate on football performance. The authors argue that temperate countres wth an average temperature around 14 C are conducve to outdoor actvtes and ths promotes sportng success whereas devatons n ether drecton are detrmental. The clmate varable s measured smply usng the squared devaton of average annual temperatures from 14 C for the captal cty of each country. Notng the footballng success of some Luso-Hspanc cultures, HLR specfy a dummy varable, LATIN, set to one for all Spansh and Portuguese speakng countres. Ths s desgned to capture the specal cultural factors that promote football n such natons, though the authors are unable to dentfy precsely what such elements mght be. In the preferred specfcaton, LATIN s nteracted wth POP, country s share of the world populaton, reflectng the fact that the margnal effect of a larger populaton 7

8 on football performance depends on the cultural predsposton to partcpate n the sport. Nether LATIN nor POP were statstcally sgnfcant when ncluded ndvdually as explanatory varables. Fnally, for countres that have acted as a host naton for the World Cup (fnals) competton, a HOST dummy varable s set to one. In studes of nternatonal tournament outcomes, host status s typcally consdered to confer enormous benefts arsng from the strength of spectator support, famlarty wth the local condtons, and the ntensty of publc expectatons. Torgler (004), for example, reports a strong favorable mpact of host status on the relatve success of Japan and South Korea n the 00 FIFA World Cup. 8 In the context of the current study, however, snce nterest s not n the outcome of a partcular event or tournament, the host varable s nterpreted somewhat dfferently by HLR. The condton of havng hosted the World Cup s taken to measure cultural affnty towards soccer because hostng typcally reflects a strong footballng tradton and wdespread publc support for the event. Naturally, cultural affnty s expected to have a postve nfluence on nternatonal performance. However, nterpretng hostng status as a proxy for football tradton s not altogether satsfactory. The set of hosts (pror to 001) ncludes, for example, the Unted States whch has a lower cultural affnty wth soccer than many countres that have never acted as World Cup hosts such as Russa, the Netherlands, Turkey, Hungary and the Czech Republc. More generally, the HOST dummy regressor may be jontly determned wth nternatonal soccer performance. In other words, the choce of host tself could be partly endogenous to a country s football world rankng, resultng n based and nconsstent estmates. Although the HOST varable relates to tournaments pror to the FIFA world rankngs for 001 that defne the dependent varable, t cannot be 8

9 consdered ndependent of these rankngs due to the hgh degree of seral correlaton n the rankngs over tme. Gven the potental endogenety of HOST, the natural approach s to search for vald nstruments, that s, exogenous sources of varaton n hostng that are unrelated to (omtted) factors that affect nternatonal football performance. As t s dffcult to thnk of any such canddate nstruments, an alternatve strategy s ether to re-estmate the equaton wth the host varable omtted or to fnd a better varable to model football tradton. We adopt the latter approach. Table 1 provdes descrptve statstcs for the varables used n the regresson analyss for the extended data set of 176 countres. III. Regresson Results HLR s results are reported n column (1) of Table. Note that ths and subsequent equatons are estmated by Ordnary Least Squares. Column () replcates the results usng the alternatve Elephant rankng ndex ELE. Gven that the scale of ths rankng measure dffers from FIFA s, the coeffcent estmates are not drectly comparable across the two equatons. 9 However, n terms of statstcal sgnfcance, t s clear that that only the coeffcent of the LATIN POP varable deterorates somewhat whle the clmatc and GNP varables have larger t-ratos. In other words, HLR s results do not appear to be too senstve to the choce of rankng measure, though ther specfcaton explans the varaton n the Elephant ponts better than that n FIFA s scale. Wth respect to the dagnostc statstcs, the null hypothess of the normal dstrbuton of the error terms s easly rejected for the HLR specfcaton reported n column (1). The worryng mplcaton of rejectng normalty s the possble nvaldty of statstcal nferences for ths equaton. However, the dagnostc tests for columns () 9

10 and (3) ndcate that substtutng the Elephant rank ndex or expandng the sample sze both amelorate the non-normal error problem evdent n the HLR study. < Table near here > Column (3) re-estmates HLR s equaton, ncludng data for 100 addtonal natons, gvng a total sample sze of 176 country observatons. Compared to column (1) the parameter estmates for GNP are essentally unchanged but those for the other explanatory varables dffer substantally. Ths provdes evdence for the presence of serous sample selecton bas n the orgnal estmates. The effect of the temperature varable s more than twce as powerful, the estmated coeffcent of the LATIN POP nteracton dummy s consderably smaller whle that of HOST s more than 50% larger n magntude. Populaton HLR fal to fnd any sgnfcant ndependent mpact of populaton sze on nternatonal football performance and so only specfy the varable as an nteracton term wth the LATIN dummy. The authors attrbute ths result to the fact that some of the world s most hghly populated countres such as Chna, Inda and Indonesa have enjoyed only very lmted success n nternatonal soccer. Snce the same pattern s also true wth respect to Olympc competton, Johnson and Al (000, 00) proceed by employng a quadratc specfcaton n populaton, usng total populaton as a proxy for the number of people n the compettve age range, and fnd a negatve coeffcent on the squared term. Ths mples a dmnshng margnal contrbuton of an addtonal person to sportng success as populaton ncreases. 10

11 Our estmated equaton, ncludng a quadratc n populaton ( POP and POP, measured n mllons), s reported n column (4) and shows that both varables are statstcally sgnfcant at the 5% level. 10 Compared to the results n column (3), the man mpact on the estmates s a modest reducton n the magntude and sgnfcance of the LATIN POP and HOST varables. Furthermore, n an unreported regresson, t was found that excludng the hghly populated countres of Inda and Chna from the sample apprecably ncreases the sze of the estmated populaton coeffcents but wth very lttle effect on other parameters. Football Hstory The unavalablty of football-specfc nput varables s a clear weakness n an equaton explanng nternatonal soccer outcomes. One factor overlooked by HLR s the mportance of football hstory. Gven a partcular level of GNP per capta, populaton, culture and clmate, nternatonal success would be expected to be ncreasng n the length of tme that a team has partcpated n nternatonal competton. Ths can be justfed theoretcally n terms of the experence benefts of learnng by dong. It takes tme to buld up a footballng nfrastructure such as domestc leagues and coachng schools. Many of the Afrcan natons, for example, entered nternatonal competton comparatvely late, begnnng n the 1950s. It s only n the past 15 years that countres such as Ngera, Senegal and Cameroon have started to perform well on the world stage and challenge the tradtonal European and Latn Amercan football elte. To measure ths hstory varable, we use the year of the frst nternatonal football match by country and label t HISTORY. 11 Of course, a long hstory of play does not guarantee success. The Phlppnes were contestng the Far Eastern games as long ago as 1913 but are ranked by FIFA n 001 just above the lowest decle of 03 countres n 11

12 179 th place. Clearly tme s only one dmenson of the development of football n a country, but t has the emprcal advantage of ease of measurement and ready avalablty. A negatve sgn for the hstory varable s antcpated snce a team wth a more recent year for ts frst nternatonal match s expected to have a lower rankng ceters parbus. A specal case s that of the former Sovet republcs. 1 Although these republcs had natonal teams pror to the Sovet era, these were dssolved after the Russan revoluton n the early 190s and replaced by a sngle USSR team for purposes of nternatonal competton. The comparatvely early start for these republcs then s somewhat offset by later poltcal developments. Ths handcap s modelled by settng a dummy varable, REPUBLICS, to one for these cases. A negatve mpact of the nterrupted partcpaton of ther natonal teams at the nternatonal level on football rankngs s expected. The results are reported n column (5). The coeffcent estmates of the two new varables dsplay the expected sgns and are statstcally hghly sgnfcant. The penalty for startng late n nternatonal football s estmated to be 3.4 ponts per year on the FIFA rankng scale all else equal. Note that the goodness of ft, controllng for degrees of freedom, has ncreased substantally from an adjusted R of n the orgnal HLR equaton to when ncludng the hstory and populaton varables for the full sample of 176 countres. The coeffcent of HOST s no longer sgnfcant wth a t- rato of 0.7. Snce the dummy for World Cup hosts s only a weak proxy for cultural affnty, ts effect loses statstcal sgnfcance when the hstory varable, arguably a better measure of football tradton, s ncluded n the specfcaton. Column (6) presents the results of re-estmatng the equaton usng Elephant rankng ponts as the dependent varable. Whle the hstory varable and Sovet Republcs dummy are robust to ths change the quadratc specfcaton n populaton 1

13 loses statstcal sgnfcance. However, ths outcome s senstve to the ncluson of the outlers of Inda and Chna. If these countres are excluded, the populaton varables are sgnfcant at the 5% level. Actual and Ftted Values Despte the addtonal data and varables, the estmates usng the FIFA scores as the regressand n column (5) explan just over half of the cross country varaton n nternatonal soccer rankngs. A comparson of actual and ftted values can provde a sense of what remans unexplaned. Usng the equaton resduals, Table 3 lsts those 30 countres wth the greatest percentage underpredcton of the actual FIFA rankng scores. It s notable that Afrcan countres are over-represented, consttutng 19 out of the 30 countres wth the largest postve resduals relatve to the actual values of the dependent varable. 13 For example, Cameroon, one of the strongest emergng Afrcan teams had a FIFA ponts score of 585 n January 001 but the model predcts only ponts. < Table 3 near here > By contrast only 5 of the 30 largest overpredctons lsted n Table 4 are for Afrcan countres. Instead t s prmarly countres ranked among the lowest FIFA scores, partcularly Asan and Pacfc natons, that domnate the more substantal negatve resduals. Ths pattern reflects the dffculty, dervng from lack of sutable cross-country data, of modellng the comparatvely low level of resources nvested n producng soccer players n these naton states. It s for these countres that the absence of suffcent football-specfc explanatory varables s partcularly problematc. 13

14 < Table 4 near here > IV. Conclusons Ths paper nvestgates the determnants of the relatve strength of natonal soccer teams as measured by rankngs of long term performance. It demonstrates the exstence of selecton bas and non-normal errors n the earler study by Hoffman, Lee and Ramasamy (00a), problems that arse from ther sample selecton procedure. Our contrbuton extends ther sample by an addtonal 100 countres, adds new varables to capture the effect of hstory and populaton, and checks the robustness of the results relatve to an alternatve non-fifa natonal football team rankng scale. Inspecton of equaton resduals suggests that addtonal soccer related varables are requred both to explan the underpredcted strength n nternatonal competton of many Afrcan teams and the weakness of some Asan and Pacfc countres. Future research could usefully extend our fndngs through the collecton of data on more cross country football related varables that are not readly avalable n standard sources, such as the number of professonal players or teams or leagues. Such nputs wll presumably account for much of the unexplaned varaton n long run nternatonal soccer performance. References Bernard, A.B. and Busse, M.R. (004) Who wns the Olympc games: economc resources and medal totals, Revew of Economcs and Statstcs 86(1):

15 Hoffman, R., Lee, C.G. and Ramasamy, B. (00a) The Socoeconomc Determnants of Internatonal Soccer Performance, Journal of Appled Economcs 5(): Hoffman, R., Lee, C.G. and Ramasamy, B. (00b) Publc polcy and Olympc success, Appled Economcs Letters 9: Jarque, C.M. and Bera, A.K. (1980) Effcent tests for normalty, homoscedastcty and seral ndependence of regresson resduals, Economcs Letters 6: Johnson, D.K.N. and Al, A. (000) Comng to play or comng to wn: partcpaton and success at the Olympc games, Wellesley College Department of Economcs Workng Paper , September. Johnson, D.K.N. and Al, A. (00) A tale of two seasons: partcpaton and medal counts at the summer and wnter Olympc games, Wellesley College Department of Economcs Workng Paper 00-0, January. Torgler, B., (004) The Economcs of the Football FIFA World Cup, Kyklos 57(): Whte, H. (1980) A heteroskedastcty-consstent covarance matrx estmator and a drect test for heteroskedastcty, Econometrca 48:

16 Table 1. Descrptve statstcs Mean Medan Maxmum Mnmum Standard Devaton FIFA rankng ponts, Y FIFA 03 countres HLR 76 countres HLR countres ELE GNP ( 14) TEMP HOST LATIN POP POP HISTORY REPUBLICS Unless otherwse ndcated, the summary statstcs refer to the extended sample of 176 countres. The varable labels are as defned n the text. 16

17 Table. Regresson Results Dependent varable Y ELE Y Y Y ELE (1) () (3) (4) (5) (6) Constant (19.3) (33.) (3.0) (18.) (7.) (8.9) GNP (.4) (3.3) (.6) (3.0) (.1) (.0) GNP ( 14) (1.7) (.3) (1.9) (.3) (.3) (.4) TEMP (.0) (3.9) (6.5) (6.6) (4.6) (4.33) HOST (1.8) (1.7) (.3) (1.7) (0.7) (1.6) LATIN POP (.) (1.3) (.) (1.7) (1.6) (1.0) POP (mllons) (.5) (1.7) (0.5) POP (.4) (1.9) (0.7) HISTORY (6.8) (8.0) REPUBLICS (.5) (3.0) Sample sze χ H (p-value) (0.9) (0.3) (0.4) (0.7) (0.6) (0.4) χ N (p-value) (0.0) (1.0) (0.3) (0.3) (0.5) (0.3) R Notes: () χ H and χ N are the Ch-squared statstcs for Whte s (1980) test for heteroskedastcty (no cross terms) and the Jarque-Bera (1980) test for non-normal errors respectvely; () R s the R statstc adjusted for degrees of freedom; () all equatons are estmated by OLS. 5 17

18 Table 3: The 30 countres wth the largest underpredcted values Country Actual FIFA ponts Predcted ponts Underpredcton % Burkna Faso Trndad and Tobago South Afrca Angola Ivory Coast Thaland Cameroon Gunea Mal Togo Ghana Lbera Saud Araba Ngera Turkmenstan Namba Oman Zamba DR Congo Tajkstan Barbados Congo Kuwat Tunsa Jamaca Morocco Gabon Paraguay Senegal St Luca

19 Table 4: The 30 countres wth the largest overpredcted values Country Actual FIFA ponts Predcted ponts Overpredcton % Surnam Samoa Gunea-Bssau Laos Djbout Camboda Yemen Nepal Belze Nger Guyana Vanuatu Sao Tome Central Afrcan Republc Equatoral Gunea Tonga Bahamas Macao Palestne Seychelles Papua NG Kyrgyzstan Brune Phlppnes Ncaragua US Vrgn s Pakstan Mongola Puerto Rco Bhutan

20 Endnotes 1 FIFA s the acronym of the Fédératon Internatonale de Football Assocaton that governs world football. We are grateful to Hoffman, Lee and Ramasamy for kndly provdng us wth a copy of ther data. 3 The algorthm takes account of goals scored n each match, whether a team s home or away, mportance of the game, venue and regonal strength over the prevous eght years on a monthly bass. 4 Avalable together wth detals of the algorthm at (vewed September 003). 5 The correlaton n terms of pure rankngs s smaller at There are also some very large ndvdual dscrepances. For example, Senegal s ranked 83 rd n the world by FIFA but 18 th by the Elephant rankngs n January 001. Eghteen months later, Senegal reached the quarter fnals of the World Cup. 6 Followng the suggeston of a referee, as an alternatve to GNP, we also expermented wth the Unted Natons Human Development Index whch s avalable for 17 of the countres n the sample (the exceptons are Puerto Rco, US Vrgn Islands, Lbera and Taht). In prncple, as an overall measure of development, ths ndex may consttute a superor proxy for the ablty of a naton to nvest resources n soccer. However, ths varable faled to acheve statstcal sgnfcance n our regressons whether specfed n lnear or quadratc forms. We also tred ncludng a dummy varable for less developed countres, but agan ths was not sgnfcant at conventonal levels. 7 By contrast, n ther study of Olympc medal outcomes, Bernard and Busse (004) prefer to use the log of GDP per capta n addton to the log of populaton sze. 0

21 8 Johnson and Al (000, 00) also report strong hostng effects for home natons on Olympc success, controllng for the economc, geographc and poltcal attrbutes of partcpants. 9 The range of the Elephant ponts scale s compared to for the FIFA scale. 10 The estmated coeffcent of POP s negatve as n Johnson and Al (000, 00). For the orgnal non-random HLR sample wth 76 countres, the quadratc specfcaton n populaton s only statstcally sgnfcant f the hghly populous Chna and Inda are omtted. However, the problems of non-normal errors and sample selecton bas stll reman. 11 The date of frst nternatonal match data are collected from The Rec. Sport. Soccer Statstcs Foundaton avalable at (vewed September 003). A referee suggested that the age of the domestc league may be a better measure of tradton effects than the date of the frst nternatonal game. Unfortunately, data on the length of tme that natonal leagues have been n operaton are not readly accessble for many countres. Instead, we collected data on a closely related varable, namely the date of foundaton of the natonal football assocaton by country, avalable at FIFA s web ste, Ths s expected to be hghly correlated wth tmng of the formal organzaton of a football league n most cases. The foundaton year varable performed well n the regressons, had the expected negatve sgn but wth slghtly lower sgnfcance than the date of the frst nternatonal match varable reported n the text. Although other parameters were largely unaffected, the goodness of ft was a few percentage ponts lower n the case of equatons usng the foundaton varable. Full results are avalable from the authors on request. 1

22 1 The former Sovet republcs are Armena, Azerbajan, Belarus, Estona, Georga, Kazakhstan, Kyrgyzstan, Latva, Lthuana, Moldova, Tajkstan, Turkmenstan, Ukrane and Uzbekstan. Russa s excluded from the dummy varable on the grounds that the contnuty between the natonal teams of the USSR and Russa was much greater than that for the smaller republcs. 13 Notce that a postve (negatve) resdual n whch the actual value exceeds (s less than) the ftted value consttutes an underpredcton (overpredcton).