Who is the Best Formula 1 Driver? An Econometric Analysis

Transcription

1 Université de Fribourg / Universität Freiburg Fkultät der Wirtschfts und Sozilwissenschften Seminr für Finnzwissenschft Who is the Best Formul 1 Driver? An Econometric Anlysis Mster Thesis under the supervision of Prof. Dr. Reiner EICHENBERGER (1 st supervisor) nd Prof. Dr. Mrtin WALLMEIER (2 nd supervisor) written by Dvid STADELMANN BA in Economics, stud. rer. nt. June th Semester Address: Phone: +41 (076) Av. Beuregrd 9 e-mil: dvid.stdelmnn@unifr.ch CH-1700 Fribourg

2 Who Is The Best Formul 1 Driver? An Econometric Anlysis i Acknowledgements I m prticulrly grteful to Prof. Dr. Reiner EICHENBERGER for detiled nd vluble comments nd suggestions on this Mster thesis. He lso proposed the topic itself s well s number of evlution ides nd ws lwys vilble for specil reserch questions. Prof. Dr. Mrtin WALLMEIER ws kindly prepred to be the second supervisor. Furthermore, I m lso indebted to CREMA (Center for Reserch in Economics, Mngement nd the Arts) for finncil support. During the Coffee, Biscuits nd Economics Seminr orgnized by the ssistnts in economics of the University of Fribourg preliminry version of this pper ws discussed. For mentioning possible solutions to problems nd referring to specil issues I m obliged to ll the prticipnts. Prticulrly, I would like to stress the constructive inputs received by Michel FUNK, Lorenz KÜNG, Mrk SCHELKER nd Florin ZAINHOFER. I decided to write this Mster thesis in English in order to exercise my writing skills. Shun SELVARAJAH nd Kevin MUSA corrected number of spelling nd grmmr mistkes. All remining errors nd shortcomings re my own responsibility.

3 Who Is The Best Formul 1 Driver? An Econometric Anlysis ii Tble of contents 1 Introduction Literture survey Sports economics nd the economics of superstrs Literture overview of sports economics Literture overview of the economics of superstrs Sttisticl evlution methods for sports Evluting the drivers Dt Defining nd constructing the vribles Descriptive sttistics of constructed vribles Initil rnking with dependence on crs Interprettion of results Limits nd problems of the pproch Comprisons of drivers in the sme cr Comprisons bsed on points in seson Interprettion of results of comprisons bsed on Points in seson Limits nd problems of the pproch Pired comprisons nd likelihood estimtes Generl setup of the pired comprison pproch Results of the pired comprison pproch Interprettions of pired comprison results Limits nd problems of the pproch Comprisons bsed on time differences within rces Interprettion of results of comprisons bsed on Time differences Limits nd problems of the pproch Econometric model with driver nd cr effects Serching dependent vribles... 52

4 Who Is The Best Formul 1 Driver? An Econometric Anlysis iii Some preliminry specifiction tests Finding the preferred specifiction Robustness tests of econometric model Rnkings on preferred specifiction nd correltion with other rnkings Limits nd problems of the pproch Compring the results of the different methods Applictions The wether s influence Compensting the risk of drop-out Problems nd limits of the pproch Preliminry estimtion of rcer s verge life cycle Estimting the impct of ge nd experience Problems nd limits of the pproch First notions of superstr effects Preliminry estimtion of superstr effects Problems nd limits of the pproch Outlook nd further reserch questions Conclusions Bibliogrphy... A1

5 Who Is The Best Formul 1 Driver? An Econometric Anlysis iv List of figures Figure 1: Box interprettion for point comprisons Figure 2: Rnkings bsed on Points in seson Figure 3: Rnking correltions for performnce mesures of pired comprisons Figure 4: Box interprettion for time comprisons Figure 5: Rnkings bsed on Time difference Figure 6: Coefficients of yer dummies in speed regressions Figure 7: Rnking correltions for different evlution methods for clssifiction Figure 8: Rnking correltions for different evlution methods for grid position Figure 9: Histogrms of life cycle vribles Figure 10: Representtion of qudrtic influence of ge nd experience on clssifiction Figure 11: Correltion of driver s tlent nd generl publicity... 82

6 Who Is The Best Formul 1 Driver? An Econometric Anlysis v List of tbles Tble 1: Summry of vribles nd definitions Tble 2: Descriptive sttistics of vribles Tble 3: Descriptive sttistics nd rnkings Tble 4: Exmple for comprison bsed on performnce mesure Points in seson Tble 5: Exmple for comprison bsed on performnce mesure Clssifiction Tble 6: Rnkings bsed on pired comprisons for severl performnce mesures Tble 7: Exmple for comprison bsed on performnce mesure Time difference Tble 8: Specifiction tests of econometric model Tble 9: Regressions for clssifictions of drivers Tble 10: Robustness tests of regressions Tble 11: Rnkings bsed on econometric model Tble 12: Spermn s rnk correltion mtrix for different specifictions Tble 13: Preliminry estimtion of superstr effects... 83

7 Who Is The Best Formul 1 Driver? An Econometric Anlysis vi List of equtions Eqution 1: Likelihood eqution (prt 1) Eqution 2: Likelihood eqution (prt 2) Eqution 3: Itertion formul (prt 1) Eqution 4: Itertion formul (prt 2) Eqution 5: Null hypothesis for likelihood tests Eqution 6: Alterntive hypothesis for likelihood tests Eqution 7: Econometric specifiction formul Eqution 8: Regression on speed with wether conditions Eqution 9: Logit model for overll drop-outs Eqution 10: Logit model for technicl drop-outs Eqution 11: Logit model for humn drop-outs Eqution 12: Regression for qudrtic influence of ges Eqution 13: Regression for qudrtic influence of experience... 79

8 Who Is The Best Formul 1 Driver? An Econometric Anlysis 1 1 Introduction Formul 1 drivers re fst if they hve good cr, but the vlue of good driver lone is still not cler. The performnce of drivers nd crs hs not yet been independently evluted. To chieve n effective comprison between drivers it is not sufficient to sum up their chieved points in seson or ccumulted points or wins over certin time frme. Points nd wins depend firstly, on the number of rces tht the driver took prt in, secondly, on his own personl driving cpbilities nd thirdly, on the cr s well s the whole tem. In this Mster thesis we shll try to seprte the driver nd the cr into two different fctors by pplying vrious pproches nd modern econometric procedures. This will llow us to estblish different rnking lists for diverse performnce mesures such s rce clssifiction, point differences, time differences, strting positions, nd so on. The min im behind the whole evlution is to estimte the impct of Formul 1 driver independently of his cr nd to compre tody s rcers with former ones. The impct of the driver s performnce cn be viewed s his tlent or his bility. This Mster thesis cn therefore lso be considered s cse study for estimting cpbility nd tlent. The first method of evlution will be tble of performnce vribles corrected for the number of rces driver prticipted in. This crude nd simple pproch gives some preliminry indiction of the strength of driver. Clerly, the effects of the crs nd the tems re still pertinent nd hve not been corrected for by using this method. The second step of the process of finding the best driver nd identifying tlent will be pired comprison methodology. As most tems employ two drivers, one pproch of seprting the impct of rcer nd cr is to use systemtic pired comprisons over time. When certin driver wins in certin cr ginst his tem prtner there is n indiction tht the winner of this intr-tem (cr) mtch is the stronger driver. As drivers chnge their crs nd tems dditionl informtion is generted nd cn be used for further comprisons. We will thereby try to bridge different ers in sports. The gol cn lso be seen s n ttempt to construct sttisticl time mchine, which llows us to estimte how driver from certin period would perform in nother. Using mximum likelihood pproch, comprble vlue cn be clculted for ech driver indicting the likelihood of winning ny pired comprison in the dt pnel used. Finlly, driver nd cr effects shll be evluted using n econometric model. The coefficients of the resulting regression model using dummies for drivers will be interpreted

9 Who Is The Best Formul 1 Driver? An Econometric Anlysis 2 s mesure of driver s skill nd bility. A number of pplictions using the estblished dtbse for this Mster thesis re shown t the end. We shll try to nswer some specific questions concerning Formul 1 rces nd economics nd ttempt to test certin hypotheses. Some of the pplictions shown might be of immedite interest for Formul 1 tems such s the estimtion of driver s verge life cycle. Other pplictions with n economic bckground such s risk evlutions nd the preliminry estimtion of superstr effects in Formul 1 will lso be performed. Further pplictions in economics nd for other purposes re lso proposed. Compring sportsmen from different ers hs been discussed widely. From sttisticl point of view, these comprisons re especilly difficult to perform without stringent hypotheses. Different methods nd ggregtion procedures cn led to dissimilr results. Nevertheless, such evlutions hve been performed for diverse sports before, 1 but very limited reserch hs been done so fr for Formul 1 nd no rticles hve compred rcers over different time periods by mens of econometric pproches. 2 However, the dt vilble re suited for such comprisons nd tody s computtionl power mkes it possible to control for lrge number of vribles in the nlysis. Using number of different evlution methods does not necessrily solve the inherent problem when evluting chievements in sports, but it shows possible wys of mesuring tlent. This Mster thesis is orgnized s follows: In chpter 2 we present literture survey covering severl rticles concerning sports economics nd the economics of superstrs. Next sttisticl evlution methods in sports re discussed. Chpter 3 strts with brief description of the dt. Some preliminry descriptive sttistics re given, followed by simple evlution pproch. Therefter, model for pired comprison is used to evlute the driver s bilities. Finlly, n econometric regression model is used to look t the dt gin nd control for number of dditionl vribles. Problems nd limits of the pplied evlution methods re discussed in ech section seprtely. After estimting nd testing the econometric model, three possible preliminry economic pplictions re presented in chpter 4. In ddition, number of other interesting reserch questions might be nswered using the model. Chpter 5 summrizes our results nd concludes. 1 See the literture survey in chpter 2 for further detils or for exmple JOE (1990), BERRY ET AL. (1999) nd KNORR-HELD (2000). 2 A serch in EconLit for the keywords Formul One, Formul 1, Schumcher, cr Ferrri nd Formul 1 rcing resulted in two rticles. One of them is cse study of Ferrri s mrketing nd the other considers ggregtion problems in rnkings with n ppliction to the 1998 Formul 1 rcing seson.

10 Who Is The Best Formul 1 Driver? An Econometric Anlysis 3 2 Literture survey The following literture survey will focus first on sports economics in generl nd on the economics of superstrs in prticulr. In the second prt, literture on specific sttisticl issues of different evlution methods with focus on sports ppliction will be reviewed. 2.1 Sports economics nd the economics of superstrs Sports mostly received mrginl ttention from economists in the pst. A number of rticles on sports business cn be found in the generl mngement literture s well s in the literture covering questions of personl mngement. Nevertheless, in the pst yers the interest in sports hs incresed nd in the yer 2000 the Journl of Sports Economics ws lunched Literture overview of sports economics In n introductory textbook TROISEN (2003) presents brod picture of sports economics. Strting with chpter on the issues in sports economics the uthor then gives n historicl introduction concerning the origins of sports economics. He subsequently reviews the bsics of the production of sports, the utility nd costs of creers in sports nd the trnsition from performnces in sports to products for sports. Afterwrds sport mrkets re identified nd severl cses of different mrkets re nlyzed. Furthermore, TROISEN (2003) dedictes chpter to the microeconomic bsics of consumption s well s the generl objectives of the sports industry. The textbook s primry focus is not necessrily on the nlysis of sports form n economic perspective but rther on number of mngement issues nd different orgniztionl concepts which re discussed nd reviewed. KAHN (2000) points out tht professionl sport offers unique opportunity for lbor reserch. Firstly, dt from sports cn be used to identify the effects of monopsony power on worker s wge. Secondly, s personl chrcteristics of sportsmen re widely known s well s their performnce the extent of discrimintion cn be estimted fr more precisely thn in other industries. Lstly, it is possible to estimte the impct of supervisor qulity nd the effect of incentives on workers behvior s well s other interesting elements of

11 Who Is The Best Formul 1 Driver? An Econometric Anlysis 4 economic theory tht re generlly hrd to estimte becuse of insufficient dt vilbility. The uthor shows in his pper tht sports owners hve some monopsony power over plyers in the sense the plyers hve the option of negotiting only with one tem. KAHN (2000) mentions tht mjor difficulty for ll lbor mrket reserch on discrimintion is the problem of unobserved vribles. Such problems re surely less severe in sports thn elsewhere s detiled dt sources llow to control for vriety of chrcteristics. Indeed, he refers to some reserch rticles identifying rcil discrimintion in Americn bsebll. The results on plyers performnces suggest furthermore tht thletes re motivted by similr forces which concern workers in generl: Py lso mtters for sportsmen. The lessons to be lerned from sports economics should not be discounted becuse of the mrket s high profile. Interesting nd vluble insights cn be gined by considering sports s reserch re in order to identify different spects of economic theory. The design of sporting contest bers close reltionship to the design of n uction ccording to SZYMANSKI (2003). The objective of his review is to discuss the contest theory literture in the context of sports. By using this pproch severl questions concerning the design of sporting contests cn be solved such s the optiml number of contestnts or how evenly blnced competing tems in different sports should be. Moreover, SZYMANSKI (2003) points out tht there re mny spects of the orgniztion of individulistic sports tht could be modeled more fully with view to estblishing n optiml design. Finlly the uthor discusses theoreticl contribution to the nlysis of tem sports: the so-clled invrince principle. This principle sttes tht chnges in ownership rights over plyer services nd certin types of income redistribution will hve no effect on competitive blnce. Most empiricl ppers reviewed wekly support the invrince principle. The methodology used in sports economics cn lso be pplied to rts reserch. SEAMAN (2003) sttes tht prticulrly rts lbor reserch cn benefit for the insights of sports economics. According to the uthor, the rts nd the sport sector exhibit rich similrities tht suggest possible collbortion nd extensive cross-referencing: ernings in both sectors tend to pek erly nd decline quickly, employment is often spordic, sports creers re short nd most rtists lso leve their creers due to limited opportunities, few become superstrs but the potentil for gret success provides inspirtion. SEAMAN S (2003) study is minly survey of sports literture which tries to motivte rts economists to consider techniques from sports economics for their own reserch. VON ALLMEN (2001) follows more specific ppliction of the economics of sports with focus on rcing. He provides description of the pyment systems in the NASCAR

12 Who Is The Best Formul 1 Driver? An Econometric Anlysis 5 Winston Cup (now known s the Nextel Cup) rcing. The Americn NASCAR s rewrd structure differs significntly from other tournment bsed sports, which tend to hve nonliner individul-performnce pyouts. The compenstion system in NASCAR consists of two structures: firly liner individul-rce rewrd system nd nonliner sesonending points rewrd system. According to the theoreticl contribution of VON ALLMEN (2001) nonliner rce-level rewrd for NASCAR my be inefficient, which mens tht the current system should not be mended. Firstly, sponsorship my provide n incentive for drivers to be consistent during the seson rther thn tking greter risks for n opportunity of single rce victory. Anyhow, he mentions tht driver s performnce in certin rce nd sponsorship revenues my be directly correlted. Secondly, the risks of rcing in close proximity t high speeds could be too high for nonliner individul-rce rewrd system. The incresed ggressiveness could led to significnt negtive externlities for other drivers. Finlly, VON ALLMEN (2001) mentions tht cr rcing depends on very high expenditures. Nonliner rce pyoffs my provide sufficient revenues for some tems to fund further expenditures, thereby potentilly skewing competitive blnce unintentionlly. From theoreticl stndpoint it seems therefore tht the liner rewrd system for rces nd the nonliner seson-ending points rewrd system my be more efficient in cr tournments. An empiricl test of VON ALLMEN S (2001) ides concerning the NASCAR rewrd system is performed by DEPKEN AND WILSON (2004). They nlyze seson-level dt from 1949 to 2001 in order to test whether n increse in performnce-points concentrtion leds to disproportionl increse in winnings concentrtion. This would correspond to n incresed tking of risk by NASCAR drivers. Indeed, the uthors find some initil evidence for the hypothesis. Anyhow no significnt results re found for the cost hypothesis stting tht non-liner rewrd system would led to skewed competitive blnce. By using Grnger cuslity tests the uthors find tht the performnce-points concentrtion does not cuse winnings concentrtion nd vice vers. Due to lck of vilble dt DEPKEN AND WILSON (2004) cnnot test the hypothesis tht sponsorship issues could ply significnt role for the choice of the liner rewrd scheme in NASCAR rcing. In the pplied mngement literture, tournments in which workers re pid bsed on their reltive performnce, received little ttention. ZAX AND LYNCH (2000) therefore compre incentive nd sorting theories of tournment performnce in rod rces. Their dt set which includes finishing times, runner nmes, rce nmes, rce distnces, runner ges, nd runner genders ws obtined from the USA Trck nd Field Rod Running Informtion Center. The dt generlly support the hypothesis tht times re fster in rces

13 Who Is The Best Formul 1 Driver? An Econometric Anlysis 6 offering higher prize money. This is minly becuse higher prizes ttrct better runners. When ZAX AND LYNCH (2000) control for driver s bility through fixed effects the incentive effects of higher prizes diminish. However, the uthors do not control for cr fixed effects. Their results suggest tht rces with high stkes only record fster times becuse of sorting or selection effect of better drivers. Higher prices per se do not encourge ll rcers to run fster. The ppliction to humn resource mngement is imminent s some literture on motivtion sttes tht higher py is not motivtor for higher performnce if single individul is concerned. Generlly it cn be noted tht the economics of sports tends to tret reserch topics tht re fr beyond the nlysis of generl economics. Mostly, reserchers in sports economics focus on relevnt question in sports nd use it to win insights into some economic problems such s done by KAHN (2000). In the Journl of Sports Economics mostly incentive schemes, sports contrcts nd questions of how to find tlent re nswered. Our econometric nlysis of Formul 1 follows this pth by concentrting on the identifiction of bility nd tlent nd distinguishing between technicl nd humn influences on performnce Literture overview of the economics of superstrs After this short survey concerning some literture on sports economics we would like to focus now on the economics of superstrs. A fory into this brnch of economic literture gives vluble insights into lbor mrket economics nd industril orgniztion. Success or filure is centrl element of every humn s lbor mrket experience nd the extent to which success trnsltes into income is highly vrible. The economics of superstrs sttes tht the distribution of rewrds often ppers to be such tht comprtively minor tlent differences cn generte enormous returns, so tht the distribution of income is not only simple re-scling of the distribution of bility. If such enormous incomes erned re the mrket s rewrd for superior tlent the superstr phenomenon my be socilly dmissible. If, on the other hnd, the source of the superstrs high incomes is not their tlent, the skewed income distributions my be perceived s inequitble by society. 3 It could therefore be rgued tht the min focus of superstr nlysis should not only lie on n endogenous vrible of success which is mesured by income but rther on 3 This depends on the socil norms nd stndrds prevlent in society nd shll therefore be not the mtter of further discussion in this Mster thesis.

14 Who Is The Best Formul 1 Driver? An Econometric Anlysis 7 mesurement of bility. 4 Our nlysis in chpter 3 nd 4 is concentrting on this spect s we try to find out empiriclly the most tlented driver. Aprt from the intrinsic motivtion of the reserch question of the thesis title, this pper cn consequently lso be seen s cse study for the mesurement of bility. In his seminl pper ROSEN (1981) introduced rigorous definition nd model of the superstr phenomenon. He mentions tht in certin kinds of economic ctivity there is concentrtion of output mong few individuls, mrked skewness in the ssocited distributions of income with very lrge rewrds t the top. The superstr phenomenon is sid to exist when reltively smll numbers of people ern enormous mounts of money nd seem to dominte the fields in which they engge. Additionlly, smll differences in bility re supposed to hve disproportionte effects on ernings. ROSEN (1981) mentions tht both demnd nd supply conditions my be involved in this mrket result. On the demnd side, lesser qulity is only very poor substitute for greter qulity. Furthermore quntity nd qulity do not hve to be substitutes either. By introducing indivisibilities in the consumption of services, consumer s ttempts to minimize costs give n dditionl dvntge to higher qulity producers. On the supply side the mrginl cost of output is lrgely ssumed to be constnt (or flling). The effect of scle economies mkes it possible to produce lrge mounts of consumble services t low or flling unit costs. In ddition, the service delivered by the superstr cn be described s form of joint consumption but property rights re clerly ssigned to the seller s opposed to public good. The uthor shows tht using these ingredients leds to model which llows explining the differences in incomes nd the convex revenue function of superstrs. In similr vein, MACDONALD (1988) presents dynmic version of ROSEN S (1981) superstr model where consumers re lbeled s the udience nd producers s performers. The implicit pricing of chrcteristics such s bility or tlent nd the ssocited convex returns re the distinguishing feture for ll superstr models but most models do to not look closer t the distribution of such personl ttributes. MACDONALD (1988) demonstrtes tht the predictive content of superstr models could be incresed by further nlyzing the distribution of tlent. He shows tht in the stedy-stte equilibrium only the young enter the occuption nd ern low incomes plying to smll crowds. Only the successful sty on in the industry. Those few successful performers ern high incomes plying to big crowds. The less successful ones drop out of the industry. Overll, there re 4 Indeed, there re not mny empiricl rticles mesuring the income of superstrs becuse of the lck of consistent dt. Superstrs do not only benefit from fixed slries but lso from sponsoring, mrketing revenues, nd so on.

15 Who Is The Best Formul 1 Driver? An Econometric Anlysis 8 few strs in the industry but s group they serve lrge frction of the udience nd ern n even lrger shre of the rewrds. According to HAMLEN (1991) the nlysis of superstrs in populr music hs focused on two different views concerning the modern recording industry for populr music. The lymn s view of the mrket for populr singers is tht most consumers of this type of music hve little pprecition for the qulity of the voice nd the singing. This is explined by ignornce bout vocl qulities. The economic view, bsed on the ides of ROSEN (1981) is tht the industry of populr music is n stonishing exmple of superstr phenomenon. Thereby, only smll differences in vocl bility cn be mgnified into disproportionte levels of success. Both ssumptions lck empiricl investigtion. HAMLEN (1991) tries to shed some light into this issue by empiriclly investigting record sles on number of different vribles including qulity mesure for singer s voice. He finds tht the strongest predictor of totl record sles is creer longevity which comes s no surprise. 5 Gender seems to ply n importnt role, s femle singers tend to sell more records thn their mle counterprts. HAMLEN S (1991) mesure for voice qulity is significnt nd positive. This indictes tht consumers of populr music do indeed discern qulity in their preferred singers but the size of the coefficient is significntly less thn one would expect if populr music would show superstr effects. The estimted elsticity in the log-liner regression function is too low to support superstr phenomenon for the populr music industry. Only smll mount of incomes is ccessible for the period of nlysis. Consequently, the effects of singer s bility on his income cnnot be nlyzed s record sles do not hve to trnslte directly into dditionl income. The empiricl pper of CHUNG AND COX (1994) exmines the phenomenon of superstrs form different perspective. Their study employs stochstic model s probbility mechnism underlying the consumer s choice of services. They predict by using this model tht the output produced will only be delivered by very smll number of lucky individuls. As mesure of rtistic success by performers their number of gold-records is used. The uthors then pply the Yule distribution to clculte numericl fits to the dt. It turns out tht the used stochstic process leds n excellent prediction of the rel empiricl distribution explining nerly 94 % of the observed gold-records mong rtists. The importnce of the contribution by CHUNG AND COX (1994) is tht their empiricl results suggest tht the superstr phenomenon could exist mong individuls with equl tlent. 5 Creer longevity could be considered s n endogenous vrible. This problem is not discussed by HAMLEN (1991).

16 Who Is The Best Formul 1 Driver? An Econometric Anlysis 9 This is explined by the fct tht their stochstic model does not use bility differences nd views the superstr phenomenon s n impliction of probbilistic mechnism underlying the record-buying behvior of consumers. The very lrge incomes re therefore prtly driven by chnce nd not by superior tlent s suggested in other studies. This result is in line with theoreticl contribution by ADLER (1985) stting tht lrge differences in ernings cn exist even where there re no differences in tlent t ll. For ADLER (1985), strdom cn be seen s mrket device to economize on lerning costs. Acquiring knowledge by consumer by discussion with other consumers is esier if ll shre the sme common knowledge. Strs cn therefore exist even if their bilities re not superior to tht of others. In the lte 1990s nd the erly 2000s concert revenues for top rock performers nd ticket prices for such concerts took off. As KRUEGER (2005) mentions, the economics of superstrs cn help to explin the long-term trends in this industry. However, the price surge beginning in 1997 cnnot by ccounted for. To test different explntions for this price increses the uthor compiled dtbse of box office reports nd dditionl dt on bnds nd performers. The first remrk to be mde is tht the concert revenues becme more skewed in the 1980s nd 1990s. To control for str s qulity KRUEGER (2005) uses the number of millimeters of print columns devoted to ech rtist in The Rolling Stone Encyclopedi of Rock & Roll. 6 The pplied regression model yields lrge nd incresing superstr effects. The uthor identifies technology-induced erosion of the complementrity between record sles nd concert tickets s the min explntion for the surge in ticket prices. Ticket prices hve sored for the reson tht recording rtists hve seen decline in their income for records sles becuse of the possibility to downlod free music. Additionlly it is likely tht the downloding of music will put further upwrd pressure on concert prices nd revenues. In generl the literture on the economics of superstrs does not try to mesure tlent directly but only ssumes tht lrge income differences re due to differences in bilities. It hs lso been shown tht differences in success cn be explined by using purely stochstic model. Mesuring bility itself my therefore contribute to solving this puzzle. Possible pproches to estimting tlent my lso be of use for other economic brnches such s the creer concerns literture for exmple (see HOLMSTRÖM, 1999). A brief look t the literture on sttisticl pproches in sports my therefore be helpful for our cse. 6 It should be noted tht this vrible could fce possibly high problem of endogeneity.

17 Who Is The Best Formul 1 Driver? An Econometric Anlysis Sttisticl evlution methods for sports There re number of different sttisticl evlution methods for sports. Some uthors mention pired comprison pproches, others try to estimte ging functions nd some even use simple Gini coefficients when compring tems or thletes. It should be noted tht most evlutions re done for the United Sttes nd sports tems overses. In generl, fr more interest is dedicted to numericl evlution of strengths, merits nd outcomes over the Atlntic thn in Europe. As shown bove some theoreticl nd empiricl economic nlysis hs been done for NASCAR rcing but not for Formul 1 even though NASCAR is fr less widely viewed thn Formul 1 in most prts of the world. Even more stonishing nd worthwhile mentioning is the fct tht reltively lrge number of pplied sttisticl methods on sports concern Americn bsebll, bsketbll or footbll. Yet, it is Europen soccer tht is likely to yield higher totl revenues nd hs lso further globl rech if you Do The Mth correctly. 7 The sme is likely to be true for Formul 1. We shll focus in this section on different models nd methods of sports evlution in generl. The min rting nd sttisticl evlution method for sports re done on the bsis of ctegoricl outcomes of pired comprisons such s wins, drws nd losses in the sport considered. The method of pired comprison hs ttrcted the ttention of people from wide spectrum of interests: sttistics, mrketing reserch, preference mesurement, nd so on. Sports competition is just one possible sector of ppliction. The min methodologicl nd mthemticl frmework ws lid within the yers from 1960 to DAVIDSON AND FARQUHAR (1976) present list of references on pired comprisons. As mture reserch brnch the Hndbook of Sttistics includes n rticle by BRADLEY (1984) on the method. JOE (1990) extends the generl model for pired comprisons to pply it for chess rtings. The extension of the model is used to estblish rnking for 64 top chess plyers since Additionlly the uthor tkes ccount of the pek of their creer periods. To clculte the pek period rtio of 0.25 for the pek creer period to the whole creer period ws tken for ll plyers. Furthermore JOE (1990) ssumes tht ll plyers improve before the pek nd decline fter the pek t the sme rte. This leds to rnking of chess plyers tht does not necessrily seem correct to chess experts. The top eight plyers re A. Alekhine, M. Botvinnik, J. Cpblnc, R. Fischer, A. Krpov, G. Ksprov, E. Lsker nd P. Morphy. JOE (1990) mentions tht the comprisons could be improved if more dt hd 7 The Forbes mgzine reports on its website ( downloded on the 10 th of April 2006) tht soccer s superior competitiveness [ ] helps explin why it ttrcts billions of sponsorship dollrs from compnies like Budweiser, Coc-Col, McDonld s, nd Yhoo! [ ].

18 Who Is The Best Formul 1 Driver? An Econometric Anlysis 11 been compiled in order to use covrite informtion. Furthermore it would be essentil to extend the chin for every pir of plyers so tht better estimtes of model prmeters were possible. Since not ll plyers were ctive in the sme decdes only limited number of pirs could be mtched which ech other. According to JOE (1990) this could hve influenced the results nd the conclusions which might be drwn in the study. The min gol of n rticle by KNORR-HELD (2000) is the dynmic rting of sporting within the frmework of cumultive link model. Such model for comprison ijα of two tems i nd j in event α is defined by P( 1) = F( θ + β β ) where F is distribution function, θ r represent different control prmeters nd β i is the ltent bility of tem i. The uthor uses n extended version of the Klmn filter lgorithm for ctegoricl dt to estimte the unknown prmeters. All tems re treted symmetriclly by the uthor s pproch nd dditionl prmeters re entered to represent possible home dvntge. It is importnt to mention tht such prmeters θ r re ssumed s time constnt nd sport s tem independent nd tht ctegoricl dt in generl does not provide much informtion bout the temporl vrition in tem s bilities. KNORR-HELD (2000) pplies his method to the Deutsche Bundeslig for the yers 1996 to 1997 nd for the sme period to the Americn Ntionl Bsketbll Assocition nd finds substntil home dvntge effects. Additionlly, he presents grphiclly the filtered nd smoothed estimted bilities of selected tems. Anyhow, the bilities re not compred with ech other but only the bility pths re commented. Another highly sophisticted model is set up by GLICKMAN AND STERN (1998) for Americn Ntionl Footbll Legue Scores. They develop dynmic predictive model tht ssumes tht tem strength prmeters follow n utoregressive process. The distribution of the dt t ech point in time is specified on number of time indexed prmeters nd n dditionl process nlyses the evolution of the prmeters over time. As for such sttespce models nlyticl inferences bout prmeters is impossible the uthors pply Mrkov chin Monte Crlo methods. The nlysis yields the Dlls Cowboys s the best tem with lmost 17 point dvntge over the worst, the New Englnd Ptriots for the period form 1988 to 1993 in the Ntionl Americn Footbll Legue. An effort to compre the different performnces of thletes from different time ers is mde by BERRY ET AL. (1999). They try to use the creer-overlps to compre plyers whose chievements were mde in different time periods. The difficulty in modeling such creer-overlps lies, ccording to the uthors, in the effects of the ging process on performnce. Therefore BERRY ET AL. (1999) develop ging functions to tke ccount of ijα r i j

19 Who Is The Best Formul 1 Driver? An Econometric Anlysis 12 the different bilities over time. In order to control for the ge, rndom curves re used to represent individul ging effects. Additionlly they try to seprte out the difficulty of plying in different time periods nd they lso chrcterize the chnging structure of the popultion of plyers. The model is pplied to Americn Ntionl Hockey Legue plyers, professionl golfers nd Mjor Legue Bsebll plyers nd provides, ccording to the uthors, resonble estimtes for ll the three sports considered. UTT AND FORT (2002) mention some pitflls ssocited with mesuring competitive using Gini coefficients. Usully Gini coefficients of winning percentges re clculted to mesure inequlity in sports legue plyoff outcomes within seson. The first problem is tht tem cnnot win ll gmes but only ll of its own gmes. The zero-sum nture of legue ply oversttes the level of competitive blnce. Furthermore host of other complexities must be overcome to chieve precise estimtes of competitive blnce. UTT AND FORT (2002) review number of works tht did not tke ccount of these fcts. They suggest using winning percentge stndrd devitions s n lterntive to Gini coefficients. KLABRODA (2000) discusses problems encountered when ggregting points in sports competitions. He uses Formul 1 rcing s cse study. An optiml ggregtion of drivers outcomes is impossible ccording to KLABRODA (2000). Such n ggregtion procedure would need to hve universl definition spce, tht is every possibly combintion of clssifictions should led to certin rnking. Furthermore, the ggregtion needs to be Preto efficient: If driver A finishes lwys before driver B the ggregtion of points needs to led to the result tht A is better thn B. Moreover, method of giving points should be independent of irrelevnt lterntives: If A wins twice ginst B nd B once ginst A, driver A should be rnked hed of driver B. However, the norml point system used in Formul 1 does not gurntee this. KLABRODA (2000) shows with simple numeric models tht chnging the method of ggregting points nd pplying, for exmple, ordinl rnkings cn led to totlly different results in the Formul 1Chmpionships of the yer The uthor s work should not be interpreted s sttisticl pproch to evlute driver s cpbility s no specific evlutions re performed. It should rther be regrded s theoreticl contribution highlighting the problems encountered when ggregting points nd when estblishing rnkings. For Formul 1 itself, some very bsic sttisticl evlution methods re used by fns nd drivers websites on the internet. Minly they re simple listing the number of wins, podium positions nd pole positions for different drivers. A comprtively dvnced rnking is provided by Autosport-Atls Wildsoft F1 Rnking. Their rnking system is bsed on the lst five yer drivers chievements. Points re

20 Who Is The Best Formul 1 Driver? An Econometric Anlysis 13 counted for such chievements s wins, poles, nd mny others, even kilometers rced. No points re given to drivers who did not pper on the strt (even if retired on the wrm-up lp) nd no points for drivers disqulified for ny reson. All resulting points for the lst 5 yers re summed up. Old Grnds Prix re removed nd new ones re dded s time is pssing through. Of course this method of evlution depends highly on the hypotheses concerning the points wrded to drivers. Chnging the ssumptions cn led to big nd unexpected chnges in the results nd in the rnking. Additionlly comprison over severl yers is not possible nd the number of rces is positively correlted with the number of points. This should not be the cse when evluting the bility of driver. Other sites show different sttistics but do not try to evlute the impct of driver nd cr seprtely. They do not even ccount for chnges in the number of points over the yers. Nor do they consider tht the relibility of the crs ws improved over the lst 50 yers. This cn only be done by using more refined sttisticl nd econometric methods nd by including severl control vribles. None of the websites tries to perform pired comprisons conditioned on experience vribles or other controls nd on the sme crs. If comprisons between drivers re done they re just representtions of the differences in points or the number of wins nd therefore do not tke ccount of the min distinguishing chrcteristic which is the tem nd the engine. In the next chpter we will pply different sttisticl nd econometric procedures to evlute driver s cpbility independently of the cr in Formul 1. In ddition, we will control for severl other vribles such s experience or technicl problems.

21 Who Is The Best Formul 1 Driver? An Econometric Anlysis 14 3 Evluting the drivers This chpter focuses on different methods used to evlute Formul 1 driver s bility independently of the cr. We strt with the description of the dtbse set up for this study. A crude evlution pproch follows imed t identifying the min drivers whose results will be presented in this pper. 8 The drivers will then be mtched with their tem prtners nd will be compred by mens of different performnce mesures. These mtches llow us to clculte the likelihood of specific driver winning ginst ny other driver in pired comprison pproch using ll vilble informtion. Finlly n econometric model will be estblished to sttisticlly seprte driver nd cr specific effects. The cpbilities of driver nd the resulting rnkings of ech evlution method will then be compred for subset of Formul 1 rcers. 3.1 Dt Our min dt comes from the FORIX Formul 1 Dtbse which is provided by the mgzine Autsport-Atls vi subscription on the internet. 9 On the FORIX website tbles cn be obtined for ll Formul 1 rces strting from 1950 until the ltest rce. For our clcultions we downloded informtion on Grnd Prix trcks, drivers, crs, rce nd wether conditions, rce clssifictions, rce times, rce points, strting grids, fstest lps, cuses for dropouts nd further specific informtion. The downloded tbles were then put together in pnel dt structure for ll rces over the period from 1950 until the end of the rcing seson Defining nd constructing the vribles Tble 1 summrizes some vribles definitions used in this pper nd focuses on their chrcteristics. Some comments on these vribles re worthwhile but no detiled comments will be mde on obvious combintions or their simple modifictions. Such mendments shll be explined in more detil during the ongoing nlysis of the dt when the vribles re used in specific context for the estimtions. 8 As there were more thn 300 drivers in Formul 1 history we hve to focus on subset of them. All results cn be obtined from the uthor s website: 9 For further detils see

22 Who Is The Best Formul 1 Driver? An Econometric Anlysis 15 Tble 1 Summry of vribles nd definitions Vrible Definition GPRIX Country where the Grnd Prix took plce GPDISTANCE Distnce of Grnd Prix circuit in kilometers GPPERIMETER Perimeter of Grnd Prix circuit in kilometers GPLAPS Lps of Grnd Prix circuit WEATHERCODE Wether conditions during Grnd Prix rce (-2 = cold, riny, overcst ; 2 = hot, dry nd sunny ) DRIVERCODE Driver nme (used s dummy vrible) DRIVERBIRTHYEAR Driver s yer of birth (severl combintion re formed using this vrible during the nlysis) DRIVERHOMEEFFECT Dummy for home field dvntge (1 if rce tkes plce in driver s ntion) DRIVEREXPERIENCE Number of rces driver took prt in DRIVERPEAK Dummy for pek of creer DRIVERNBCARS Number of different crs used during ctive period (modifictions for tyres nd lubriction re used during the nlysis) DRIVERNBWINS Number of ccumulted wins driver hs ccomplished DRIVERNBPODIUMS Number of ccumulted podium positions of driver CARCODE Cr identifier bsed on tem nme nd engine TYRES Identifier for tyre produces LUB Identifier for lubriction used GRIDCLASS Strt position (severl combintion re formed using this vrible during the nlysis) GRIDTIME Time of chieved strt position (severl combintion re formed using this vrible during the nlysis) CLASSCLASS Clssifiction of driver in rce (severl combintion re formed using this vrible during the nlysis) CLASSTIME Time of chieved clssifiction (severl combintion re formed using this vrible during the nlysis) CLASSPOINTS Points of chieved clssifiction TECHNICALOUT Dummy vrible for technicl reson of dropout during rce HUMANOUT Dummy vrible for humn reson of dropout during rce (eg. collusion) FASTESTLAP Time of driver s fstest lp in rce Source: Author s definitions nd designtions. For every Grnd Prix in ech yer there is specific trck informtion vilble. We minly concentrte on the number of lps, the distnce in kilometers, the wether conditions nd the country in order to construct home field dvntge vrible. Wether conditions from FORIX were only vilble s plin text nd hd therefore to be trnsferred into integers to be used for n econometric nlysis. We coded the conditions into five different ctegories strting from -2 to 2. Lower vlues indicte cold, riny nd overcst wether conditions. Higher vlues indicte hot, dry nd sunny conditions. The vlue 0 represents the ctegory of cloudy/overcst, mild, prtilly wet wether. The totl number of drivers tking prt t lest once in Formul 1 Grnd Prix is 790. As more thn 50 % of these drivers did not score ny points during their Grnd Prix ppernces we left them out of the evlution procedure. 300 out of the 790 drivers from 1950 to the end of the rcing seson 2005 scored t lest one or more points during their

23 Who Is The Best Formul 1 Driver? An Econometric Anlysis 16 ctive period. These 300 drivers nd the rces they took prt in shll represent the min dtbse lthough only subset of 50 Formul 1 runners will be explicitly represented in this pper due to lck of spce for such n enormous number of rcers. Additionl vribles concerning drivers re their ge in yers, ntionlity, experience nd creer peks. The experience vrible is n integer tht counts the number of rces driver took prt in. To find out the creer pek of Formul 1 rcer we use the rnking of the driver in Grnd Prix. A driver s creer pek is identified s the seson or sesons when driver ccomplished his personl best clssifiction in rce. As result, every Formul 1 rcer will hve t lest one pek seson. JOE (1990) mde the ssumption tht 25 % of the creer cn be considered s the pek period in his evlution of chess plyers. Drivers prticipting over long time intervls my lso hve severl peks periods. If driver rced for only one seson, tht is identified lso s his pek yer. For the 300 drivers in points there is totl number of 750 different cr models. A cr model in our nlysis is defined s the nme of the cr registered for the Grnd Prix in tht it is tking prt. Usully the cr registered is combintion of the tem s nme nd reference to the engine instlled. Sometimes the registered cr nme lso represents combintion of the tem s nme nd the yer of entry. It is importnt to mention here tht s the sme engines re used in different crs nd the tem nmes often do not chnge over time, the used identifiction for the cr in this study cptures t the sme time the tem s influence nd the technology. This choice helps us to significntly reduce the number of independent vribles nd cr controls without possibly ffecting the results. Furthermore, we distinguish between ten different tyre producers (including unknown producers coded s unknown ). Informtion is lso vilble on eight different types of lubriction (including the type nmed unknown ). The tyres nd the lubriction will enter our nlysis s dummy vribles where pproprite. As fr s the prticulr rnking vribles re concerned we differentite between lrge number of performnce mesures. The dt ws gin mtched form the FORIX tbles to the driver nd to the Grnd Prix to mintin the pnel structure. For the clssifiction in the rce itself we hve mtched the points, officil rnkings nd the times. From these vribles other mesures such s wins, podiums, n ccumulted winning vrible for ech driver nd similr vribles re constructed. The informtion on the rcing times for ech driver is converted into second mesures. This posed specific problem: If driver is one or more lps behind, only the time when this driver pssed the finishing line in his round is vilble. For exmple, if M. Schumcher wins with two lp difference to R. Brrichello the second mesures for M. Schumcher

24 Who Is The Best Formul 1 Driver? An Econometric Anlysis 17 nd his rivl cn be very close becuse R. Brrichello does not finish the rce but his time is stopped s soon s he psses the finishing line fter M. Schumcher. To solve this problem we use the vilble times of drivers tht finished the rce in the sme round s the winner did nd clculte n verge time per lp. This verge is then multiplied with the number of lps driver is behind the winner nd the obtined vlue is dded to the driver s time mesure. In generl this procedure underestimtes the time of drivers who re one or more lps behind, s the drivers who finish the rce in the sme round s the winner hve lower lp verge thn the ones tht do not finish in the sme lp. Nonetheless, we think tht it is resonble proxy for the rel driver s chievements. This is minly becuse there is considerble difference in finishing one or more lps behind but the time difference within one round is rther smll. Additionlly ny djustment of the obtined time mesures by fctor would be possible but rbitrry s such fctor would hve to be bsed on individul specific lp times which re not vilble. Finlly, this procedure of clculting times nd time differences enbles us to compre different drivers tht re one or more lps behind with drivers tht finish in the sme round s the winner. Other performnce mesures re the strting grid positions nd the time of the fstest lp. 10 There is lso informtion on the resons of dropping out of rce which is coded s HUMANOUT or TECHNICALOUT. FORIX nottions for drop-outs such s ccident, collision, not clssified, suspension, disqulified, physicl re considered s humn outs in our evlution nd re correspondingly coded. Nottions like fuel lek, gerbox, brkes, electricl, trnsmission, xle, oil lek, engine re tken s technicl resons for drop-outs. Prticulrly, the technicl brekdowns might be influenced by humn error. Overloding the engine, for exmple, is considered in our evlution s technicl out lthough it is possibly humn fult tht could hve been prevented. Vice vers collisions might be cused by technicl problems with the brkes. Although we re wre of such problems there is no possibility of correcting them. In spite of this, the overll picture of the nlysis will be more ccurte by dding theses vribles thn by not using them in further evlutions Descriptive sttistics of constructed vribles The process of mtching results in pnel of 750 Grnd Prix, 300 driver, 750 crs nd ltogether lines times 40 column entries (driver, cr, tyre nd lubriction dummies 10 In the beginning of the Formul 1 the informtion on the fstest lp of driver is not lwys vilble.