The Impact of Performance Measures in Football Players’ Transfer Market Value

i The Impac o Pe o mance Measu es in Foo ball Playe s’ T ans e Ma ke Value Miguel da Sil a B i o Pacheco Fe ei a Supe ised by B uno Miguel Pin o Damásio Disse a ion p esen ed as equi emen o ob aining he Mas e ’s deg ee in S a is ics and In o ma ion Managemen , wi h a specializa ion in Business In elligence ii NOVA In o ma ion Managemen School Ins i u o Supe io de Es a ís ica e Ges ão de In o mação Uni e sidade No a de Lisboa THE IMPACT OF PERFORMANCE MEASURES IN FOOTBALL PLAYERS’ TRANSFER MARKET VALUE by Miguel da Sil a B i o Pacheco Fe ei a Disse a ion p esen ed as equi emen o ob aining he Mas e ’s deg ee in In o ma ion Managemen , wi h a specializa ion in Business In elligence Ad iso : B uno Miguel Pin o Damásio Oc obe 2021 iii ABSTRACT This documen p o ides he disse a ion p esen ed as equi emen o ob aining he Mas e deg ee in In o ma ion Managemen wi h he specializa ion in Knowledge Managemen and Business In elligence in No a In o ma ion Managemen School o Uni e si y o Lisbon. Foo ball is he mos popula spo in Eu ope whe e playe s assume a key ole. In ecen yea s, we ha e assis ed o an in la ion o he playe s p ice which may ep esen a p o ligacy p oblem o he Eu opean oo ball eams. Consequen ly, is impo an o unde s and which ac o s in luence he ans e ma ke alue o oo ball playe s. Recen s udies sugges ha he ans e ma ke alue depends on many ac o s, including he pe o mance measu es. These measu es quan i y he abili ies ha each playe execu es in he pi ch. Despi e he de elopmen s made on his ield, ew s udies conside ed he speci ica ions o each posi ion in he pe o mance measu es selec ion. The e o e, his s udy aims o unde s and he impac o he pe o mance measu es in he playe s o op six Eu opean leagues in he las h ee seasons, conside ing each posi ion g oup. Fo his, ixed e ec eg ession was un and he esul s e ealed ha goalkeepe s ma ke alue has a posi i e co ela ion wi h he numbe o games wi hou concei ing goals. The de ensi e duels and he ae ials duels won pe minu e ha e a nega i e co ela ion o he de ende s. The numbe o assis s a ec s posi i ely he ans e ma ke alue o mid ielde s and goals ha e a g ea impac in hese playe s and a acke s’ alue. This esea ch in en o p oduce ele an insigh s o agen s ha ha e an ac i e ole in oo ball ans e ma ke . KEYWORDS Foo ball, Playe s, Ma ke Value, Panel da a, Pe o mance Indica o s i INDEX 1. In oduc ion .................................................................................................................. 1 2. Li e a u e Re iew ......................................................................................................... 3 2.1 Eu opean Foo ball T ans e Ma ke O e iew ...................................................... 3 2.2 Foo ball Playe Ma ke Value ................................................................................ 4 2.2.1 Playe s Cha ac e is ics .................................................................................... 4 2.2.2 Playe Popula i y ............................................................................................ 6 2.2.3 Team pe o mance indica o s ........................................................................ 6 2.2.4 Playe pe o mance indica o s ....................................................................... 6 3. Me hodology ................................................................................................................ 9 4. Da ase and desc ip i e s a is ic ................................................................................ 10 4.1 Da ase ................................................................................................................. 10 4.2 Desc ip i e S a is ics ............................................................................................ 10 4.2.1 Goalkeepe s .................................................................................................. 10 4.2.2 De ende s ..................................................................................................... 11 4.2.3 Mid ielde s ................................................................................................... 11 4.2.4 A acke s ....................................................................................................... 12 5. Resul s......................................................................................................................... 13 5.1 Goalkeepe s ......................................................................................................... 13 5.2 De ende s ............................................................................................................ 13 5.3 Mid ielde s ........................................................................................................... 14 5.4 A acke s .............................................................................................................. 15 6. Conclusion .................................................................................................................. 16 7. Bibliog aphy ................................................................................................................ 18 8. Appendixes ................................................................................................................. 22 8.1 Appendix 1 ........................................................................................................... 22 8.2 Appendix 2 ........................................................................................................... 25 8.3 Appendix 3 ........................................................................................................... 26 8.4 Appendix 4 ........................................................................................................... 29 8.5 Appendix 5 ........................................................................................................... 29 8.6 Appendix 6 ........................................................................................................... 30 8.7 Appendix 7 ........................................................................................................... 30 TABLES INDEX Table 1 - Foo ball Playe s cha ac e is ics indica o s .................................................................. 5 Table 2 - Foo ball playe s popula i y indica o s ......................................................................... 6 Table 3 – Team pe o mance indica o s .................................................................................... 6 Table 4 - Foo ball playe s pe o mance indica o s .................................................................... 7 Table 5 – Goalkeepe s da a desc ip i e s a is ics .................................................................... 11 Table 6 – De ende s da a desc ip i e s a is ics ....................................................................... 11 Table 7 – Mid ielde s da a desc ip i e s a is ics ...................................................................... 12 Table 8 – A acke s da a desc ip i e s a is ics ......................................................................... 12 Table 9 – Hausman Tes esul s pe Posi ion G oup ................................................................ 13 Table 10 – Fixed E ec eg ession esul s ime and en i y e ec s o Goalkeepe s ............... 13 Table 11 – Fixed e ec s eg ession esul s ime and en i y o De ende s ............................. 14 Table 12 – Fixed e ec s eg ession esul s ime and en i y o Mid ielde s ........................... 15 Table 13 – Fixed e ec s eg ession esul s ime and en i y o A acke s .............................. 15 1 1. In oduc ion Associa ion oo ball, o socce , is go e ned by Fédé a ion In e na ionale de Foo ball Associa ion (FIFA) ha ep esen s he highes body in oo ball (FIFA, 2020). The Union o Eu opean Foo ball Associa ions (UEFA) is he go e ning body in Eu ope, whe e he main clubs’ compe i ions a e he UEFA Champions League and UEFA Eu ope League. Pa icipa e in hese compe i ions he bes anked eams om he 12 di e en na ional leagues. Acco ding o UEFA (2020), he op six anked Eu opean leagues a e: La Liga in Spain, P emie League in England, Se ie A in I aly, Bundesliga in Ge many, Ligue 1 in F ance and Liga NOS in Po ugal. Foo ball is he mos popula spo in Eu ope whe e clubs a e ollowed by millions o ans. Season a e season, oo ball clubs gene a e eno mous e enues. Fo he i s ime, in 2019 a oo ball club, F. C. Ba celona, eached he 800 million eu os ba ie (Deloi e, 2020). As a esul , some au ho s a gue ha oo ball is no jus a spo , bu a well- un business, whe e oo ball clubs can be compa ed o companies (Op ean & Op ison, 2014, p. 1850). In his mul i-million-indus y, oo ball clubs gene a e e enues h ough di e en ac i i ies, including he acquisi ion and disposal o oo ball playe s (Ami & Li ne, 2005). Foo ball playe s a e he mos impo an elemen s in a oo ball club ha ing an o e weigh ole in bo h spo s and economic oo ball dimensions. They a e hi ed wi h he expec a ion o inc ease eam pe o mance and b ing inancial bene i s o he club in he u u e (Ruijg & Ophem, 2015; Ami & Li ne, 2005). Clubs cons uc hei eams in wo di e en ways ha can be combined – hey ec ui oo ball playe s in a e y young age and a e ha , hey ecei e a oo ball educa ion passing h ough he young eams un il hey achie e he p o essional eam, o /and con ac o loan p o essional playe s using he in e na ional ans e ma ke . In Eu ope, he oo ball ans e ma ke is cha ac e ized o be a ee ma ke whe e he e a e wo ypes o ans e s be ween clubs: ans e o playe s unde con ac and playe s wi hou any con ac (Ami & Li ne, 2005). I a playe has a con ac wi h ano he oo ball club a ans e ee mus be paid in o de o compensa e he loss o he eam pe o mance and he in es men s ha we e made in he pas wi h him. Each yea , oo ball clubs spen a as amoun o money hi ing new playe s. In Eu ope, his alue is ising in he pas yea s, e en wi h he limi a ions imposed by he UEFA Financial Fai Play Regula ion. In ecen yea s, we ha e assis ed o he in la ion o oo ball playe s p ices which may ep esen a p oblem o p o ligacy by he Eu opean oo ball clubs. T ans e ees paid by he club a e in luenced by he ans e ma ke alue o oo ball playe s which p o ides an es ima ion o he amoun o money ha a club can sell he oo ball playe con ac o ano he oo ball club. T ans e ma ke alue is ex emely used in ans e nego ia ions be ween clubs and oo ball playe s. I is also used o e i y i he oo ball playe has a ai p ice. Ne e heless, i is di icul o de ine he ma ke alue o a oo ball playe as i depends on many ac o s (Op ean & Op ison, 2014). Recen esea ches s udied he ac o s ha in luence he playe s’ ans e ma ke alue in he op Eu opean leagues. Among se e al ac o s, An e (2019) concluded ha i depends o he pe o mance indica o s. These indica o s quan i y he di e en abili ies ha a playe de elop du ing a game and seasons. Howe e , oo ball is a collec i e spo whe e each indi iduali y occupies di e en posi ions and de ains se e al oles (Di Sal o e al., 2017; Hughes e al., 2012). This ac highligh s he impo ance 2 o he pe o mance indica o s selec ion when we p e end o analyse he ela ionship be ween hese indica o s and he playe s’ ans e ma ke alue. Despi e he ad ancemen s made on his ield, ew s udies conside ed he speci ica ion o each posi ion in he selec ion o he pe o mance indica o s and he ela ion ha hey ha e wi h he ans e ma ke alue. Addi ionally, due o he speci ic cha ac e is ics o he goalkeepe posi ion, hese playe s we e e en excluded om some esea ches. The e o e, his s udy p e ends o s udy he ela ion be ween he pe o mance indica o s o playe s and hei ma ke alue conside ing he ou posi ions g oups: goalkeepe s, de ende s, mid ielde s and a acke s. Fo his we use da a om he bes six anked compe i ions in Eu ope in he las h ee seasons – 2018/2019, 2019/2020 and 2020/2021. Once hese indica o s a y om season o season, we use Panel Da a eg essions o es ima e and analyse he ela ionship be ween hese a iables and he ans e ma ke alue. This s udy o e s ele an insigh s o he di e en oo ball agen s, no edly he ones ha ha e an ac i e ole in he Eu opean oo ball ans e ma ke . 3 2. Li e a u e Re iew 2.1 EUROPEAN FOOTBALL TRANSFER MARKET OVERVIEW In Eu ope, he oo ball ans e ma ke is cha ac e ized o be a ee ma ke whe e oo ball playe s mo e o any club i hey do no ha e any con ac ual ela ionship. Howe e , be o e 1995 Eu opean oo ball playe s we e unable o sign in o a new club wi hou he consen o he club ha de ain he con ac , e en when he con ac was expi ed. This si ua ion was sol ed by a ule known as Bosman, which educed he powe o he clubs in he ascendency o he oo ball playe s (Op ean & Op ison, 2014). A e 2001, Eu opean oo ball ans e s become limi ed by wo di e en pe iods: he summe and he win e windows. The mon hs ha hese wo windows comp ise depend on he compe i ion. In 2001, he Eu opean Commission, h ough he commissione Ma io Mon i, limi ed he maximum du a ion o a oo ball playe con ac o i e yea s. Diel e al. (2008) a gue ha hese e en s inc eased he eedom o mo emen s o playe s and esul ed in he inc ease o he oo ball clubs ma ke powe in Eu ope. In he oo ball ans e ma ke , he goal is o de ec he mos p omise playe s soone han he opponen s. Usually, hey a e iden i ied by p o essionals called scou s ha a e esponsible o disco e ing he bes and mos p omise playe s, some imes in ea lie s ages. Ano he impo an ole in his ma ke is he oo ball agen . On one hand, he ep esen s a oo ball playe and is esponsible by nego ia ing con ac s o achie e he bes ou come o hei clien s. On he o he hand, he agen can also ep esen he clubs in o de o ill hei needs wi hin new playe s. Bo h scou s and agen s ha e a key ole in he acquisi ion and disposal o playe s in ans e ma ke by he clubs. In 2019, he e we e comple ed mo e han 12 housand ans e s in Eu ope, which ep esen mo e han 68% o he o al ans e s in he wo ld (FIFA, 2019). CIES Foo ball Obse a o y analysed he ou goings o oo ball clubs om he i e mos ele an Eu opean leagues in he las nine yea s. Du ing his pe iod, hey e i ied ha he in es men s made on new playe s ha e g own mo e han ou imes (Poli e al., 2019). Manches e Ci y, a club om he P emie League, has in es ed mo e han 1.6 billion eu o in new playe s since 2010. F. C. Ba celona, Chelsea F. C., Pa is S -Ge main (PSG) and Ju en us spen mo e han one billion eu os du ing he same pe iod. In 2019, he majo pa o oo ball clubs om he bes anked leagues in Eu ope showed a nega i e ne balance alue (FIFA, 2019). In o he wo ds, he alue ha he op Eu opean clubs spen in oo ball ans e s was highe han hei season e enues. Since 2009, UEFA Financial Fai Play Regula ion (FFP) has imposed a se o inancial ules o b ing a ionali y o Eu opean oo ball clubs inances. This ule de ends ha oo ball clubs should keep hei playe s’ expendi u es wi hin he e enues ob ained om he se e al oo ball club ac i i ies du ing a pe iod o h ee inancial yea s (UEFA, 2018). As we can see, his ule is no being ollowed by some oo ball clubs and, ecen ly, UEFA accused Manches e Ci y o b oken FFP and ied o penalize his oo ball club abolishing i om he UEFA Champions League compe i ion (Conn, 2020). Ano he ele an ac om he Eu opean ans e ma ke is he inc easing p ice o e he las yea s. Acco ding o FIFA (2019), he a e age playe s’ p ice has inc eased mo e han 50% since 2011. Howe e , Poli e al. (2020) es ima es ha i has inc eased 15% pe yea since 2010, eaching he peak o 26% in 2017. 4 In 2016, Paul Pogba, a F ench oo ball playe was he i s oo ball playe o be ans e ed by 100 million eu os and in 2017, he B azilian playe Neyma u ned in he mos expensi e playe in he oo ball his o y, wi h a ans e p ice highe han 200 million eu os (Lowe & Aa ons, 2017). These e en s con ibu ed o he hype in la ion o oo ball ans e p ices (Magee, 2017). Foo ball clubs hi e hese s a s wi h he expec a ion o inc easing he oo ball eam pe o mance in bo h spo s and inancial dimensions. Ye , oo ball clubs mus ensu e ha he es ima ed gains compensa e he as in es men made, pa icula ly in spo s dimension. 2.2 FOOTBALL PLAYER MARKET VALUE The oo ball ma ke is cha ac e ized by a high le el o in o ma ion asymme y, because he oo ball club does no know an exac assessmen o he o e all index o abili ies and laws o a ce ain playe and canno be assu ed o he playe s pe o mance (Op ean & Op ison, 2014). Addi ionally, i is di icul o e alua e i he oo ball playe s’ ma ke alue is adjus ed o he spo and inancial bene i s ha he oo ball playe will b ing o he club ha hi ed him. Addi ionally, i is ha d o ind public in o ma ion ega ding his heme. T ans e ma k 1 is one o he ew sou ces ha es ima es he oo ball playe s ans e ma ke alue. Based on a c owdsou cing model, use s can p opose a alue o a oo ball playe based on hei pe o mance and discuss he es ima e p oposed wi h he o he membe s o he communi y. Al hough T ans e ma k uses a hie a chical app oach – no all he use s es ima ion ha e an equal alue – he e a e some limi a ions associa ed o his model: membe s do hei es ima ing ma ke alues based on a bi a y indica o s, i is no possible o ep oduce he model and canno be upda ed ma ch by ma ch, use s end o bene i he mos known playe s and inally, once he alues a e public, his model does no o e a compe i i e ad an age o oo ball clubs in ans e nego ia ions (Mülle e al., 2017). Howe e , ecen esea ches on he oo ball ans e ma ke ield we e based on he in o ma ion p o ided by his websi e (He e al., 2015; An e, 2019; Mülle e al., 2017; Ruijg & Ophem, 2015; S anoje ic & Gya ma i, 2016; Rod iguez, 2020). Acco ding o An e (2019), he ma ke alue o a oo ball playe can be explained by h ee indica o s: playe s cha ac e is ics, indi idual and collec i e pe o mance indica o s and playe s popula i y. In he las yea s, some s udies iden i ied he ac o s ha in luence he ans e ee, he sala ies and he ans e ma ke alues. Acco ding o B yson e al. (2012) he playe s’ sala ies a e in luenced by he same ac o s ha in luence he ans e ee o he ans e alue. 2.2.1 Playe s Cha ac e is ics Foo ball playe s cha ac e is ics encompass he in insic a ibu es ha do no depend on he playe s pe o mance. Some s udies sugges ha age ep esen s a p oxy o expe ience and po en ial o a oo ball playe ma ke alue (Ca michael & Thomas, 1993). Some au ho s a gue ha he oo ball playe ma ke alue inc ease in o hei mid- wen ies and declines he e o e (B yson e al., 2012; Lehmann & Schulze, 2008). O he esea ches ela e he sala ies and he age o he oo ball playe s sugges ing ha a e he 28 yea s, oo ball playe s sala ies end o dec ease, ega ding he dec easing o physical pe o mance and he g ea e suscep ibili y o ha ing an inju y (Luci o a & Simmons, 2003). This pa e n is no shown in leagues ha a e no so ma u e, whe e oo ball clubs o e a as sala y o playe s a he end o hei ca ee – which is he case o U. S. Majo League Socce (Kue he & Mo amed, 2010). Felipe e al. (2020) show ha he bi h mon h o oo ball playe s may a ec hei ma ke alue, 1 A ailable in h ps://www. ans e ma k .com/ 11 Table 5 – Goalkeepe s da a desc ip i e s a is ics 4.2.2 De ende s This da ase is composed by 2497 obse a ions and 1352 di e en playe s. The a e age ma ke alue o de ende s is 9,1 million eu os wi h a s anda d de ia ion o 12,5 million eu os. We obse e ha on a e age he de ende s won 0,051 de ensi e duels pe minu e, conque ed 0,023 ae ials duels pe minu e, execu ed 0,009 ackles and in e cep ed 0,01 shoo s pe minu e. The playe s ep esen ed in his da ase ca ied ou 0,013 ouls pe minu e. The subsequen able exposes all he measu es ela ed wi h he de ende s’ da ase a iables. Table 6 – De ende s da a desc ip i e s a is ics 4.2.3 Mid ielde s Mid ielde s da ase has 2442 obse a ions wi h a ound 1396 di e en playe s. On a e age, hey ha e a 12,5 million eu os ma ke alue wi h a s anda d de ia ion o 16,9 million eu os. The maximum alue o he playe s o his posi ion is 180 million eu os. Mid ielde s achie ed on a e age 0,001 assis s, did 0,0139 ackles and played 0,079 c osses pe minu e and season. The playe s om his posi ion won an a e age o 0,06 de ensi e duels and 0,05 o ensi e duels pe minu e and season. The ollowing able Va iable Measu emen Mean Median S anda d De ia ion Min Max Ma ke alue Million Eu os 6,419 4 6,965 0,050 35 Co ec passes pe minu e To al p.m.s. 0,169 0,160 0,050 0,0656 0,375 De ensi e duels won pe minu e To al p.m.s. 0,014 0,001 0,025 0 0,098 Ae ials duels won pe minu e To al p.m.s. 0,003 0,004 0,005 0 0,012 S ops pe minu e To al p.m.s. 0,719 0,690 0,367 0,077 1,734 Concei ed goals pe minu e To al p.m.s. 0,015 0,015 0,004 0,005 0,030 Games wi hou concei ing goals Games p.s. 5,634 5 3,767 0 18 Fouls pe minu e To al p.m.s 0,014 0 0,024 0 0,096 P e en ed goals pe minu e To al p.m.s. 0 0 0,003 -0,009 0,009 Exis s pe minu e To al p.m.s. 0,015 0,015 0,005 0 0,037 To al p.m.s. – To al pe minu e and season; Games p.s. – Games pe season; N = 421 Va iable Measu emen Mean Median S anda d De ia ion Min Max Ma ke alue Million Eu os 9,099 4 12,477 0 110 Co ec passes pe minu e To al p.m.s. 0,446 0,411 0,167 0,133 1,472 De ensi e duels won pe minu e To al p.m.s. 0,051 0,048 0,018 0,015 0,164 Ae ials duels won pe minu e To al p.m.s. 0,023 0,021 0,013 0 0,155 Tackles pe minu e To al p.m.s. 0,009 0,005 0,017 0 0,142 In e cep ed shoo s pe minu e To al p.m.s. 0,010 0,005 0,020 0 0,174 Fouls pe minu e To al p.m.s. 0,013 0,012 0,007 0 0,084 Goals pe minu e To al p.m.s 0 0 0 0 0,008 Assis s pe minu e To al p.m.s. 0 0 0 0 0,007 Shoo s on a ge pe minu e To al p.m.s. 0,002 0,001 0,001 0 0,010 Success c osses pe minu e To al p.m.s. 0,009 0,005 0,014 0 0,130 Success d ibbles pe minu e To al p.m.s. 0,012 0,007 0,015 0 0,200 O ensi e duels won pe minu e To al p.m.s. 0,019 0,014 0,018 0 0,322 Accele a ions pe minu e To al p.m.s. 0,013 0,006 0,020 0 0,176 To al p.m.s. – To al pe minu e and season; N = 2497 12 shows in de ail he mean, median, s anda d de ia ion, minimum and maximum alue o he o he pe o mance indica o s and he nume ical a iables. Table 7 – Mid ielde s da a desc ip i e s a is ics 4.2.4 A acke s This subse is composed by 1118 obse a ions and 663 di e en a acke s. These playe s ha e a ans e ma ke alue a e age o 16 million. The maximum alue is 200 million eu os, he highes conside ing all posi ion g oups. On a e age hey sco ed 0,0036 goals pe minu e and execu ed 0,0103 shoo s pe minu e. These playe s usually win 0,06 o ensi e duels pe minu e and de elop 0,02 accele a ions pe minu e. These and o he nume ical measu es a e shown in he succeeding able. Table 8 – A acke s da a desc ip i e s a is ics Va iable Measu emen Mean Median S anda d De ia ion Min Max Ma ke alue Million Eu os 12,466 6 16,888 0 180 Co ec passes pe minu e To al p.m.s. 0,491 0,440 0,221 0,094 2,152 De ensi e duels won pe minu e To al p.m.s. 0,057 0,052 0,024 0,011 0,199 Ae ials duels won pe minu e To al p.m.s. 0,017 0,013 0,014 0 0,127 Tackles pe minu e To al p.m.s. 0,014 0,006 0,0247 0 0,185 In e cep ed shoo s pe minu e To al p.m.s. 0,018 0,002 0,038 0 0,267 Fouls pe minu e To al p.m.s. 0,022 0,019 0,012 0 0,151 Goals pe minu e To al p.m.s 0,001 0,001 0,001 0 0,010 Assis s pe minu e To al p.m.s. 0,001 0,001 0,001 0 0,008 Shoo s on a ge pe minu e To al p.m.s. 0,005 0,004 0,004 0 0,027 Success c osses pe minu e To al p.m.s. 0,008 0,005 0,010 0 0,163 Success d ibbles pe minu e To al p.m.s. 0,027 0,020 0,025 0 0,261 O ensi e duels won pe minu e To al p.m.s. 0,051 0,043 0,036 0,003 0,368 Accele a ions pe minu e To al p.m.s. 0,018 0,013 0,018 0 0,166 To al p.m.s. – To al pe minu e and season; N = 2442 Va iable Measu emen Mean Median S anda d De ia ion Min Max Ma ke alue Million Eu os 16,076 7 24,140 0 200 Co ec passes pe minu e To al p.m.s. 0,288 0,246 0,152 0,075 1,272 De ensi e duels won pe minu e To al p.m.s. 0,035 0,029 0,023 0,002 0,203 Ae ials duels won pe minu e To al p.m.s. 0,036 0,025 0,036 0 0,289 Tackles pe minu e To al p.m.s. 0,030 0,027 0,016 0,004 0,125 In e cep ed shoo s pe minu e To al p.m.s. 0,024 0,002 0,045 0 0,272 Fouls pe minu e To al p.m.s. 0,025 0,021 0,017 0 0,130 Goals pe minu e To al p.m.s 0,130 0,003 0,002 0 0,017 Assis s pe minu e To al p.m.s. 0,001 0,001 0,001 0 0,009 Shoo s on a ge pe minu e To al p.m.s. 0,010 0,010 0,004 0 0,031 Success c osses pe minu e To al p.m.s. 0,007 0,004 0,014 0 0,255 Success d ibbles pe minu e To al p.m.s. 0,029 0,023 0,024 0 0,231 O ensi e duels won pe minu e To al p.m.s. 0,061 0,053 0,035 0,006 0,317 Accele a ions pe minu e To al p.m.s. 0,016 0,011 0,020 0 0,254 To al p.m.s. – To al pe minu e and season; N = 1118 13 5. Resul s In o de o decide which model o use o each da ase , we pe o med he Hausman Tes . This es esul s show he exis ence o endogenei y o all g oup posi ions (see he ollowing able), and o his eason he null hypo hesis can be ejec ed. Consequen ly, we an he FE eg ession o he exis ing da ase s. Table 9 – Hausman Tes esul s pe Posi ion G oup Posi ion G oup p- alue Chi-Squa ed Deg ees o F eedom Goalkeepe s < 0,00001 64,986 11 De ende s < 0,00001 196,714 14 Mid ielde s 1,00 -4452,986 14 A acke s < 0,00001 771,249 14 5.1 GOALKEEPERS A e pe o ming he FE eg ession wi h he ime (seasons) and en i y e ec s (playe s’ id), he esul s exp essed ha he es ima ed a iables coe icien s a e no s a is ically signi ican . As we e i y in he model esul s, he p- alue a iables a e highe han 0,05 o a 95% o con idence, which means ha he goalkeepe s pe o mance indica o s selec ed do no ha e in luence on he ans e ma ke alue o goalkeepe s. Al hough, he same si ua ion does no occu o he a iable games wi hou concei ing goals. FE model esul s e eal ha an inc ease o one game wi hou concei ing a goal will lead o a 20% o inc easing in he playe ans e ma ke alue. This coe icien alue demons a es a posi i e co ela ion be ween his pe o mance indica o and he ans e ma ke alue. The coe icien and espec i e p- alue o each a iables a e illus a ed in he ollowing able. Table 10 – Fixed E ec eg ession esul s ime and en i y e ec s o Goalkeepe s Pe o mance Indica o Coe icien P- alue Co ec Passes pe minu e 2,0131 0,7866 De ensi e Duels won pe minu e 7,3178 0,3881 Ae ial Duels won pe minu e 102,08 0,5683 S ops pe minu e 1,2767 0,2223 Concei ed Goals pe minu e -41,544 0,6107 Fouls pe minu e 15,417 0,0943 Exi s pe minu e -79,322 0,3363 Games wi hou concei ing goals 0,2099 0,0447 The o he s s a ic panel da a models’ esul s can be obse ed in Appendix 4. 5.2 DEFENDERS The FE eg ession esul s wi h ime and en i y e ec s (de ende and season yea ) illus a e ha he mos pa o he a iables do no ha e signi ican in luence on he ans e ma ke alue o he de ende playe s. Al hough, he same does no occu o he a iables co ec passes, de ensi e duels won, ae ials duels won and shoo s on a ge pe minu e. All hese a iables show a p- alue lowe han 0,05 and as consequence, an in luence on he dependen a iable unde obse a ion. The esul s 14 demons a e ha an inc emen o one co ec pass pe minu e will lead o a ise o ou million eu os in he de ende ma ke alue. As An e (2019) e e ed, his s udy also demons a es a posi i e co ela ion be ween his pe o mance indica o and he de ende s’ ma ke alue. The coe icien s o he de ensi e and ae ial duels won pe minu e e eal a con adic o y esul . Acco ding o he model esul s, an inc emen o one de ensi e duel won pe minu e will lead o a dec ease o 38 million eu os in he playe ans e ma ke alue. The same happens o he ae ial duels won pe minu es, e ealing a nega i e co ela ion wi h he playe ans e ma ke , con a ily o wha was e e ed by An e (2019). Conside ing he posi ion unde analysis, hese esul s do no di ulge he expec ed ou pu . This model also sugges s ha an inc emen o one shoo on a ge by minu e by a de ensi e playe , will lead o a gain o 363 million eu os in he ans e ma ke alue o he de ensi e playe s. The coe icien s and espec i e p- alue a e illus a ed in he ollowing able. Table 11 – Fixed e ec s eg ession esul s ime and en i y o De ende s Pe o mance Indica o Coe icien P- alue Co ec Passes pe minu e 4,2284 0,0025 De ensi e Duels won pe minu e -38,773 0,0029 Ae ial Duels won pe minu e -45,073 0,0269 Tackles pe minu e 11,820 0,1320 In e cep ed Shoo s pe minu e 6,1222 0,3667 Fouls pe minu e -51,684 0,1166 Goals pe minu e -235,05 0,3723 Assis s pe minu e 129,70 0,5198 Shoo s on Ta ge pe minu e 363,5 0,0081 Success C osses pe minu e -5,1332 0,5990 Success d ibbles pe minu e -17,175 0,2457 O ensi e duels won pe minu e 20,946 0,3488 Accele a ions pe minu e 9,6713 0,1749 The esul s o he o he panel da a models a e a ailable in Appendix 5. 5.3 MIDFIELDERS The FE eg ession esul s expose some pe o mance indica o s wi h a signi ican in luence on he mid ielde s ans e ma ke alue. Acco ding o hem and as expec ed, he goals and assis s ha e a posi i e co ela ion wi h he a ge a iable. An inc emen o a goal pe minu e lead o he inc easing o 941 million eu os in he mid ielde ma ke alue. The same inc emen le el on assis s pe minu e e lec s on a gain o mo e han 880 million eu os in ma ke alue o he playe . This model also con i ms he impo ance ha hese wo pe o mance measu es, pa icula ly he assis s pe minu e, ha e in he mid ielde ole. Al hough, hese esul s demons a e ha he impac o goals in he mid ielde s’ ans e ma ke is highe compa ing o assis s pe minu e. Thus, as Simmons (2003) e e ed o a acke s, he same e i y o mid ielde s. Ano he a iable ha ha e a posi i e co ela ion wi h he playe ans e alue is he o ensi e duels won pe minu e. Con a ily, he success d ibbles pe minu e a ec nega i ely he ans e ma ke alue o a mid ielde om he op six Eu opean oo ball leagues. The coe icien s a e exposed in he ollowing able. 15 Table 12 – Fixed e ec s eg ession esul s ime and en i y o Mid ielde s Pe o mance Indica o Coe icien P- alue Co ec Passes pe minu e -2,2917 0,1370 De ensi e Duels won pe minu e -19,004 0,1761 Ae ial Duels won pe minu e -28,059 0,2594 Tackles pe minu e 7,2534 0,3075 In e cep ed Shoo s pe minu e 4,4108 0,3767 Fouls pe minu e -47,086 0,0945 Goals pe minu e 941,29 0 Assis s pe minu e 883,26 0 Shoo s on Ta ge pe minu e 120,24 0,1940 Success C osses pe minu e 24,504 0,2966 Success d ibbles pe minu e -82,695 0,0174 O ensi e duels won pe minu e 54,014 0,0310 Accele a ions pe minu e -15,269 0,1827 The o he esul s can be consul ed in he Appendix 6. 5.4 ATTACKERS Acco ding o he esul s o he FE eg ession, only one a iable has impac on he ans e ma ke alue om he a acke s’ playe s ha ing a signi icance le el highe han 0,05 o a 95% o con idence. The a iable is he a acke s’ pe o mance measu e mo e aluable: goals pe minu e. Acco ding o he eg ession, his measu e has a posi i e co ela ion wi h he a ge a iable. An inc emen o one goal pe minu e conduc s o aise o mo e han 640 million eu os in he playe ma ke alue. This esul highligh s he impo ance o his measu e in he ma ke alue o he playe s o his posi ion g oup con i ming he esul s p oduced by p e ious esea ches (Ca michael e al., 1999; B yson e al., 2012; Ca michael & Thomas, 1993; Ge a d & Dobson, 2000; Luci o a & Simmons, 2003; Dobson e al., 2000). The coe icien s o hese and o he pe o mance indica o s a e desc ibed in he ollowing able. Table 13 – Fixed e ec s eg ession esul s ime and en i y o A acke s Pe o mance Indica o Coe icien P- alue Co ec Passes pe minu e -6,7001 0,2704 De ensi e Duels won pe minu e -54,444 0,1129 Ae ial Duels won pe minu e -22,282 0,3813 Tackles pe minu e -36,863 0,3698 In e cep ed Shoo s pe minu e -3,6251 0,6147 Fouls pe minu e -36,486 0,3673 Goals pe minu e 646,00 0,0049 Assis s pe minu e 362,94 0,2587 Shoo s on Ta ge pe minu e -17,711 0,8984 Success C osses pe minu e 14,107 0,6552 Success d ibbles pe minu e 75,688 0,1974 O ensi e duels won pe minu e 21,744 0,5760 Accele a ions pe minu e 14,960 0,4422 The o he model esul s’ can be e i ied in he Appendix 7. 16 6. Conclusion This s udy exposes he ela ionship be ween speci ic pe o mance indica o s and he ans e ma ke alue conside ing he posi ion g oup ha oo ball playe s occupy in he pi ch. I also con i ms he ela ionship be ween hese measu es and he playe s’ ma ke alue e e ed by p e ious esea ches and in oduces new indica o s, ne e s udied be o e. A e ga he ing da a om he op six Eu opean leagues in he las h ee seasons, we applied he Fixed E ec s eg ession in o de o iden i y he coe icien s and he co ela ion be ween hese measu es and he a ge a iable, he ans e ma ke alue. As we a e only conside ing speci ic oo ball leagues and he oo ball ans e ma ke is dynamic, he da ase s used a e unbalanced. Despi e he ac ha mos o he a iables e ealed a e s a is ically insigni ican , we e i ied ha some in luence he ans e ma ke alue o he playe s. Fo goalkeepe s, we con i med ha he games wi hou concei ing a goal ha e a posi i e co ela ion wi h hei ans e ma ke alue, inc easing i in 20%. Fo he i s ime, his esea ch conside ed he speci ici ies o his posi ion and p oduced he eg ession model wi h pe o mance measu es adap ed o goalkeepe s’ cha ac e is ics. Acco ding o he s udy esul s, he e is a posi i e co ela ion be ween he co ec passes and he de ende s ma ke alue. This ou pu highligh s he impo ance o his indica o in he de ende playe e alua ion and he impac ha hey ha e in he game cons uc ion. I is also con i med ha shoo s on a ge pe minu e ha e a posi i e e ec in he ans e ma ke alue o de ende s. Con a y o wha was expec ed, he esul s demons a e a nega i e co ela ion be ween he de ensi e and ae ials duels won pe minu e and he playe ma ke alue. Mid ielde s demons a e a posi i e co ela ion be ween hei ans e ma ke alue and he goals and assis s pe minu e. Howe e , esul s co obo a e ha he goals pe minu e ha e a highe impac on mid ielde s’ alue. O he measu e ha in luences posi i ely his alue is he o ensi e duels won pe minu e. Ye , he success d ibbles pe minu e a ec nega i ely hei alue. Finally, his s udy suppo s he impo ance o goals in he a acke s ans e alue. As s a ed in his esea ch, an inc emen o a goal pe minu e inc eases in mo e han 600 million eu os he a acke ans e ma ke alue. The main limi a ions o his in es iga ion a e ela ed wi h he numbe o seasons analysed and oo ball leagues conside ed. I was in e es ing o englobe in his esea ch o he Eu opean na ional leagues and playe s’ da a om mo e han h ee seasons. Foo ball is a collec i e spo whe e each playe has a speci ic ole. Fo his eason, u u e esea ch should analyse he ela ionship be ween he pe o mance measu es and he speci ic posi ion om a ce ain posi ion g oup. A s udy o his ype allows o in es iga e he exis ing di e ences be ween he oles o , o ins ance, de ende s. The insigh s p oduced could help o dis inguish he ela ionship be ween he pe o mance indica o s and he ans e ma ke o winge s o Cen e de ende s. Ano he impo an componen migh be s udying he ela ionship be ween he ans e ma ke alue and he popula i y measu es, like social ne wo k da a. In an age whe e oo ball clubs ac like companies, wi h a s ong ma ke ing componen , he acquisi ion o a oo ball playe can ha e an impac in comme cial ac i i ies. 17 E e y oo ball game is unp edic able, like some ans e s a e no comp ehensible o he de ou suppo e s. Howe e , da a analy ics is becoming mo e ele an when i comes o p oduce insigh s ha will hold he decisions o all s akeholde s in ol ed. This s udy is jus one mo e example ha in ends o ein o ce he decisions o he agen s in ol ed in he oo ball ans e ma ke alue. The esul s p oduced e eal o he oo ball clubs and oo ball agen s he impac o some pe o mance measu es in he playe s’ ans e ma ke alue pe posi ion g oup suppo ing he decisions o signing a con ac wi h a new oo ball playe . 18 7. Bibliog aphy Ami , E., & Li ne, G. (2005). Accoun ing, Valua ion and Du a ion o Foo ball Playe Con ac s. Jou nal o Business Finance & Accou ing, 32 (3) & (4), pp. 549-586. An e, L., (2019). De e minan s o T ans e s Fees: E idence om he Fi e Majo Eu opean Foo ball Leagues. 10.13140/RG.2.2.18356.91526/1. B yson, A., F ick, B., & Simmons, R. (2012). The e u ns o sca ce alen : oo edness and playe emune a ion in Eu opean socce . Jou nal o Spo s Economics, 14 (6), 606–628. Ca ling, C., W igh , C., Nelson, L.J. and B adley, P.S. (2014) Commen on ‘Pe o mance analysis in oo ball: A c i ical e iew and implica ions o u u e esea ch’. Jou nal o spo s sciences 32, 2- 7. Ca michael, F., & Thomas, D. (1993). Ba gaining in he ans e ma ke : heo y and e idence. Applied Economics, 25(12), 1467-1476. Ca michael, F., Fo es , D., & Simmons, R. (1999). The labou ma ke in associa ion oo ball: who ge s ans e ed and o how much? Bulle in o Economic Resea ch, 51 (2), 125–150. Conn, D. (2020). Manches e Ci y banned om Champions League o wo seasons. The Gua dian. Re ie ed Decembe 12, 2020 om h ps://www. hegua dian.com/ oo ball/2020/ eb/14/manches e -ci y-banned- om- champions-league- wo-seasons- p-ue a Deloi e. (2020). Eye on he p ize Foo ball Money League. Deloi e Spo s Business G oup. Re ie ed Decembe 12, 2020, om h ps://www2.deloi e.com/con en /dam/Deloi e/uk/Documen s/spo s-business- g oup/deloi e-uk-deloi e- oo ball-money-league-2020.pd . Di Sal o, V., Ba on, R., Tschan, H., Calde on Mon e o, J., Bachl, N., Pigozzi, F., (2007). Pe o mance Cha ac e is ics Acco ding o Playing Posi ion in Eli e Socce . In e na ional jou nal o spo s medicine. 28. 222-7. 10.1055/s-2006-924294. Diel , H. M, F anck, E. & Lang, M. (2008). Why Foo ball Playe s may bene i om he “Shadow o he T ans e Sys em”. Eu opean Jou nal o Law and Economics, 26, pp. 129-151. Dobson, S., Ge a d, B., & Howe, S. (2000). The de e mina ion o ans e ees in English nonleague oo ball Applied Economics, 32(9), 1145-1152. Fédé a ion In e na ionale de Foo ball Associa ion. (2019). Global T ans e Ma ke Repo 2019 (Men P o essional Foo ball). Re ie ed Decembe , 12, 2020, om h ps:// esou ces. i a.com/image/upload/global- ans e -ma ke - epo -2019- men.pd ?cloudid=x2w qjs wjoailnncnod Fédé a ion In e na ionale de Foo ball Associa ion. (2020). FIFA Membe Associa ions. Re ie ed Decembe 12, 2020, om h ps://www. i a.com/associa ions/. 19 Feess, E., & Muehlheusse , G. (2003). The impac o ans e ees on p o essional spo s: an analysis o he new ans e sys em o Eu opean oo bal Scandina ian Jou nal o Economics, 105(1), 139- 1. Felipe, J. L. Fe nandez-Luna, A., Bu illo, P., de la Ri a, L. and Sánchez-Sánchez, J. and Ga cía-Unanue, J. (2020). Money Talks: Team Va iables and Playe Posi ions ha Mos In luence he Ma ke Value o P o essional Male Foo balle s in Eu ope. Sus ainabili y. 12. 3709. 10.3390/su12093709. F anck, E., & Nüesch, S (2008). Mechanisms o Supe s a Fo ma ion in Ge man—Empi ical E idence. Eu opean Spo Managemen Qua e ly, 8, 2008, 145–164. F ick, B. (2007). The Foo ball Playe s' Labo Ma ke : Empi ical E idence om he Majo Eu opean Leagues. Sco ish Jou nal o Poli ical Economy, 54(3), 422-446. F y, T. R. L., Galanos, G., & Posso, A. (2014). Le ’s ge Messi? Top-sco e p oduc i i y in he Eu opean Champions League. Sco ish Jou nal o Poli ical Economy, 61 (3), 261–279. Ga cia-del-Ba io, P., & Pujol, F. (2007). Hidden monopsony en s in winne - ake-all ma ke s–Spo and economic con ibu ion o Spanish socce playe s. Manage ial and Decision Economics, 28 (1), 57–70. Ge a d, B., & Dobson, S. (20 0 0). Tes ing o monopoly en s in he ma ke o playing alen –E idence om English p o essional oo bal Jou nal o Economic S udies, 27 (3), 142–164. He, M., Cachucho, R., & Knobbe, A. (2015). Foo ball playe ’s pe o mance and ma ke alue. In P oceedings o he 2nd wo kshop o spo s analy ics, Eu opean Con e ence on Machine Lea ning and P inciples and P ac ice o Knowledge Disco e y in Da abases (ECML PKDD). Re ie ed Ma ch 14, 2017, om h ps://www. esea chga e.ne /publica ion/321623604_Foo ball_playe 's_pe o mance_and_ ma ke _ alue. Hend iks, I. (2017). Modelling he ans e p ices o oo ball playe s (Mas e 's hesis, Tilbu g School o Economics and Managemen Tilbu g Uni e si y, Tilbu g, Ne he lands). Re ie ed om h p://a no.u .nl/show.cgi? id=144559 He m, S., Callsen-B acke , H. M., & K eis, H. (2014). When he c owd e alua es socce playe s’ ma ke alues: Accu acy and e alua ion a ibu es o an online communi y. Spo Managemen Re iew, 17(4), 484-492. He old, M., Goes, F., Nopp, S., Baue , P., Thompson, C. and Meye , T. (2019) Machine lea ning in men’s p o essional oo ball: Cu en applica ions and u u e di ec ions o imp o ing a acking play. In e na ional Jou nal o Spo s Science & Coaching 1747954119879350. Hughes, M., Caud elie , T., James, N., Redwood-B own, A., Donnelly, I., Ki kb ide, A., Duschesne, C. (2012). Moneyball and socce - An analysis o he key pe o mance indica o s o eli e male socce playe s by posi ion. Jou nal o Human Spo and Exe cise. 7. 10.4100/jhse.2012.72.06. Kie e , S. (2014). The impac o he Eu o 2012 on popula i y and ma ke alue o oo ball playe s. In e na ional Jou nal o Spo Finance, 9(2), 95-111. 20 Ki schs ein, T., Liebsche , S. (2018). Assessing he ma ke alues o socce playe s – a obus analysis o da a om Ge man 1. and 2. Bundesliga. Jou nal o Applied S a is ics. 46. 1-14. 10.1080/02664763.2018.1540689. Kue he, Todd & Mo amed, Mesbah. (2009). Re u ns o S a dom: E idence om U.S. Majo League Socce . Jou nal o Spo s Economics. 11. 567-579. 10.1177/1527002509354268. Lehmann, E. E., & Schulze, G. (2008). Wha does i ake o be a s a ? The ole o pe o mance and he media o Ge man socce playe s. Applied Economics Qua e ly, 54 (1), 59–70. Lowe, S. & Aa ons, E. (2017). Neyma pledges o ‘coque he iles’ o PSG a e wo ld eco d £198m mo e. Re ie ed Decembe 12, 2020, om h ps://www. hegua dian.com/ oo ball/2017/aug/03/psg-neyma -buy-ou - ejec ed-la-liga- ba celona Luci o a, C., & Simmons, R. (2003). Supe s a e ec s in spo : e idence om I alian socce . Jou nal o Spo s Economics, 4 (1), 35–55. Magee, W. (2017). Fans a e al eady disconnec ed o m hei clubs – a summe o enzied ans e hype in la ion only makes i wo se. Re ie ed Decembe 12, 2020 om h ps://www.independen .co.uk/spo / oo ball/ ans e s/p emie -league-summe - ans e - window- eco d-spending-ne -spend- omelu-lukaku-paul-pogba-a7853226.h ml Medcal e, S. (2008). English league ans e p ices: is he e a acial dimension? A e-examina ion wi h new da a. Applied Economics Le e s, 15(11), 865-867. Mülle , O., Simons, A., Weinmann, M. (2017). Beyond C owd Judgmen s: Da a-d i en Es ima ion o Ma ke Value in Associa ion Foo bal Eu opean Jou nal o Ope a ional Resea ch. h ps://doi.o g/10.1016/j.ejo .2017.05.005 Op ean, V. B., Op ison T. (2014). Accoun ing o Socce Playe s: Capi aliza ion Pa adigm s. Expendi u e. P ocedia Economics and Finance, 15, pp. 1647-1654. Poli, R. M, Ra enelm L., Besson R. (2019). CIES Foo ball Obse a o y Mon hly Repo nº47 – Sep embe 2019 – Financial analysis o he ans e ma ke in he big 5 Eu opean leagues (2010-2019). Re ie ed Decembe , 15, 2020, om h ps:// oo ball-obse a o y.com/IMG/si es/m /m 47/en/ Poli, R. M, Ra enelm L., Besson R. (2020). The eal impac o COVID on he oo ball playe s’ ans e ma ke . Re ie ed Decembe , 15, 2020, om h ps:// oo ball- obse a o y.com/IMG/si es/m /m 58/en/ Richau, L., Folle , F., F enge , M., Em ich, E. (2019). Pe o mance indica o s in oo ball: The impo ance o ac ual pe o mance o he ma ke alue o oo ball playe s, in: Sciamus - Spo und Managemen 10(4), 41-67. Rod iguez, Ma ibel. (2020). Fac o analysis o he ma ke alue o high-pe o mance playe s o h ee majo Eu opean associa ion oo ball leagues. Managing Spo and Leisu e. 1-24. 10.1080/23750472.2020.1771197. Ruijg, J., Ophem, H. (2015). De e minan s o oo ball ans e s. Applied Economic Le e s, 22:1, 12-19. 27 # S o e alues o checking homoskedas ici y g aphically i ed als_pooled_OLS = pooledOLS_ es.p edic (). i ed_ alues esiduals_pooled_OLS = pooledOLS_ es. esids # 3A. Homoskedas ici y impo ma plo lib.pyplo as pl # 3A.1 Residuals-Plo o g owing Va iance De ec ion ig, ax = pl .subplo s() ax.sca e ( i ed als_pooled_OLS, esiduals_pooled_OLS, colo = 'blue') ax.axhline(0, colo = ' ', ls = '--') ax.se _xlabel('P edic ed Values', on size = 15) ax.se _ylabel('Residuals', on size = 15) ax.se _ i le('Homoskedas ici y Tes ', on size = 30) pl .show() ## PLOT - HOMOSKEDASTICITY TEST om s a smodels.s a s.diagnos ic impo he _whi e, he _b euschpagan pooled_OLS_da ase = pd.conca ([da ase , esiduals_pooled_OLS], axis=1) pooled_OLS_da ase = pooled_OLS_da ase .d op(['START_SEASON_YEAR'], axis = 1). illna(0) exog = sm. ools. ools.add_cons an (da ase [[ 'PLAYER_CORRECT_PASSES_PER_MINUTE', 'PLAYER_DEFENSIVE_DUELS_WON_PER_MINUTE', 'PLAYER_AERIEALS_WON_PER_MINUTE', 'PLAYER_TACKLES_PER_MINUTE', 'PLAYER_INTERCEPTED_SHOOTS_PER_MINUTE', 'PLAYER_FOULS_PER_MINUTE', 'PLAYER_GOALS_PER_MINUTE', 'PLAYER_ASSISTS_PER_MINUTE', 'PLAYER_SHOOTS_ON_THE_TARGET_PER_MINUTE', 'PLAYER_SUCCESS_CROSSES_PER_MINUTE', 'PLAYER_SUCCESS_DRIBLES_PER_MINUTE', 'PLAYER_OFFENSIVE_DUELS_WON_PER_MINUTE', 'PLAYER_ACCELARATIONS_PER_MINUTE' ]]). illna(0) # B eusch-Pagan-Tes b eusch_pagan_ es _ esul s = he _b euschpagan(pooled_OLS_da ase [' esidual'], exog) labels = ['BPT LM-S a ', 'BPT LM p- al', 'BPT F-S a ', 'BPT F p- al'] #p in (dic (zip(labels, b eusch_pagan_ es _ esul s))) ## BREUSH-PAGAN TEST RESULT # Non-Au oco ela ion # Du bin-Wa son-Tes om s a smodels.s a s.s a ools impo du bin_wa son du bin_wa son_ es _ esul s = du bin_wa son(pooled_OLS_da ase [' esidual']) p in (du bin_wa son_ es _ esul s) ## DURBIN-WATSON TEST RESULT # FE und RE model - h ps:// owa dsda ascience.com/a-guide- o-panel-da a- eg ession- heo e ics-and- implemen a ion-wi h-py hon-4c84c5055c 8 om linea models impo PanelOLS om linea models impo RandomE ec s exog = sm. ools. ools.add_cons an (da ase [['PLAYER_CORRECT_PASSES_PER_MINUTE', 'PLAYER_DEFENSIVE_DUELS_WON_PER_MINUTE', 'PLAYER_AERIEALS_WON_PER_MINUTE', 'PLAYER_TACKLES_PER_MINUTE', 'PLAYER_INTERCEPTED_SHOOTS_PER_MINUTE', 'PLAYER_FOULS_PER_MINUTE', 'PLAYER_GOALS_PER_MINUTE', 'PLAYER_ASSISTS_PER_MINUTE', 'PLAYER_SHOOTS_ON_THE_TARGET_PER_MINUTE', 'PLAYER_SUCCESS_CROSSES_PER_MINUTE', 'PLAYER_SUCCESS_DRIBLES_PER_MINUTE', 'PLAYER_OFFENSIVE_DUELS_WON_PER_MINUTE', 'PLAYER_ACCELARATIONS_PER_MINUTE']]) endog = da ase ['PLAYER_MARKET_VALUE_EUROS'] # FIXED EFFECT # ENTITY AND TIME EFFECTS model_ e = PanelOLS(endog, exog, en i y_e ec s = T ue, ime_e ec s = T ue) e_ es = model_ e. i () #p in ( e_ es) # RANDOM EFFECT model_ e = RandomE ec s(endog, exog) e_ es = model_ e. i () p in ( e_ es) # Hauman-Tes impo numpy.linalg as la om scipy impo s a s 28 # HAUSMAN TEST de hausman( e, e): b = e.pa ams B = e.pa ams _b = e.co _B = e.co d = b[np.abs(b) < 1e8].size chi2 = np.do ((b - B).T, la.in ( _b - _B).do (b - B)) p al = s a s.chi2.s (chi2, d ) e u n chi2, d , p al hausman_ esul s = hausman( e_ es, e_ es) p in ('chi-Squa ed: ' + s (hausman_ esul s[0])) p in ('deg ees o eedom: ' + s (hausman_ esul s[1])) p in ('p-Value: ' + s (hausman_ esul s[2])) 29 8.4 APPENDIX 4 Panel Da a Model Resul s o Goalkeepe s Pooled OLS Fixed E ec s Random E ec s Pe o mance Indica o Coe icien P- alue Coe icien P- alue Coe icien P- alue Co ec Passes pe minu e 11,804 0,0617 20,131 0,7866 10,129 0,0647 De ensi e Duels won pe minu e 31,118 0,0424 73,178 0,3881 20,117 0,0132 Ae ial Duels won pe minu e -123,26 0,5162 102,08 0,5683 -2,8656 0,9855 S ops pe minu e 2,5363 0,0314 12,767 0,2223 1,1651 0,1632 Concei ed Goals pe minu e -294,47 0,0022 -41,544 0,6107 -127,78 0,0634 Fouls pe minu e 6,6595 0,5698 15,417 0,0943 16,265 0,0589 Exi s pe minu e -213,36 0,0034 -79,322 0,3363 -153,62 0,0196 Games wi hou concei ing goals 0,2555 0,0844 0,2099 0,0447 0,2235 0,0164 8.5 APPENDIX 5 Panel Da a Model Resul s o De ende s Pooled OLS Fixed E ec s Random E ec s Pe o mance Indica o Coe icien P- alue Coe icien P- alue Coe icien P- alue Co ec Passes pe minu e 28,513 0 42,284 0,0025 12,674 0 De ensi e Duels won pe minu e -115,59 0 -38,773 0,0029 -58,023 0 Ae ial Duels won pe minu e -6,0677 0,806 -45,073 0,0269 -23,23 0,1441 Tackles pe minu e 8,1152 0,5909 11,820 0,1320 14,742 0,069 In e cep ed Shoo s pe minu e 13,25 0,1884 61,222 0,3667 6,8716 0,3008 Fouls pe minu e -269,92 0 -51,684 0,1166 -158,82 0 Goals pe minu e 1151,6 0,0044 -235,05 0,3723 255,31 0,3211 Assis s pe minu e 1751,8 0,0022 129,70 0,5198 690,84 0,0004 Shoo s on Ta ge pe minu e 759,86 0,0004 363,5 0,0081 529,61 0 Success C osses pe minu e -9,0257 0,5416 -51,332 0,5990 -5,3771 0,5789 Success d ibbles pe minu e -47,641 0,0005 -17,175 0,2457 -26,931 0,557 O ensi e duels won pe minu e 45,853 0,0337 20,946 0,3488 23,702 0,1418 Accele a ions pe minu e 9,2964 0,4146 96,713 0,1749 8,732 0,2106 30 8.6 APPENDIX 6 Panel Da a Model Resul s o Mid ielde s Pooled OLS Fixed E ec s Random E ec s Pe o mance Indica o Coe icien P- alue Coe icien P- alue Coe icien P- alue Co ec Passes pe minu e 25,201 0 -2,917 0,1370 9,6799 0 De ensi e Duels won pe minu e -85,02 0 -19,004 0,1761 -40,89 0,001 Ae ial Duels won pe minu e -1,5784 0,9502 -28,059 0,2594 -45,692 0,0167 Tackles pe minu e 7,5092 0,6074 72,534 0,3075 5,4408 0,4398 In e cep ed Shoo s pe minu e 0,9552 0,929 44,108 0,3767 5,867 0,2263 Fouls pe minu e -221,29 0 -47,086 0,0945 -148,73 0 Goals pe minu e 2439,2 0 941,29 0 1515,3 0 Assis s pe minu e 2266 0 883,26 0 1269,1 0 Shoo s on Ta ge pe minu e 486 0,0057 120,24 0,1940 245,57 0,0042 Success C osses pe minu e -180,23 0,0001 24,504 0,2966 -26,985 0,2224 Success d ibbles pe minu e 90,949 0,0772 -82,695 0,0174 -17,481 0,5672 O ensi e duels won pe minu e -68,955 0,0493 54,014 0,0310 10,178 0,6352 Accele a ions pe minu e -24,327 0,1432 -15,269 0,1827 -19,865 0,0796 8.7 APPENDIX 7 Panel Da a Model Resul s o A acke s Pooled OLS Fixed E ec s Random E ec s Pe o mance Indica o Coe icien P- alue Coe icien P- alue Coe icien P- alue Co ec Passes pe minu e 28,694 0,0001 -6,7001 0,2704 19,22 0 De ensi e Duels won pe minu e -133,1 0,0009 -54,444 0,1129 -113,05 0,0001 Ae ial Duels won pe minu e -23,077 0,1381 -22,282 0,3813 -39,119 0,0311 Tackles pe minu e -80,057 0,0905 -36,863 0,3698 -60,854 0,0966 In e cep ed Shoo s pe minu e -0,4787 0,9648 -36,251 0,6147 -0,6376 0,9314 Fouls pe minu e -214,45 0 -36,486 0,3673 -97,245 0,0072 Goals pe minu e 1169,3 0,0097 646,00 0,0049 697,58 0,0024 Assis s pe minu e 3407,7 0 362,94 0,2587 1262,6 0,0001 Shoo s on Ta ge pe minu e 1356,5 0 -17,711 0,8984 526,16 0,0001 Success C osses pe minu e -63,512 0,0256 14,107 0,6552 5,1267 0,8622 Success d ibbles pe minu e 214,53 0,0036 75,688 0,1974 180,22 0,0003 O ensi e duels won pe minu e -105,84 0,0357 21,744 0,5760 -76,851 0,025 Accele a ions pe minu e 21,796 0,3418 14,960 0,4422 12,501 0,5208 Page | i