Cristiano Ronaldo or Lionel Messi, who is more consistent in scoring goals? The evidence from CFM exploratory analysis

POST-PRINT acce pted for publication in M ovem ent & Sport Sciences - Science & M otr icité Cristiano Ronaldo or Lionel Messi, who is m ore consistent in sc oring goals? The evidence from CFM exploratory analysis Sams ul Anwar 1 ,* , S iti Munawa rah 2 , Radhiah Radhiah 3 1 ,2 Uni versitas Syiah Kuala, Department of Statist ic s, Banda A ceh , Indonesia 3 Uni versitas Syiah Kuala, Department of Mathematics, Banda Aceh, Indonesia Received 27 February 2024, Accepted 7 Novem ber 2025, Publish ed 29 Marc h 2026 Abs tr ac t - - The rivalry be twee n two f oot ball super stars Cris t i ano Ronal do and Li onel Mess i ha s alwa ys been a subject of extensive disc ussion. This s t ud y a imed to com pare the l evel of consis t e ncy b etween the two playe rs in sco r in g go als t hrough 6 way s: r i g ht -footed ki cks, l e f t - footed kicks , penal t y k icks, direct f r ee k i ck s, l o ng-range kicks, and headers. The dat a analy zed wa s the durat i o n of t ime ( minutes) each playe r too k to s core a goal in ever y match they played. The data was obtained f ro m a f o otball we bsite call ed Transfermarkt.com. Co m pet in g Failure Modes (CF M) was used to measure the reli a bili t y of t he two pl a yers in sco rin g goa ls based on t hose vario us ways . The resu l t s of CFM e xpl o rat ory ana lysis sh o wed that Ronal do an d Messi h ad the sa me l e vel of consis t e ncy in scor ing go als f or m o re t han 17 years of t hei r pro f e ssional f o ot ball career. Bot h hav e b ee n am o n g m o st ta l e nted players in the m o der n foot ball era w i t h individual and t eam achievem ents t hat are f ar a bove other footballers around the wo rl d . Keywords : compe t ing fail ure m o des, foot ball , go al sco r in g r eliabili t y , tr ansf ermarkt Résumé - Cristiano Ronaldo ou Lionel Messi, qui est le plus régul ier p our marquer des but s? Une preuve t irée des r ésu ltats de l’anal yse exploratoire CFM. La riv a li t é e ntre le s deux superstar s du f o o tball Cris tiano Ronal do et L i o nel Messi a t oujours fai t l' o bjet de nombreuses discussi o n s. Cett e étude visai t à co m parer le niveau de co héren ce e ntre les deux joueurs da ns la not ation des buts de 6 m a nières: coups de pi ed dro i t , coups de pi ed gauche, t i rs au but, co ups fran c s di r ects, coups de pi ed lointains et coups de t ête. Les do nn ées analysées ét ai e nt la dur ée (mi nut es) que chaque j o ueur m et t ai t pour marquer un but dans chaque m at ch qu 'il a d i sput é. Les donn ées o nt été o btenue s à part i r d'un site web de f ootball appel é T ransfermarkt.co m . Des Com pet i ng F ailure M o des ( CFM ) ont été utilisés pour m esurer la fi a bilité des deux j o ueurs à marquer des buts en f o nct i o n de ces diffé rentes maniè res. Les résul t ats de l' a nalyse expl o rato ire du CFM ont m ont ré que R o nal do et Mes s i avaient m ê me nivea u de régul ar i t é po ur ce qui est de marquer de buts pendant plus de 17 ans de leur carriè re de footballeur pro f essionne l . T ous deux compten t parm i l e s j o ueurs l es pl u s tal ent ueux de l'ère du f o otball moderne, av ec des réalisat ions individuelles et co ll ect iv es bien supérieures à celles des aut res footballe urs du monde. Mots clés: m o des de déf aillance co ncurrents, football , fiabili té des buts marqués , t ransf ermarkt *Corresponding author: sams ul.a nwa r @us k. ac.id This articl e has been peer-reviewe d and accepted for public at i o n in t he j o urnal “M ovement & Sport Sci e nces – Sci e nce & Motrici t é” on November 7, 2025. The j o urnal is cu rrently transi t i o ning to Episci ences, a diamond open access publishing platform , and t his arti cle wil l be made freely available on t he new website of t he journal at t he en d of t hi s t ransi t i o n. 2 1 Introductio n Football is the world's m o st popula r sport si nce it is pl a yed in a lm ost every country aro und the wor l d ( Busey & W ar in g, 2012 ). Th e worl d football f ed eration, F éd érat i o n Int ernati o nale de Football Associati on ( FIFA), est im at es t hat there are currently around 250 m il li o n football players and m o re t han 1.3 billi o n people in t erest ed in f oot ball ( Giulianott i et al ., 2021 ) . Every o ne in foot ball starting from gen era l managers and coachin g sta ff to fans and media are in terest ed in evaluat in g playe r ’s perfor m a nce ( Pelechrini s & Wins t o n, 2021 ). His t o ric a lly, f o otball has had many t alen t ed p lay ers who serve as ins pirational m ode ls f o r young f o ot ball ers and are st il l discussed a nd f o ll o wed to day . A f o ot ball legend is a p l a yer who man aged to carve his name in the f o ot bal l his tory books, not only b ased on his personal success records, but also for a t eam he played on. In t he m o dern era of foo tball in t he 21st century, there are t wo pl a yers w ho are a lways associ ated wi t h each other, nam e ly C r ist i a no Ronaldo and Li o nel Messi. Apa rt f ro m Ronal do and Messi, there are in deed se veral o ther fam o u s m o der n f o ot ball p layers such as Zlatan Ibrahim o vić, Ne ymar, Luis Suár ez, Moham ed Salah, Ro bert Lewa ndowski , K ar im Benzem a a nd ot hers. But al l t hese p layers hav e been rarely in the media spot li ght li ke Ro naldo and Messi since t hese two playe r s p layed on the well regarded Spanish La Li ga c lubs, namely Re al Madrid C.F. and FC Barce l o n a in 2009. Ac cord ing to Castañer et al . (2017) , both are c onsi d ered the best f o ot ball players ev er. Ronal do and Messi w ere l is ted as the m o st f oot ball er s to win the FIFA Best P layer award or known as t he FIFA Ball o n d' Or . F rom 2008 to 2023 , Mes s i won 8 times and Ronaldo 5 time s. In add i t i o n, t hes e two f o ot ball superstars have made numerous achiev ements. Base d on tro phi es at c l u b level, Messi has wo n 38 trophies w i th FC Barcel o na, Paris Sain t -Ger main F.C. a nd Inter M iami CF w hile Ronal do has won 31 tro phi e s t hroughout his career at sev era l clubs he has p layed f o r, in c luding S port in g CP, Manches t er Uni t ed F.C., Real Madrid C.F., Juv e ntus F .C. and Al Nassr FC. Furthermore, f o r t rophies with t he nat i onal t eam , Ronaldo succeede d in bringing Portugal to wi n two t rophies, n a m ely t he UEFA Euro 2016 Cup an d t he 2019 UEFA Na tions L eague. On the other hand, Mes s i m a naged to bring Argentina to win the Copa América (2021 and 2024) a nd t he 2022 W o rl d Cup. There are many o t her in d ividual a nd tea m ac hievemen ts of t he two playe r s t hat are not m e nt i o ned here. We can easily find it in their bi o grap hies which are published in vari o us exist ing li t erat ure. The debate o ver who is greater between Ronaldo and Messi w ill never stop until both h a ng up t hei r boot s. A cco rding to S he rgo l d (2016) , t he debate ab o ut t hese two f o ot ball superstars will neve r end. These t wo fi gures have be e n very attractive to t he football wo rld co mmuni t y . T ia go et al . (2016) claime d t hat f o r most athl et es includin g f o ot ball p layers, soc i a l media is a powerful t oo l to t ake advan t age of their t im e in the spotligh t. Fa ns of bot h wil l never t ire of cl a iming t hei r respective i do ls as the best one. A study by Kassing (2020) sh o wed t hat fans used in t er net sport s m e mes to beli t t le of their r iv a l oppo nen t s and idolize thei r o wn play er s. Based on the data c o ll ected in a sport, rese ar che r s are able to perform qua nti tat ive analysis on t he perf or mance of p layers and t eams ( Rahimi an & T oka, 2022 ). C o nsisten cy in showing the b est perf o r m a nce in every ma tch is an important i ndicato r in assessing t he career path of a professi o n a l foot ball player. In order to p rove who is m o re domi na nt b etween these two most fam o us p l a yers, sev eral sc ientifi c studies have b een conducted. A research by Castañer et al . (2016) usin g a p o lar c oo rdina te analy s is appro ach s hows t hat Messi is a p layer who is m o re dominant in using his lef t foot. Messi has excellent laterali t y skills (left-right brain balance ) as a f o otball player. Furt herm o re, Shergold ( 2016) , who c o nducted resea rch us ing desc r i pt i ve compa rat ive analysis w hen bot h p l a yed in t he Spanish La Li ga since t he 2009-10 season st ated t hat Messi mana ged to score 270 goals in 252 matches, p lay ed for 21,218 mi nut es and s hot 953 times . Ronaldo m a naged to sc or e 270 goals in 247 m at ches, playe d f o r 21,206 minutes and s hot 1,318 tim e s. The study sh o wed t hat Messi ha d a shot conv ersion rat e of 28. 77%, whil e Ronal do had 20. 03%. Apart f ro m having a high level of accuracy , bot h als o have unique ness in m o t o r s k ills t hat are diffe r ent from other football players. Magee ( 2025) sh o wed that h a vin g more attack in g pl a yers on the p i t ch will re sult a higher rat e of scoring goals, signifying the im po rtance of the f o rwards in helping the team to secure t he game . Various studies fro m several co mpe t i t io ns denoted around 40 to 50% of goals were sco red by at tacking players, indicating a consis tency in scor in g goal s is im po rtant and represen t t he abili t y of a f oot ball er , especially forwards, in adapting t he ch a nge t hat occurs fro m a season to sea son ( Acar et al ., 2009 ; M. Mi t rot asi os & A r matas, 2014 ; Μ. Mi t rot asi os et al., 2006 ). Whe re t he opponents they mi g ht have fa ced were likely als o changed in t er m s of t hei r p laye r co mpositi o n, st rategy implemented, l e vel of p lay , a nd so o n. Accord in g ly, it is important to m e asure t he level of consistency in scoring goals over a long per i o d of t ime as an in d icator to co m pare the professi o nal c areer pat hs of Ronaldo and Messi as f o rwards. Unf o rt unately , the pr evi o us st udi e s hav e not b een able to an swer who had m o re co nsi st ent performanc e betwe en Cristiano Ronal do and L i o n e l Me ssi during their entire careers as professi o nal f o o t ball players. The co mpa r is on carr ied out in t he fi r st study f o cused m o re on com par ing the physic al a bili t ie s between t he t wo players , while t he co mparison in t he seco nd study w as m o re directed at t he performanc e between the two playe r s t hrough a nalysis using aggregate data espe c i ally w hen both were pl a ying in La Liga, so that the concl usio ns obtain ed are not ver y accurat e and only app ly to that t im e per i o d. To sci ent ifically pro ve who had m or e consi stent perf o r m ance be t wee n Ronaldo an d Mess i , this stud y employed an alternative appro ach based on tim e intervals to score a goal . To t he bes t of o ur kn o wl edge, t hi s is t he f irst study app lying t his approach in measuring r eli a bili t y of a foot ball player in scoring goals. Apart f ro m the number and durat i o n of t ime needed to score a go al , thi s st udy also consi dered different way s of scoring goals. In f o otball , there are several wa ys to score a go al , through penal t y kick, header, direct free k i ck, long-range k i ck, r i g ht- f o o ted kick an d left-footed ki ck. Each of these way s of scoring goals has a different level of d iffi c ult y . 3 Theref o re, t he objective of t he curr ent study was to compa re the go a l sc or ing re li a bili t y between Cr istiano Ro nal do and L i o n e l Messi to fin d o ut who h ad m o re c o nsis tent perf o r m ance be t wee n t he se t wo recognizabl e p l ayers dur ing their a lm ost ent i re ca reer as professi o nal foot ball p laye rs. This expl o rator y study has added some o bject iv e assessment indic ato rs f o r t hose who may require co m paring perfor m a nce of pro f e ssi o nal foo tball p layers, especi a lly between Ro naldo and Messi. 2 Met hods 2.1 Data, m ethods and vari ab l es Ac cord ing to Collett (2015) , surviv al a nalysis is st atis t i ca l analy s is of dur ation t ime data f r om t he beginning of the stud y until cert ain events occur. In this st ud y , t he event was de fined as go al s s cored by Cr ist i a no R onaldo and L i o nel Messi in ever y match they p layed. T he data examine d in t his st udy was the duration of t im e ( in mi nut es) each player took to sco re a goal cal culated s ince Ro naldo and Messi began to be dep l o y ed to play on the pitch . In general , survi va l data can be d ivi ded in t o 2, nam e ly cens ored data (in co mplete) and un ce ns or ed data (complete data). In t hi s study , when t he player successfully scored a goal durin g t he ga me, the time dur ation dat a was categoriz ed as u ncensored data. Conv ersely, if the player d i d not score any goa l , t he data was ca t egoriz ed as ce nsored data. Comm o nly, an even t that occurs in the obj ect of r esearch in sur vival a na ly s is is o nly c aused by o ne m o de. Howeve r, in practice , t he sam e event m ay o ccur due to sev e ra l possibl e m o des. Compe t i ng Failure Modes (CFM) an a lysi s is one of the analy t ical methods used to an a lyze t his su ch e vent ( Reli aSo ft, 2015 ). Jus t li k e ot her m et hods in survival analysis, CFM could also be appli e d to ot her various fiel ds. Th e curr ent s t udy tr ied to apply t his analys is in t he field of spo rt s, especially f o ot ball . In a f o ot ball ga me, a goal ca n be sco red in several wa ys ( m o des) such as through a r i g ht-foot ed kick, l e f t - foot ed kick, pe nal t y kick, free kick, l o ng-range k ick, and head header. CFM a nalysis was used to m easure the reli a bili t y of Ro naldo an d Messi in scorin g goals by considering those d ifferent way s of go als scored. Sim p ly put, CF M a nalysi s in this stud y measured the combine d reliabili t y of all t hese way s of s co ring goa ls. In other words, t he probabili t y of a p layer still n ot s coring any goa l a fter he p l a yed f o r a s pecifi c t im e period. Accordin gly, a pl ayer with l o wer re li a bility value was cons i d ered bett er in sco rin g goals than thei r co unterpart. To estim at e t he reli a bili t y value of each mode of t he ev e nt (a goal scored in t his stud y ), t he non-parametri c m ethod Ka plan-Me ier was used. We considered e mpl o ying a non- parame tr ic m et hod b ecause it di d n o t requi re ce r tain pro babili t y dis t r ibution a ssu mptions so t hat t he com par ison of t he dur ation of tim e taken to score a g o al between the t wo players was done without a need to di st inguish the probabili t y d istribut i o n of t he data. Through the CFM expl o rat ory analysis , it becam e k nown who was m o re co nsis t ent in s coring go als between Ronaldo and Messi . The da ta on t he dura t i on of t im e t aken by t he two playe rs to score g o al s used in this stud y was t he secondary dat a ex tr acted f r o m a German- ba sed foot ball we bsi t e called T ransfermarkt (https://www . transf ermark t. com/ ). The website has provi ded all inf o r m at i o n about f oot ball matches aro und t he wor ld including scores, resul t s, st atistics , t ransf er news , and fixtures and recorded all g ame s t at i st ics both f o r team s and players f o r eve ry seas on. Th ere w ere m o re than 60.000 ga mes f ro m many s easons in all major football co m pet i tions. The websi t e (at t he tim e of conductin g this stud y ) was available in f o urt een l anguages and the play er dat ab ase containe d deta il s of more than 800,000 professi o nal f o o t ball ers. Transfermarkt o b t a in ed dat a about these p layers f ro m m o re t han 1 milli o n of t heir r egis t ered users around the world who kept track of how many minutes each play er spends on t he pitch, m edical history, contra ct durati o n, and many more. Wi t h more than one billio n pa ge views per m o n t h, Transf er markt has beco m e o ne of t he wo rl d’s larges t f o o tball webs i t es. T he websi t e has b eco me the unoffi cial p laye r appraiser of t he football wor l d. Many t o p cl u bs an d i nter nat i o nal media ( e.g. E SPN, L' Équ i pe, The Guardian, and La Gazzett a dell o Spo rt) ci t e Transfe r markt as a source ( Keppel & C laessens, 2020 ). The data peri o d used in this study spans f r o m the 2002 - 03 seas on to t he 2020-21 s eason. Thi s per i o d was chosen because Ronal do began hi s prof essional career as a f o ot ball pl a ye r in t he 2002-03 seas o n, whil e Messi m ade his debut as a prof essiona l f o o tball player two seasons l ater. In analyzing t hes e two recognizabl e foot ball er s’ careers , Ro dri guez a nd Vill a blanca (2024) suggested an a ly z i ng the da ta since the beginning of t heir professi o nal career just like we d i d in t his study. In add i t ion, to reduce pot enti a l biases due to thi s different starting time career, we em p l o y ed a survival a nalysis approach t hat focused m o re on the durati o n of t i me an event o ccurs rather t han the number of samples analyze d. The variables analyzed in this stud y consisted of t he duration of t ime t aken to sc or e a goal ( T ), st atus of cens o ring data ( d ) and t he ways of go als scored ( X ) as shown in Ta ble 1. 2.2 Research procedures Data analy sis in this st udy was carried out separately between Cr istiano Ro nal do an d Li o nel Messi using R software versi o n 4.0. 3 with the survival package. T his study was conducted usi ng a nine-step pr o cedure. The first one was colle ct in g research d ata, nam e ly game stat ist i cs of Ronal do and Messi in all co mpe titions start i ng from the 2002 -03 seas o n to the 2020- 21 season. T he data co nsi sted of t he time durat ion nee d ed to score a g o al and ot he r v ar iables related to t hi s stud y . The second st ep was se paratin g the dat a f o r both p lay ers ba sed on t he way t he goals were scored ( pen alty k i ck, head header, direct f ree ki ck, long-range ki ck, right-footed ki ck an d lef t - f o o ted kic k). The thi rd one wa s conduct in g desc r ipt ive stat is tics analy s is to obtain an o vervi ew of t he data character i st ics of the time duration it too k f o r both pl ayer s to sc o re a g oa l . 4 Table 1. Study Var iables Var iab les Description Scale Category  Duration of time taken to score a goal ( in mi nutes) Rati o -  Status of censoring data Nominal 0 : Censored 1 : Uncensored  Way s of go als sc ored Nominal 1 : P enal t y Ki c k 2 : Head Header 3 : Direct Free Kick 4 : Long Dis tance Kick 5 : Right-Footed Kick 6 : Left-Foot ed Ki ck To quantify the per form a nce, t he playe r wh o had more goals per mi nut e of ga m e p lay ed was awarded 1 point, and t he total po ints earn ed by each pl a yer were com pared f o r t he fi rst half (minutes 1 - 45 ), s eco nd half ( minutes 46 - 90 minut es) and extra time ( mi nut es 91 - 120). The fourth o ne was e m ploying n o n-parametric Kaplan- Meier m ethod to estim at e t he r eliabili t y val ue of each way of scorin g goa ls f o r bot h playe r s. The Kaplan-Meier reli a bilit y value (   󰇛  󰇜 󰇜 was calculated us in g Equat i o n (1).   󰇛  󰇜             (1) whe re   is t he numbe r of events (i .e. go al s) t hat ha ppened at time   (time whe n at l east one eve nt happened) and   is number of obs er vat i o n t hat h a ve not y et had an event up to t im e   ( Re li aSo f t , 2015 ). The fi f t h step was perf o r mi ng L og Rank tests to e valuate the dif fere nce in Kaplan-Me ier r eli a bili t y cur ves be twee n Ronal do and Me ssi in each way of scorin g goa l s. The six t h one was est ima t in g the overall reliabili t y value (    󰇛󰇜 ) and its 95% c o nfiden ce intervals using C FM approach which was the pro duc t of reli a bili t y of e ac h ways of scor in g goals. The o verall reliabili t y value is defined as Equat i o n (2) .    󰇛  󰇜      󰇛 󰇜           ( 2) Note t hat if a modality of scorin g goa l was limi t ed, t hen CFM o nly consi dered the wa y of sco ring go als w ith a suf ficient number of go a l s. The e st im at e 95% confidence intervals of each ways of scor in g go als is defined as Equat i o n (3).    󰇛  󰇜   󰇛  󰇜   󰇛  󰇜        󰇛  󰇛  󰇜 󰇜   󰇛  󰇜 󰇡  󰇛  󰇜 󰇢    󰇛  󰇜   󰇛  󰇜   󰇛  󰇜        󰇛  󰇛  󰇜 󰇜   󰇛  󰇜 󰇡  󰇛  󰇜 󰇢  (3) whe re   󰇛  󰇛  󰇜 󰇜 is t he e st im ate variance of the r eliabilit y values ( ReliaSo f t , 2015 ). If the c onfi d e nce i nterval be t wee n two or m o re com pared gro ups o verlap, it can be concluded t hat t he diffe r ences b et ween t he groups were not si g nifi ca nt ( Cummi ng and Finch, 2005 ). The sev enth step was p l o tt i ng and co m par ing the overall reliabili t y v a lues in sc or ing go a l s (    󰇛  󰇜 ) of Ronal do and Messi based on CFM analysis. The eight o ne was in t erpret in g t he resu l t s of the stud y and d iscussing the compa r is o n of goal scor in g reliabili t y be tween Ro nal do an d Messi . Finally, t he last step was drawi ng conclusio ns based on the results and discussi o n s that were carrie d o ut bef o re. 3 Results 3.1 Overview of research data Table 2 provides dat a characteristics and go als distrib ut i on of Crist i a no Ro nal do and Li o nel Messi based on censorin g status and t he way s of goa l scored. Based on Table 2, it can be inferred t hat in every match he p layed, Ro nal do m anaged to score 0.72 goals , whil e Messi was sligh t ly higher at 0.80 goals/match. Moreover, R o nal do m a naged to score m o re t han 100 goal s t hrough 4 d ifferent ways nam ely through ri g ht- f oot ed kicks, lef t - footed kicks, penal t ies a nd head headers. On the ot her hand, l eft- footed kicks were t he only way Mess i scored m o re than 100 go als. Note t hat the numb er of ga mes p layed differs f r o m t he total data set analyze d, as a p l a yer might not score any goals, score o ne go al , t wo goals and so on f o r ever y game the y playe d. In addi t i o n to descri pt ive statis t i cs based on censoring status and t he way goals were scored, t he com pa r i so n of go a l dis t r ibution between t he t wo pl a yers is also pr esen t ed in m o re detail for each mi nut e of the games they p layed. Figure 1 describes the number of goal s scor ed by both players in ever y minute of t he game including t he ex t ra time. 5 Table 2. Data cha r acteris t i cs and goa l s d istr ib ut i on Var iab les Cr istiano Ronaldo Lionel Messi Frequency Perce n tage Frequency Perce n tage Numb er of ga mes P laye d 1,089 100.00 941 100.00 Status of censoring data Censored (did n ot sc o re a goal) 564 41.75 449 37.32 Unc enso red (scored a goal ) 787 58.25 754 62.68 Tot al dat aset analyzed 1,351 100.00 1,203 100.00 Way s of go als sc ored Penal t y Kick 137 17.41 99 13.13 Head Header 136 17.28 28 3.71 Direct Free Kick 57 7.24 57 7.56 Long Distance Kick 11 1.40 1 0.13 Ri ght- Foot ed Ki ck 303 38.50 92 12.20 Lef t - Footed Kick 143 18.17 477 63.26 Numbe r of games scor in g at l east 1 Goal 525 48.21 492 52.28 Figure 1. Distrib ut i on numbers of go a l s sco red ba sed on minute of playing A comparison of go al scoring reliability between Ronaldo an d Messi can be ma de by look in g at wh o had more goals in eve r y minute of t he game s t hey playe d. Tot al po ints earned by both players in ea ch minute of p l a ying are presented in Table 3. Table 3. Total po ints r epresen t the superi o r i t y in the number of goals b et ween Cr i st ian o Ronal do and Li o n e l Messi Superior Pl ay e r Minutes of Playing 1 - 45 46 - 90 91 - 120 Points % Points % Points % Cris t i ano Ronal do 19 42,22 22 48,89 7 23,33 Li o ne l Messi 19 42,22 19 42,22 4 13,33 Draw 7 15,56 4 8,89 19 63,33 Tot al 45 100,00 45 100,00 30 100,00 Based on T able 3, it is known that overall Ronaldo mana ged to gain 48 po in t s, or 6 poin t s m o re t han M essi. 3.2 Reliabilit y compa rison in scoring g oals between Ronaldo and Messi Figure 2 presen t s t he Kaplan Meier r eliabili t y curves of scorin g r eliabili t y f o r C ristiano Ro nal do an d Li o nel Mes s i b ased on 6 ways of go als sco red. 6 Figure 2. Ka p lan Meier reliabili t y curves for pena l t y kick (A), head he ader (B), direct free ki ck ( C), l o ng-range k ick (D), right- f o o ted kic k (E) and lef t - footed ki ck (F) While t he Log rank test resul t s are presen t ed in Table 4. Table 4. Lo g rank test on Kap lan-Meier reliabili t y cur ves of Cris t i a no Ronaldo and Li o n el Messi Ways of Goals Sco r ed Chi-square statistics p-value Penal t y kick 0.90 0.300 Head hea d er 0.00 0.800 Direct free kick 0.40 0.500 Long-range k ick - - Ri ght- f o ot ed kic k 0.50 0.500 Lef t - foot ed ki ck 0.50 0.500 Based on Fi gure 2. A, it is k nown tha t t he reli a bili t y curves of Ro naldo and Mess i in scor in g goa l s thro ugh Penal t y kicks overlap w i t h eac h ot her starting f r o m t he f i r st minute of the game they p layed to t he 50s. Al t h o ugh t he re liabili t y cur ves l oo k sli ght ly d ifferent especially in t he 50s to 90t h mi nut e t im e in t er val of the games t hey played, t he l o g ran k t est p ro ved that the diff erence was not si g nificant since p-value of the test was higher than the significance level of 0. 05 (Table 4). Figure 2.B shows that Ro nal do and Messi's r eliabili t y curves f or goals s cor ed using hea der s in t ersect each o t he r in many o bservation t im es, starting from the first minute of the game they played to t he 110th mi nut e (extra time ). T his resu l t was reinf o rced t hrough L o g Ran k test in g which sho wed t hat t he reliabili t y cur ves of the two pl a yers w ere not si g nificantly diffe r ent. Al t h o ugh the reli a bili t y cur ves for the di rect free ki ck in Figure 2.C appeared to be separate, further test ing proved that the diffe rence was not si g nificant. On t he other hand, the reliabili t y cur ve f or goal s scored fro m long-ran ge k ic k s (Figure 2.D) looks sl ight ly different f ro m the ot hers. The obs ervations f o r bot h pl a yers di d not r each t he 90t h mi nut e of t he normal time. Thi s was due to t he f act t hat nei t her Ronaldo nor Messi 7 scored any goal s t hrough long-ran ge kicks above t he 60th minute of the ga m e s they play ed. In addition, Messi's reliabili t y curve l o o ks ve r y simple and only takes t he f o rm of a ladder. This was because the number of goal s scored by Messi through l o n g-r ange kicks was o nly 1 goa l . Meanwhile, R onal do was able to sco re 11 g o als through l o ng-range ki ck s dur in g his 17 ye ars of career. Even so, t he numbe r of o bs ervations in t his analy s is wa s very small, es p ecially for Messi a nd did n o t all o w further analysi s thro ugh the Log Rank t es t . Ronal do a nd Messi's reliabili t y curves f o r g o als scored usin g r ight- f o ot ed kic k s (Fi gure 2.E) appear to o ve r l ap alm o st thro ughout the observati on t im e, st art in g fro m t he fi r st to the final minut e of t he game t hey p layed. This was in line wit h the resul ts of t he Lo g Ran k t est (p-val u e m o re than 0.05). Fin a lly, al though t he reliabili t y curves for l eft- f o ot ed ki ck s of both ke y playe r s seemed to be separate ( especi a lly in the span of 15 and 60th min ut es), f ur ther t es t ing pro ved t hat t he reliabili t y curv e s of t he t wo pl a yers (Figure 2.F) were not si gnif ican tly different. It sh o ul d be noted t hat, b ased on the resul ts of the p revious reliabili t y analysi s (Figure 2.D) , it is kno wn t hat th e number of goals scored by both pl a yers t hrough l o ng-range k i cks wa s limi t ed. Therefore, the CFM a nalysis in this study onl y considered t he reli ability values of 5 ways of sco rin g goa l s, namely t hrough penal t y k ick, head header, di rec t free k ic k, r i g ht-footed ki ck a nd l e f t- foot ed ki ck. T he C FM reliabili t y value of each player is s imply t he m u ltiplicat i o n of t hose fi ve reliabili t y values of the ways go als sco red. Figure 3 presen t s the CFM reli a bili t y curves f o r Cr i st iano Ronal do and L i o nel Mess i along wi t h i t s 95% confidence in t ervals. Figure 3. CFM reliabili t y cur ves of Cr istiano Ro nal do and Li o ne l Mess i The CFM reliabili t y curves for t he two playe rs in Figure 3 are sh o wn by different colors, bl ue f o r Cristian o Ro nal do and red f or Li o nel Messi. Th e con t inuous li ne sh o ws the C F M reliabili t y value, an d t he dashed l ine shows t he 95% conf idence in t er val . B a sed on Figure 3, it is kno wn that R onaldo and Messi's CFM re liability cur ves a nd i ts confidence i nter vals overlap with each ot her alm o st throughout the observ at i o n time, starting from the firs t m inute of t he games they played to the en d of the extra tim e (120 minutes). In line w i t h t he Ka p lan Meier reli a bili t y curves for each way of goals scored, the CFM reliabili t y cur ves f o r t he t wo playe r s also did not differ si g nificant ly bas ed on Cu mming and Finch's co nf ide nce in t er val criter ia. 4 Discussion The o bj ect ive of t hi s stud y was to compa re the level of reliabili t y in sco rin g goa ls between Cristiano Ronaldo and Li o ne l Messi dur in g m o st of their prof essional careers as f o o tballers. T he current study thro ugh CFM expl o ra tor y analys is sh o wed that Cris t i ano Ronal do and L i o n e l Messi had t he sa me reliabili t y in scor ing goal s in thei r golden era starti ng f r om t he 2002-03 season to the 2020-21 season. The recent st udy is in li ne w ith a st udy con ducted by Ande rson et al. (2020) who stated that voting f o r the b est soccer playe r in t he wo rld ( i . e. The Ballo n d’Or) was t i ght, es peci ally in 2016. While Messi rece ived a hi g her percentage of t he fi r st plac e vot es c o m par ed to Ronal do (24 . 1% vers us 23.1%), Ronal do achi e ve d highe r av erage po i nts com pared to M essi on the second pl ac e v o t es ( 1.78 poin ts ve rsus 1.73 p o in t s). However, there are ot her s t udies t hat favored Messi m o re than Ronal do or vi ce versa. Hussaini (2021) argued that Messi was the fi r st an d bes t pl a yer in t he worl d, whi le Cr istian o Ronal do was the 6th b est play er in the world us ing the 2021 FIFA Ba ll o n d'Or sta tist i cs. On t he ot her ha nd, Salv ado r et al. (2022) st ated that Ronal do was in t he first ranking while Messi in t he second based on dat a of the 2019/2020 s eason. Interestin g ly, a s t ud y by Grbec et al. (2024) usin g longer per i ods of dat a showed t hat bot h were n ot even i ncluded in top t en r ankin g. In t hei r study , Ronal do was in t he t welf t h pos i t i o n, while Messi was in t he top 14. The diff erent i at i o n am o ng t he m ent i o ned stud ies was due to the div er sity of t he seas o ns evaluated, m et hods empl o y ed and factor s i nvest igated since so far t here was no standard approach to m e asure t he perform a nce of a f o ot ball er. A st udy by Aror a (2024) rev ea led d iff ere ntiation of skill s and ro l es of Ronaldo and Mess i on t he pitch. Messi h as been well-known f or hi s pl a ymak in g, visi o n , and dr ibbling pro wess. His lightning-fast di rect i on c ha nges and i llustrious lef t f oot h ave been so dangero us f or t he opponen t s on the pi t ch. Messi c reated opport uni t i es a nd sco res goal s by playing as an o ffensi ve midfi e lder or forward. On the other hand, Ro naldo has bee n known for hi s fi n ishing, aer ial abili t y , and p hysicality. H is quic k ness, agili t y , and heading pro wess has made him a v ersat il e f o rward w i t h an excellen t goal scor ing abilit y. Whil e Messi was often praised for his natura l skill and co nsi st ent pl ay, Ronal do was praised for his dedicat i o n, wo rk ethic and versat ili t y across a range of leagues. Both R onaldo and Me ssi h a ve ac hieved un pre cedented success, be co mi ng global icons an d set t in g numer ous rec o rds. Thes e ind ividual a nd tea m ac hievements show t hat both were the m o st promi ne nt playe r s in the m o dern era of fo otball , where the quali t y of both was qu ite equal but far above other pl ayers around the wo rld. Ho weve r , both had different charac ters in terms of thei r scor in g st yl es where Ronaldo was m o re domi na nt in s coring go als with his r ight f oot, whi le Messi w i t h hi s l e f t f o ot ( Lam a & Praveen, 2017 ) . Yuw o no an d Rachman (2021) mentioned t hat t he kicking po wer of a foot ball p layer is si g nificant ly re lated to his traini ng m et hod and leg strength. Uniquely, Ronaldo h as a s pe cial t echnique ca lled knuckling shot in do ing free kicks ( Ho ng et al ., 2012 ). Al t h o ugh it l o o ks easy , sco rin g go als through penal t y k icks requires a str ong m e nta li t y and hi g h se lf - confidence ( Mardhika 8 & D imyat i , 2015 ). Our study re vealed that more th a n 17% of the go als scored by Ronaldo and 13% of t he go als scored by Messi over t hei r 17- year career ca me f ro m pe nal t y kicks . This pro ve d t hat both h a ve a goo d m e ntali t y and high co nfiden ce in executin g penal t y k icks. Furt herm o re, both were equal ly ad ept at sc o ring f ro m d i rect free k icks. Around 7% of t he tot al go als scored by bot h p l a yers o ver more t han the i r 17 - year pro f essional c areers c a me fro m direct f ree ki ck s. H o wever, Ronal do had a bett er accuracy rat e in scor in g g oals through hea d ers ( Mu mi n in, 2015 ). The data revealed t hat 17.28% of Ronal do ’ s goals were created by his h ead, while Mes s i o nl y scored 3.71% of his tot al goals through heade rs. Both players also had the highes t number of s hots on goa l per game of a ny player in t he wor l d in the last two decades. Messi had 6.1 sh ot s per gam e, while Ronaldo had 6.8 sh o t s/game ( Mazurek, 2018 ). Note t hat min ut es played, go als scored, assi st s scored, and t i t l es won ha ve a si gnif icant p o sit iv e infl u e nce on a f o otball p layer ma rket val ues ( Herberger & We d lich, 2017 ). Accord in g to Tran s fermarkt databas e, Ronal do reach ed the hi g hest market value when he p l a yed f o r Real Madrid C. F. at € 120 . 00 mi llion in 2014, 2015 an d 2018 at ages of 29, 30 and 32 yea r s ol d ( Transfe r markt , 2022b ) while Messi ac hiev ed the peak of m arket val u e at € 180.00 milli o n in 2018 at age of 30 years when he played for FC Barcel o na ( Transf ermarkt , 2022a ). In anot he r st udy , Mazurek (2018) t ri ed to i de nt if y a fi gur e that bears m o st r esembl a nce to Mes s i . His fi nd ing was surprising t hat Phili ppe Co utinh o , a Brazili a n f oot ball er t ha t playe d with him at Barce l o na during 2018- 2021 seasons was identifi e d as t he m ost resemblanc e to Messi . In add i t ion , t he study also ident ifi ed P ierre-E m er ick Aubameyang, now playing as capt ain of t he Gabon national tea m , as t he most simila r fi gur e w i t h Ronaldo usi ng a dat aset f ro m the 2017/2018 seas on. U nf o rt unately , bot h Co utinh o and Aubamey a ng we re not in cluded in t he to p 20 pl a yers based on dat a of t he 2000/2001-2022/2023 seasons ( Grbec et al ., 2024 ). Mor e complex a nalysis for det ermi n ing the best seas o n and career of a football er ca n be done us ing t he ModK f o r mula pro posed by Salvador et al. (2022) . However, a lot of fa cto rs nee d to be considered in t he f or mula. It in c ludes individual indicators in national tea m s a nd clubs, in d icator s of ga mes and titles in national t eams an d clubs, the im pact of the athl et e on national teams and c l u bs, and also t he usage of point s per m at ch ( i .e. t he ave r age po in t s earn ed durin g the presence of the athlete in t he team). Sar m e nto and A raú j o (2020) stated that an ex pert perf o r m ance and high achievement of a football pla y er emerge f r o m circumstances r esu l t i ng from t he self - or ganiza t i o n of several p er f or mers-envi ro nmenta l facto rs. Ronal d o and Mess i are indisputable examples of ide al foot ball p layers who have fulfilled a ll requirements (e.g. s peed, strength, agi lit y, enduranc e, men ta li t y, etc.) to be the b est am ong others. It is not surprising that t he current study proved that b ot h playe r s had simila r consistency in scoring goals in m ost of their pro f essional careers as football players. Finally , Clegg and Robinson (2022) argued in t hei r boo k that t he dis cus sion of “ Ro naldo or Messi ?” f o r milli o n s of people around t he g l obe is not simply a barr oom argum e nt or an affirmat ion of fando m , b ut ra ther a phil o sophica l stat ement. Indeed, t he phil o sophical debates may have contributed to t he comme rcializat i o n of f o otball, b ecause t he t wo play ers h ave likely driven si g nificant c ommercial i ntere st and reven ue for clubs, leagues , and brands. As a result f oot ball st rengthen i t s global reach w i t h t hes e two icon playe r s in t urn ins pir ing new y o ung football p laye r s at tract ed by t he va lue and image of g l obal f o o tball t oday, and perhaps m o t iv at ed to shape the future of f o o tball . There are sev era l limi t at i ons of t his st ud y t hat ne ed to be highlighted in c luding the absence of a stat i st i ca l method that all o wed the researchers to c o m par e the CFM re li a bili t y curves of Cristian o Ronal do an d Li o nel Messi. To overco m e t his limi t at i o n, we ut ili zed confidence interval t heor y approach to draw con cl us i o n s from t he CF M an a lysis. Furtherm o re, other factor s havi ng t he pot ential to aff e ct the per form a nce of the playe r s w ere a lso not i ncluded in the analysis due to da t a limi t at i o ns, suc h as phys ical fi t ness while playing, post-injur y conditions , m at ch i mport ance an d home/away st atus. In addition, Ro nal do an d Messi did not al wa ys play in t he sam e compe t ition. Fo r exam p le, dur in g t he r esearch per io d t hey o nly playe d in the s a me league when Ro naldo defen ded Real Madrid C.F. and M essi playe d f o r FC Barcelona in the Spanish La Li ga f o r t he 2009 -10 to 2017- 18 seas o ns. Neve rt hel es s, examining data f ro m the 19-y ear career of Cristiano Ronal do as professi o nal foo tball p layer and 17- ye ar career of Lionel Mess i are beli e ved to be able to pr o vi de significant inf o r mati o n regarding the com par ison of t he sc or in g re li abilities of t wo extraordinary players in t he modern football era. 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