Game Indicators Determining Sports Performance in the NBA

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1 Joural of Huma Kietics volume 37/013, DOI:10.478/huki Sectio III Sports Traiig Game Idicators Determiig Sports Performace i the NBA by Kazimierz Mikołajec 1, Adam Maszczyk,Tomasz Zając 3 The mai goal of the preset study was to idetify basketball game performace idicators which best determie sports level i the Natioal Basketball Associatio (NBA) league. The research material cosisted of all NBA game statistics at the tur of eight seasos (003-11) ad icluded 5 performace variables. Through detailed aalysis the variables with high ifluece o game effectiveess were selected for fial procedures. It has bee prove that a limited umber of factors, mostly offesive, determies sports performace i the NBA. The most critical idicators are: Wi%, Offesive EFF, 3rd Quarter PPG, Wi% CG, Avg Fauls ad Avg Steals. I practical applicatios these results coected with top teams ad elite players may help coaches to desig better traiig programs. Key words: basketball, NBA, performace variables, regressio model, optimizatio. Itroductio Statistics i sports have bee a importat tool for coaches to evaluate the team ad player sports performace (Hughes ad Fraks, 004; Ortega et al., 009; Leite et al., 009; Oliver, 004). Throughout the years of competitive basketball, umerous methods of game registratio ad aalysis have bee created, with the objective to precisely ad objectively evaluate particular players ad the whole team. These methods evolved from simple stat sheets, filled out by had durig the game by assistat coaches to fully computerized procedures that automatically register all of the sigificat variables of the game ad calculate the ecessary idices (Lorezo et al., 010; Oliver, 004). Curretly, basketball is oe of the most aalyzed sport disciplies. The aalyses of the statistical reports allow coaches to evaluate the techical ad tactical efficiecy of players ad teams, ad to compare them durig sigle game performace, as well as durig the whole seaso. They also help players to develop basketball skills based o recorded factors (Gomez et al., 009, 010; Ibaez et al., 008; Sampaio ad Jaeira, 003; Oliver, 004). Curretly the NBA (Natioal Basketball Associatio) registers games ad performs statistical aalysis of them icludig the smallest details (Oliver, 004). The obtaied data cosist of iformatio of particular players ad teams. The wier of the NBA competitio is uofficially classified as a world champio. For that reaso recorded statistics have bee so valuable for further aalysis. Team statistics are related to the level of tactical preparatio ad game strategy The ivestigatio i this area has bee coected with several issues: game efficiecy depeds o geder (male, female), age (kadet, seior), ad sport performace (atioal leagues, Euroleague, NCAA, World Chapioship, Olimpic Games), compariso of wiig ad losig teams (Triić et al., 00; Kozar et al., 1994; Lorezo et al., 010) ad differet parts of the seaso regular, play-offs (Sampio ad Jaeira, 00; Oliver, 004), as well as player s court positio. Some research has also aalyzed game performace as a fuctio of a competitio phase (Oliver, 004; Gomez et al., 008) or tactical strategies (Gomez et al., 008; Oliver, 004). Several studies have bee coected with the 1 - Departmet of TeamSports, Academy of Physical Educatio i Katowice, Polad. - Departmet of Sports Theory, Academy of Physical Educatio i Katowice, Polad. 3 - Huma Performace Laboratory, Academy of Physical Educatio i Katowice, Polad.. Authors submitted their cotributio of the article to the editorial board. Accepted for pritig i Joural of Huma Kietics vol. 37/013 o Jue 013. Dowload Date 7//17 10:1 PM

2 146 Game idicators determiig sports performace i the NBA differece i the fial score (close, balaced ad ubalaced games). Ufortuately, the umber of cosidered games ad variables have bee restricted. Also a limited umber of studies have bee coducted o top-level competitio. Therefore, the aim of the preset study was to idetify basketball game performace idicators which best determie sports level i the NBA. Material ad Methods Sample ad variables The data were obtaied from the Natioal Basketball Associatio (NBA) (official statistics gathered live) for the seasos All data were collected from official boxscores of NBA ad icluded 5 variables that characterized offesive ad defesive efectiveess of 30 teams. Through a detailed aalysis of these variables, we excluded those that did ot have a sigificat effect o game performace ad selected those that had a high impact for fial aalysis. The depedet variable was the result achieved by a particular team i a certai seaso (Y). Eight NBA seasos (003-11) were take ito cosideratio i the preset study. The empirical, progostic ad exploratory studies as well as model ecoometrics, factor aalysis ad cluster aalysis as statistical methods were used i this research (Maestas ad Preuhs, 000). The scheme of the study icluded the followig structure of variables: RX Y (oe multivalet depedet variable Y ad multivalet idepedet variables X respectig the rule of purposeful selectio). Descriptive statistics were used to compare the correlatios of variables ad to determie the most importat oes for data predictio ad mathematical modelig. The distributio of all variables for each NBA team was verified. The aalysis of calculated coefficiets of variace (V) revealed the largest diversity i the followig variables: umber of ball possessios, average score per game, umber of scored poits i the first quarter, average umber of 3 poit shots made, average biggest poit advatage, total umber of shots made, 3 poit shots made, average umber of fouls. Very similar diversity was observed i all NBA teams. Due to the skewess idex all variables were characterized by ormal distributio with moderate right or left asymmetry. Accordig to scietific procedures (Mc Cullough ad Wilso, 005; Keele ad Kelly, 006) the agglomeratio Ward method was used i order to group the subjects. All teams were divided ito five groups: 1/ Dever, Golde State, Phoeix, / Dallas, LA Lakers, Sacrameto, 3/ Bosto, Clevelad, Housto, Idiaa, Miami, Milwaukee, New York, Okla City, Orlado, Sa Atoio, Toroto, Washigto, 4/ Detroit, New Jersey, New Orleas, Portlad, 5/ Atlata, Charlotte, Chicago, LA Clippers, Memphis, Miesota, Philadelphia, Utah (the order is radom). The the relatioship betwee all variables was defied by meas of the Pearso s correlatio coefficiet (r) takig ito cosideratio the evaluated years. Due to a large umber of variables with a statistically sigificat value of the Pearso s coefficiet (48), their umber was reduced usig factors aalysis ad appoited the vectors R1 ad R0. The correlatio coefficiets for 9 explaatory variables were calculated accordig to the followig formula: (i, j = 1,,...,m) Thus, the relatioship betwee aalysed variables ad matrix of correlatio coefficiets betwee explaatory variables ad the vector of the explaatory variable Y with potetial explaatory variables were determied as preseted below: r i r ij t1 t1 ( y t ( yt y) ti ( xti xi) t1 t1 ( x y)( xti xi) t1 t1 xi)( xtj xj) ( xti xi) ( xtj xj) ( i = 1,,...,m) As a result, the vector R0 was determied. The the method of correlatio coefficiets for determiatio of correlatio matrix, correlatio vectors ad optimal predictats selectio was used. The critical value of correlatio coefficiet was calculated by meas of the followig formula: r * ( t*) ( t*) For the level of sigificace =0,1 ad = degrees of freedom, 30-=8 the value of statistic Joural of Huma Kietics volume 37/013 Dowload Date 7//17 10:1 PM

3 by Mikołajec K. et al. 147 ad critical value was t=1,70, r* = 0.30, respectively. All variables with diagosed iequality rj r*, were elimiated as ot sigificatly correlated with the depedet variable Y. The obtaied result was verified by factor aalysis. Thus, the most correlated 9 variables were calculated. Usig procedures described above, the optimal combiatio of variables was determied (Table 1). The obtaied model explaied 99% of variability which proves its adjustig to the iput data. The matrix set icluded 9 variables divided ito five groups of factors. Thus, the optimal combiatio of variables i order to create the regressio models was selected. Table 1 The results of factor aalysis for 30 NBA teams Factor Factor Factor Factor Factor Variables Wi% Seaso 0,087 0,936 0,077 0,191-0,066 Wi% Home 0,13 0,894 0,094 0,097-0,107 Wi% Away 0,038 0,86 0,050 0,66-0,014 Wi% CG (close games) -0,079 0,710 0,057 0,005-0,064 Possesio P.G 0,864-0,38 0,096 0,143-0,0 Possesio P.G Home 0,84-0,301 0,14 0,135-0,15 Possesio P.G Away 0,843-0,337 0,060 0,14-0,18 PPG 0,919 0,34 0,080 0,67 0,065 PPG Home 0,89 0,4 0,09 0,8 0,031 PPG Away 0,883 0,09 0,061 0,9 0,100 1st Qrt PPG 0,831 0,63 0,031 0,3 0,0 d Qrt PPG 0,843 0,164 0,009 0,37 0,056 3rd Qrt PPG 0,788 0,78 0,077 0,9 0,013 4th Qrt PPG 0,78 0,115 0,175 0,41 0,14 Pts Avg 0,635 0,081-0,095-0,744 0,04 3 Pts Avg 0,336 0,150-0,158 0,907 0,065 Avg Biggest Lead 0,179 0,739 0,065 0,06-0,066 FGM 0,931 0,10-0,9 0,03 0,098 FGA 0,73-0,43-0,49 0,058-0,6 3 Pts Made 0,336 0,15-0,158 0,906 0,064 3 Pts Att. 0,310 0,081-0,155 0,915 0,017 FTM 0,95 0,076 0,800-0,114-0,07 FTA 0,16 0,035 0,906-0,139-0,075 3 Pts % 0,197 0,16-0,09 0,948 0,059 Pts % -0,197-0,16 0,09-0,948-0,059 Free Throw % -0,039 0,106 0,943-0,139 0,011 FTA per Offesive Play -0,019 0,154 0,918-0,138 0,04 Stls (steals) 0,10 0,07 0,14-0,109-0,85 Stls per Defesive Play -0,015 0,131 0,11-0,147-0,80 Editorial Committee of Joural of Huma Kietics Dowload Date 7//17 10:1 PM

4 148 Game idicators determiig sports performace i the NBA Statistical Aalysis The most commo ad comprehesively verified statistical methods were used to optimize the coclusios of the aalyses which were carried out i this study. The itercorrelatios betwee aalysed variables were calculated by the Pearso s coefficiet (Ferguso ad Takae, 1997; Maestas ad Preuhs, 000; Gree, 003; Keele ad Kelly, 006). Accordig to sport results, the regessio aalysis was used (Jaccard, 1990; Gieva ad Splitstoe, 004). Idetificatio of the optimal combiatio of explaatory variables were doe by the correlatio matrix of variables, Pearso s coefficiet ad factor aalysis (Gree, 003; McCullough ad Wilso, 005; Keele ad Kelly, 006). The impact of variables o the value of Y (explaatory variable) was aalysed by multivariate fuctio of regressio with parameters calculated by the data characterizig the structure of followig fuctio: Y t = f [X 1, t-1,x, t-1,..., X, t-1] + t After the simpificatio, the biometric model took the followig structure: k Y x Y i1 j j The above preseted statstical aalysis was completed by Statistica PL icludig module Neural Networks (StatSoft Polad) ad Excel Microsoft Office 010 software (Microsof Polad). Results The optimal combiatio for all NBA teams icluded 9 variables. I the ext stage the regressio aalysis of results i the league as the depedet variable was coducted for chose idepedet variables. The results are preseted i Table. Due to this procedure the followig structural parameters i the form of the equatio of regressio were revealed: (Y) =, ,08 Wi % + 0,18 Avg Fauls + 1,33 Offesive EFF+,46 Wi% CG + 3rd Qrt PPG + 0,8 Avg Steals The statistically sigificat predictors of team s rak positio are variables i weight order by value of Beta idex: Wi % (percet of wis durig the whole seaso), Offesive EFF (offesive efficiecy), 3rd Quarter PPG (average umber of poits i the 3rd quarter), Wi % CG (percet of wis i the close games), Avg Fauls (average umber of fauls) ad Avg Steals (average umber of steals). The variables explaied 86% of variace for Y (depedet variable) ad the multiple correlatio betwee exogeous variables ad edogeous oe was equal 0,93. Additioally, the verificatio of the model idicates that a icrease i ay parameter would improve rakig. For example if the umber of wis durig the NBA seaso chages positively by 1% the the team would receive 50 rakig poits more. Table Summary of regressio for depedet variable NBA rak for 30 teams N=40 R=,98 R^=,964 R=,963 F(6,33)=1059,5 p<0,0000 Std. dev. error of estimat.: 1,6518 b* St. error b St. error t p Itercept,865 5,19 4,457 0,001 Wi % 1,03 0,00 59,081 1,194 49,456 0,001 Avg Fauls 0,034 0,013 0,188 0,073,56 0,011 Offesive EFF 0,084 0,04 1,333 6,6 3,406 0,003 Wi % CG 0,035 0,0159,464 1,09,55 0,05 3rd Qrt PPG 0,045 0,019 0,303 0,131,30 0,0 Avg Steals 0,07 0,013 0,84 0,137,066 0,031 Joural of Huma Kietics volume 37/013 Dowload Date 7//17 10:1 PM

5 by Mikołajec K. et al. 149 Discussio The literature review coected with sports performace i basketball idicates o a limited umber of cosidered variables ad games. Furthermore, a restricted umber of studies have bee coducted o top-level competitio. Therefore, the aim of the preset study was to idetify basketball game performace idicators which best determie sports level i the NBA ad wether they remai stable or chage from seaso to seaso. The study icluded 5 performace variables, both offesive ad defesive. Through a detailed aalysis the variables that did ot have a sigificat impact o game performace were excluded. After completig a series of mathematical calculatios the most importat game idicators were selected for further aalysis. It seems that each ew seaso i the NBA is differet from the previous oe takig ito accout the factors ifluecig the game results. Meawhile, it has bee prove that champioships i the NBA have bee determied for the past few years by the same factors. These factors chage oly slightly i stregth ad their relatioships. The most critical idicators which determiate the success at the ed of the eight cosidered NBA seasos were: Wi %, Offesive EFF, 3rd Quarter PPG, Wi % CG, Avg Fauls ad Avg Steals. The combiatio of variables preseted above differs from the results obtaied by other authors. Csataljay et al. (009) revealed 6 factors havig the highest impact o the fial score i basketball game: 3 PTA (3 poits attempts), FG % (field goals efficiecy), FTM (free throws made), FT% (free throws efficiecy), D- REB (umber of defesive rebouds), TOR (umber of turovers). The research was coducted based o Euroleague statistics. The correlatio betwee the umber of assists ad wi/defeat ratio was the aim of the study by Melik (001). The sample icluded NBA games from 5 seasos ( ). By meas of the Spearma s coefficiet of rak correlatio a sigificat relatioship betwee these variables was show (from 0,4 to 0,71). The best results i the NBA league were observed i teams playig best offese ad defese. Ibáñez et al. (003) aalyzed 870 games of the Spaish league - LEB 1 (6 seasos). Obtaied data showed that the result was affected by three mai factors: assists, steals ad blocks which explaied 8,4% of the depedet variable. The umber of assists was the most importat variable determiig success. The results of may studies (Akers et al., 1991; Ittebach ad Esters, 1995; Karipidis et al., 001) cofirmed that wiig teams achieved better shootig efficiecy ad a higher umber of defesive rebouds. Besides, Kozar et al. (1994) revealed that accordig to close games, the umber of fouls ad free throws effectiveess was most sigificat. The data preseted by some authors idicate small ifluece of offesive rebouds, steals, turovers ad assists o basketball performace. It suggests that wiig teams base their game o correct decisios, shootig efficiecy ad better strategies ad tactics used i competitio (Triić et al., 00). Sampaio ad Jaeira (003) idicated the importace of defesive rebouds which icreased the umber of ball possessios, what resulted i a opportuity for higher percetage of offesive actios. Oliver (004) selected 4 factors most affectig sport results i basketball: shootig efficiecy, umber of turovers, offesive rebouds ad free throws made. It was stated that wiig teams achieved a high level i three out of the four listed above variables. The same author suggested that effective offesive play led to success i the NBA (Oliver, 004). The best teams i this area wo 79% of games. The high umber of missed shots created possible fast break opportuities for oppoets. Additioally, too may turovers decreased the umber of possessios ad had a importat ifluece o field goal attempts. Aother aspect was a icreased umber of offesive rebouds which allowed to score more poits. Due to this factor best teams ca sigificatly improve their offesive efficiecy. A large umber of free throw attempts allowed to score more poits with higheffective shots. It also created foul troubles ad madatory substitutes for the oppoet (Oliver, 004; Sampaio et al., 008). The developmet of set plays (Gomez et al., 008; Triić et al., 00), umber of assists (Hoofler ad Paye, 1997), higher level of physical fitess (Royal et al., 006), umber of defesive rebouds as a factor limitig the oppositio s chaces to score (Gomez et al., 008; Hoofler ad Paye, 1997) are importat elemets of game Editorial Committee of Joural of Huma Kietics Dowload Date 7//17 10:1 PM

6 150 Game idicators determiig sports performace i the NBA statistics that mostly iflueced game results. Gomez et al. (008) also stressed the importace of 3 poits shots that ca make a major differece betwee wiig ad losig teams. However, obtaied results poited out that i balaced games the teams had to be more effective i short distace field goals to wi the match. The coducted research also revealed a small importace of assists i playoff games. This ca be explaied by a less frequet teamwork ad more idividual plays selected by the best players i decisive games. It ca be cocluded that the fial game result is affected by may variables, which may ot always be importat durig particular matches, but costat effort to maitai them at the highest level gives a advatage over less orgaized teams. The mai factors which ifluece sports results i the NBA idicated i the preset study are much more coected with offese tha defese. It suggests that this area of basketball game is more importat. Most coclusios defied by other authors ad preseted above are similar ad cofirm results obtied i this research. However, the importace of idividual factors ca be expressed i a differet way. I practical applicatios, these results coected with top teams ad elite players may help coaches to desig better traiig programs. Refereces Akers M, Wolff S, Buttross T. A empirical examiatio of the factors affectig the success of NCAA divisio I college basketball teams. Joural of Busiess ad Ecoomic Studies, 1991; 1: Csataljay G, James N, Hughes M, Dacs H.Performace idicators that distiguish wiig ad losig teams i basketball. It. J Perform Aal Sport, 009; 9: Durkovic T, Gjergja D, Marelic N, Atekolovic L, Resetar T. The aalysis of two groups of basketball teams based o the situatioal parameters of the game. I D. Milaovic ad F. Prot (Eds.), 4th Iteratioal Scietific Coferece o Kiesiology, Proceedig Book Sciece ad Professio Challege for the Future: ; 005 Ferguso GA, Takae Y. Statistical aalysis i pedagogical ad psychological sciece. Wydawictwo Naukowe PWN, 1997; 18-7 Gieva ME, Splitstoe DE. Statistical Tools for Evirometal Quality Measuremet; 004 Gomez MA, Lorezo A, Sampaio J, Ibaez SJ, Ortega E. Game related statistics that discrimiated wiig ad losig teams from the Spaish me s professioal basketball teams. Collegium Atropol, 008; 3(): Gomez MA, Lorezo A, Ortega E, Sampaio J, Ibaez SJ. Game-related statistics discrimiatig betwee starters ad ostarters players i Wome s Natioal Basketball Associatio League (WNBA). J Sport Sci Med, 009; 8:78-83 Gomez MA, Lorezo A, Ibaez SJ, Ortega E, Leite N, Sampaio J. A aalysis of defesive strategies use by home ad away basketball teams. Percept Motor Skill, 010; 110 (1): Greee W. Ecoometric Aalysis. New Jersey: Pretice Hall; 003 Hofler RA, Paye JE. Measurig efficiecy i the Natioal Basketball Associatio. Ecoomics Letters, 1997; 55: Hughes M, Fraks IM. Notatioal Aalysis of Sport. Systems for better coachig ad performace i sport. Lodo: Routledge; 004 Ibáñez SJ, Sampaio J, Feu S, Lorezo A, Gomez MA, Ortega E. Basketball game-related statistics that discrimiate betwee teams seaso-log success. Eur J Sport Sci, 008; 8(6): 1-4 Ittebach RF, Esters IG. Utility of team idices for predictig ed of seaso rakig i two atioal polls. J of Sport Behavior, 1995; 18: 16-5 Jaccard J, Turrisi W. Iteractio Effects i Multiple Regressio. Quaitative Applicatios i the Social Scieces, 1990; 70-7 Joural of Huma Kietics volume 37/013 Dowload Date 7//17 10:1 PM

7 by Mikołajec K. et al. 151 Karipidis A, Fotiakis P, Taxildaris K, Fatouros J. Factors characterisig a successful performace I basketball. J of Huma Movemet Studies, 001; 41: Keele L, Kelly NJ. Dyamic Models for Dyamic Theories: The Is ad Outs of Lagged Depedet Variables. Political Aalysis, 006; 14: Kozar B, Vaugh RE, Lord RH, Whitfield KE. Importace of free- throws AT various stages of basketball games. Perceptual ad Motor Skills, 1994; 78: Leite N, Baker J, Sampaio J. Paths to expertise i Portuguese atioal team athletes. J Sport Sci Med, 009; 8(4): Lorezo A, Gomez MA, Ortega E, Ibaez SJ, Sampaio J. Game related statistics which discrimiate betwee losig uder-16 male basketball games. J Sport Sci Med, 010; 9: Lyos M, Al-Nakeeb Y, Nevill A. The impact of moderate ad high itesity total body fatigue o passig accuracy i expert ad ovice basketball players. J Sport Sci Med, 006; 5(): 15- Maestas C, Preuhs RR. Modellig volatility i political time series. Electoral Studies, 000; 19(1): McCullough BD, Wilso B. O the accuracy of statistical procedures i Microsoft Excel 003. Computatioal Statistics ad Data Aalysis, 005; 49: Melick MJ. Relatioship betwee team assists ad wi-loss record i The Natioal Basketball Associatio. Percept Mot Ski, 001; 9(): Oliver D. What wis basketball games, a review of Basketball o paper: Rules ad tools for performace aalysis. Polomac Books, 005; 6-85 Ortega E, Villarejo D, Palao JM. Differeces i game statistics betwee wiig ad losig teams rubgy teams i the six atios touramet. J Sport Sci Med, 009; 8(4): Royal KA, Farrow D, Mujika I, Halso SL, Pye D, Aberethy D. The effects of fatigue o decisio makig ad shootig skill performace i waterpolo players. J Sport Sci, 006; 4(8): Sampaio J, Jaeira M. Home advatage i Portuguese Basketball league: differeced betwee regular seaso ad playoff. I M. Jaeira ad E. Bradao (Eds.) Estudos 3 CEJD Porto: FCDEF-UP, ; 00 Sampaio J, Jaeira M. Statistical aalyses of basketball team performace: uderstadig teams wis ad losses accordig to a differet idex of Ball Possessio. It. J of Perform Aal i Sport, 003; 3: Sampaio J, Ibáñez SJ, Feu S. Discrimiative power of basketball game-related statistics by level of competitio ad sex. Perceptual motor Skill, 004; 99: Sampaio J, Lago-Peñas C, Drikwater E. Explaatios for the Uited States of America s domiace i basketball at the Beijig Olympic Games. J Sports Sci, 008; 8(): Triić S, Dizdar D, Dezma B. Pragmatic Validity of the Combied Model of Expert System for Assessmet ad Aalysis of the Actual Quality Overall Structure of Basketball players. Coll. Atr, 00; 6: Triić S, Dizdar D, Luksić E. Differeces Betwee Wiig ad Defeated Top Quality Basketball Teams i Fial Touramets of Europea ClubChampioship. Coll. Atr, 00; 6(): Correspodig author: Mikołajec Kazimierz Departmet of TeamSports, Academy of Physical Educatio i Katowice, Katowice, Mikolowska Str. 7a Polad. Phoe: Editorial Committee of Joural of Huma Kietics Dowload Date 7//17 10:1 PM

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