BOLETIM TECNICO DA PETROBRAS VOL. 61, Maochun Lin Physical Education College of Shihezi University, Shihezi , China

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1 BOETIM TECNICO DA PETROBRAS VO. 6, 207 Guest Edtors: Hao WANG, M DUAN Copyrght 207, PB Publshg ISBN: ISSN: EISSN: Aalyss ad Emprcal Study of Basetball Techology Statstcal Idex Based o Correlato Coeffcet / Aálse e Estudo Empírco do Ídce Estatístco da Tecologa de Basquete Baseado o Coefcete de Correlação Maochu Physcal Educato College of Shhez Uversty, Shhez , Cha Abstract: I the basetball game, fdg the ey wg factors ad related dcators ca mprove the wg percetage. I ths paper uses the research method of the combato of correlato coeffcet aalyss ad logcal aalyss, accordace wth the basc laws of basetball, to carry out qualtatve aalyss for the relatoshp amog techcal dcators. It uses the correlato aalyss method to carry out emprcal study by aalyzg the techcal statstcal data rato of the 23 smulato games. Combg wth the rules of basetball ad game practce, t reveals the wg factors ad techcal ad tactcal characterstcs ad dscusses the commo relatoshp amog the techcal statstcs dcators, whch provdes theoretcal referece for Cha s basetball research wor cotet, costructo ad trag of basetball team ad -depth aalyss of basetball games. Keywords: correlato coeffcet, cotrbuto rate, techcal statstcal dcators, emprcal aalyss Resumo: No jogo de basquete, ecotrar os prcpas fatores vecedores e os dcadores relacoados podem melhorar a porcetagem vecedora. Neste artgo utlza o método de pesqusa da combação de aálse de coefcetes de correlação e aálse lógca, de acordo com as les báscas do basquete, para realzar aálses qualtatvas para a relação etre os dcadores téccos. Ele usa o método de aálse de correlação para realzar estudos empírcos, aalsado a relação de dados estatístcos téccos dos 23 jogos de smulação. Combado as regras da prátca de basquete e jogo, revela os fatores vecedores e as característcas téccas e tátcas e dscute a relação comum etre os dcadores de estatístcas téccas, que forece referêca teórca para o coteúdo de trabalho de pesqusa de basquete da Cha, costrução e treameto da equpe de basquete e em - aálse detalhada dos jogos de basquete. Palavras-chave: coefcete de correlação, taxa de cotrbução, dcadores estatístcos téccos, aálse empírca SEPTEMBER

2 Itroducto Nowadays, sports have bee popular all over the world, ad basetball s oe of the most popular sports udoubtedly. Wth the obsesso to basetball, more ad more basetball professoal leagues are held varous coutres. I every ferce game, from the players to the coach, all the people try ther best to fght ad do everythg possble to fd the oppoet s weaesses ad fd offesve opportutes from subtletes to brea the deadloc ad w the overall vctory of the game. How to seze the power of tatve the ferce competto, how to fd the oppoet s weaess to couterattac, whch s Cha s basetball league ad atoal me s basetball team eeds to stregthe. Nowadays, usg correlato aalyss to aalyze the correlato betwee techcal statstcs ad the results of basetball games s the most effectve way to fd the wg factors ad to fully uderstad the characterstcs of the team ad explore the laws of basetball. 2. Judgmet ad calculato of correlato coeffcet 2. Judgmet of correlato coeffcet For the qualtatve judgmet of the correlato degree, geerally, there are two ways: frst, to judge whether there s the relatoshp accordg to the relevat fgures ad the relevat tables, secod, to calculate the correlato coeffcet based o data. For the both ways, the correlato coeffcet ca summarze the related form ad degree coeffcet more tutvely, whether the lear or o-lear. The rage of correlato coeffcet s from to +, ad r represets the correlato coeffcet ( «r + ). The closer the correlato s, the closer the correlato coeffcet r s to ±, whereas the weaer the correlato s, the closer the correlato coeffcet r s to 0. If the correlato coeffcet r = ±, the the two pheomea are completely related, whe the correlato coeffcet s +, t represets postve correlato, whe the correlato coeffcet s, t represets egatve correlato; ad whe the correlato coeffcet r = 0, t meas completely rrelevat. The scatter plot of the fgure below gves a descrpto of ths correlato. Fgure shows a postve correlato, whe the correlato coeffcet s, t dcates ts the perfect postve lear correlato amog the varables. I the fgure, the large X coordate value correspods to a large Y coordate value. Fgure 2 shows a egatve correlato, whe the correlato coeffcet s, t meas that ts the perfect egatve lear correlato amog the varables, I the fgure, the X coordate value wth large scatter plot correspods to a small Y coordate value. Fgure 3 shows that whe the correlato coeffcet s 0, there s o lear correlato betwee the two varables. Fgure Scatter plot whch correlato coeffcet s Fgure 2 Scatter plot whch correlato coeffcet s BOETIM TECNICO DA PETROBRAS 375

3 2.2 Calculato ad characterstcs of correlato coeffcet 2.2. Smple correlato coeffcet The smple correlato coeffcet refers to the statstcal aalyss dctors of the correlato degree betwee the two pheomea uder the codto of lear correlato. The basc formula s show as follows: xy r = σ σσ x 2 y () Fgure 3 Scatter plot whch correlato coeffcet s 0 I the actual pheomeo, the correlato coeffcet s r = ± ca ot be see commomly, the commo correlato coeffcet s show as Fgure 4 ad Fgure 5. The two formulas (2) ad (3) ca be deduced from the basc formula (), whch are the commoly used formulas r = r = ( x x) ( y 2 2 ( x x) ( y xy ( x)( x ( x) y ( (2) (3) I formula (), σ ( x x) ( y xy = s called covarace; σ x = ( x x) s the stadard devato of the varable x; σ y = ( y s the stadard devato of the varable y. Fgure 4 Scatter plot whe correlato coeffcet s The characterstcs of the correlato coeffcet The correlato coeffcet r has the followg characterstcs: ) Whe r =, t shows there s full lear correlato betwee the varable x, y. 2) Whe 0 < r <, there s a certa lear correlato betwee the varables x ad y. The geeral crtero s that r <0.3 s a very wea lear correlato, 0.3 < r < 0.5 s a low lear correlato, 0.5 < r < 0.8 s a sgfcat lear correlato, 0.8 < r s hgh lear correlato. 3) Whe r > 0, there s a postve correlato betwee varable x, y; whe r < 0, there s a egatve correlato betwee varable x, y. 4) Whe r = 0, there s o lear relatoshp betwee the varable x, y, but there may be o-lear correlato. 3. The applcato of correlato coeffcet basetball techcal statstcal dex aalyss 3. Use the correlato coeffcet to calculate the team s offesve effcecy Fgure 5 Scatter plot whe correlato coeffcet s 0.69 A team offesve effcecy ca be used to show the shootg rate, therefore, the offesve effcecy ot oly represets the team s overall offesve capablty, but also reflects the team SEPTEMBER

4 players superb shootg slls. Shootg percetage refers to the rato of FGM-A (except the umber of throwg free ball) ad the feld goal attempts, that s, the shootg percetage = umber of FGM-A / feld goal attempts. Set x, x 2,, x, represets a tea s total scores, y, y 2,, y, represets a team players shootg percetage. r = ( x x) ( y 2 2 ( x x) ( y The r represets a team s offesve effcecy. I geeral, whe the shootg percetage s hgh, the total scores are hgh, o the cotrary, whe the shootg percetage s low, the total scores are low, the so-called dstcto s to dstct the coeffcet betwee hgh shootg percetage ad low shootg percetage. If r > 0, t shows that the shootg percetage of the team players who get hgh total scores s relatvely hgh, whch dcates that the shootg percetage plays a ey role the game; f the 0.3 r 0.4, t s thought that the team s offesve effcecy s hgher; f r > 0.4, t s thought that the team s offesve effcecy s very good; whe r < 0.3, t dcates that the team s offesve effcecy s ot hgh, ad t eed to stregthe the trag of players. It s worth otg that whe r s a offesve effcecy dctor, the evaluato crtera for the teams who have dfferet potetal ca be slghtly dfferet, such as the NBA game, ts requremet for the team s hgher, geerally t s r > 0.4, ad for the geeral atoal college studets league, the offesve effcecy requremet should be slghtly lower. To a certa extet, the offesve effcecy descrbes the ablty of the team players, geeral, the hgher the offesve effcecy s, the hgher the team stregth s. 3.2 Use correlato coeffcet to calculate the cotrbuto rate of shootg percetage I 2., the total scores of the teams are raed from small to large: x x 2 x 3 x, the shootg percetage of these s: y, y 2, y 3,, y. The total scores of these teams are dvded to three groups: hgh-score group, low-score group ad geeral-score group, whch 25% of the total umber s the respectve umbers of hgh ad low group, the obta: x x2 x3 x low-score group ( group) y y y y hgh-score group ( H group) 2 3 x +, x + 2, x +, + 2, y y y (4) The correlato coeffcets of group ad H group were calculated respectvely: x r xy = ( x x )( y y ) 2 ( x x ) ( y y ) 2 ( x + xh)( y yh ) rh = = xy + 2 H ( x x ) ( y + y H ) 2 = x, y = y, xh = x +, yh = x (5) (6) + I whch: rxy + rhxy Set rxy =, r 2 xy s called the cotrbuto rate of shootg percetage I geeral, f the shootg percetage s hgh, there must be r Hxy > 0, f r Hxy > 0, the r Hxy + r xy > 0 ; t also ca be 2 sad that the greater r Hxy + r xy s, the stroger the lear relatoshp betwee the shootg percetage ad the total scores s, ad the greater the cotrbuto of shootg percetage to the total scores; o the cotrary, whe r Hxy + r xy s egatve value, t dcates that oe of the followg crcumstaces ca occur: ) r xy s egatve value; 2) r Hxy s egatve value; 3) r xy ad r Hxy are egatve value; Whatever happes, t shows that the shootg percetage has less or egatve mpact o the total scores, at ths tme, we say that the shootg percetage cotrbutes less to the total scores. If r xy s a egatve value, t dcates that there s at least oe less tha 0 betwee r xy ad r Hxy, the t ca be determed that the shootg percetage s low, the daly shootg trag of the players should be stregtheed. Cotrbuto s a relatve amout, the same team ad the ufed game, the correspodg cotrbuto of dfferet players shootg percetage rate must be dfferet, but a game, for a player, r xy ca be used as a evaluato dcator of the performace stregth ths game. 4. Emprcal study of correlato coeffcet aalyzg wg factors Ths paper chooses the shootg percetage of a basetball team ad oppoets amog the 23 games as a research object. BOETIM TECNICO DA PETROBRAS 377

5 4. Costruct basetball game techcal statstcs based o the correlato aalyss For the statstcal aalyss of basetball techology, t eed to meet the followg pots:. combe the basc prcples of basetball; 2. o the bass of the research team, compare the same techcal dcators wth other teams. I order to facltate the processg of statstcal data, the basetball game, combg the prcple that the score s the oly crtero for judgg the outcome of the basetball game, t try to mae the two groups techcal statstcs data the two teams to a group, that s the score rato s used to determe the outcome of the game. Therefore, set: the research object team s a techcal statstcs s a set A the felds a game, the techcal statstcs data o the seral umber s a (K), =, 2, 3,...,, the [ ] A = a (), a ( 2),, a ( ); Therefore, set: the oppoet team s a techcal statstcs s a set B the same agast game, the techcal statstcs data o the seral umber s a (K), =, 2, 3,...,, the [ ] B = b (), b ( 2),, b ( ); Set: the techcal statstcs data rato of the two s C, a a C = [ c(), c( 2 c ]= () ),, ( ) b (), ( 2) b ( 2), a ( ), 2 b ( 2) I ths way, the study ca use several sets C = [c (), c (2),, c ()] of the techcal statstcs data rato of the two sdes of a match, where the score dctor s C (), to carry out correlato aalyss. Accordg to the above study, the method of costructg the correlato aalyss data s obtaed, through arragg ad processg, the total scores rato ad shootg percetage rato betwee the team ad the oppoet 23 games s obtaed: (see Table ) Table The shootg percetage rato of a basetball team ad ts oppoet oppoet feld score goal attempts shootg percetage A oppoet B oppoet C oppoet D oppoet Aalyzg wg factors based o correlato coeffcet I order to aalyze whether the shootg percetage s the wg factor the smulato game, the correlato coeffcet s used to show the lear correlato betwee the score rato ad the shootg percetage rato. The greater the correlato coeffcet s, the greater the lear correlato s, ad the greater the mpact o the outcome of the game s, whch also shows that the larger the shootg rate dfferece s betwee the team ad the oppoet; the smaller the correlato coeffcet value s, dcatg that the dfferece techcal statstcs s small, the smaller the mpact o the outcome of the game s. Carry out the correlato aalyss of the score rato to the data Table through the formula (5) ad (6), the the aalyss results obtaed s show Table 2. The calculato wors are show as follows: Frst, through the sortg of total score rato of the team ad ts oppoets, the groups are dvded to group, H group ad geeral group, the groupg result s show as follows (do ot cosder the geeral group): The scores of group are show as follows: 0.8 (feld 4), 0.9 (feld 8), 0.92 (3,4), 0.93 (20,2); The scores of group are show as follows:.33 (feld 22),.28 (feld 5),.2 (feld ),.6 (feld 0),.5 (feld 7),. (feld ) Accordg to the formula (5), to calculate the group correlato coeffcet: r xy = ( x x )( y y ) 2 ( x x ) ( y y ) 2 = ( )(.02.06)+( )( )+( )(.04.06)+( )( )+( ) (0.9.06)+( )(0.7.06)/[( ) 2 +( ) 2 +4( ) 2 +4( ) 2 ] 0.5 [(.02.06) 2 +( ) 2 +(.04.06) 2 +( ) 2 +(0.9.06) 2 +(0.7.06) 2 ] 0.5 = SEPTEMBER

6 Smlarly, r Hxy = 0.604,the r Hxy + r xy = The correlato s show as follows Fgure 6, Fgure 7 ad Fgure 8: Thus, by aalyss, because r Hxy pluses r xy s more tha zero, t meas that there s a greater correlato betwee the shootg percetage ad the total scores, that s, the hgher the shootg percetage s, the more the total scores are, o the cotrary, the lower the shootg percetage s, the less the total scores are. Therefore, the rest may be deduced by ths, we ca also calculate the correlato coeffcet through the aalyss of other techcal dcators, whch becomes the ey of the team achevg good results the game. Fgure 6 ear relatoshp betwee H group score ad shootg percetage 5. Cocluso Combed wth the basc rules of basetball game, ths paper selects the shootg percetage as the object of aalyss, carres out the emprcal aalyss for the techcal statstcs; explores the correlato of the techcal statstcs ad scores from the commo law of basetball competto. Whch lays the foudato for the -depth study of basetball game techcal statstcs dcators. Ths d of data processg method whch apples the correlato coeffcet to the statstcal aalyss of basetball techology has acheved good research results the emprcal research stage, ad ca reflect the actual stuato of the game through the correlato betwee the techcal dex ad the scores, ad reasoably aalyze each team s wg reaso ad tactcal characterstcs of the game, but also ca fd out the oppoet s weaess, to w the game. However, ths method s stll the study ad applcato stage, there s o large-scale expermet, there are stll a few problems eed to mae closer specto ad verfcato. Fgure 7 ear relatoshp betwee ad shootg percetage Fgure 8 ear relatoshp betwee the total scores ad the shootg percetage 6. Acowledgemet The research s supported by humates ad socal sceces research fud for youg scetsts of Shhez Uversty (No. RWSK6-Y24). Referece [] Zhao Xcag, Zha Feq. Statstcs. Bejg: Bejg Normal Uversty Press, 200. [2] Zha. Research o Correlatve Relato betwee the Wg Percetage Home ad Away Match ad the Scorg wth Result Ra CBA Basetball Match. Cha Sport Scece ad Techology, 200, 46 (6): [3] Jag Hao, Che jua. Aalyss of Decsve Factors aers Wg the Fals NBA Seaso. Joural of Jl Isttute of Physcal Educato, 20, 27 (3): [4] Joh Hollger. Pro Basetball Prospectus: 2003 Edto. USA, [5] Joh Hollger. Pro Basetball Forecast. Brassey s [6] Guo Yogbo, Wu Zeta. A aalyss of core factors for BOETIM TECNICO DA PETROBRAS 379

7 wg me s basetball games played the 30th Olympc Games. Joural of Physcal Educato, 204 (): 0 3. [7] u Gaowe. A Comparatve Study o Offesve ad Defesve Ablty of Chese Me s Basetball Team Recet Three Olympc Games. X a: Shaax Normal Uversty, 200. [8] Jag Hao. Aalyss ad Emprcal Study o Statstcal Idex of Basetball Techology Based o Correlato Coeffcet. Wuha: Wuha Sport Uversty [9] Ye Sogzhog. Regresso Aalyss o Techcal Idex ad Effcecy Value of CBA Athletes Seaso. Movemet, 20, 2: 0. [0] Zheg Yue. Research o the Curret Stuato ad Developmet of Chese Me s Basetball Team Based o Statstcal Aalyss of odo Olympc Games. Master s Thess of Schua Normal Uversty, 203(2). SEPTEMBER

Chapter Business Statistics: A First Course Fifth Edition. Learning Objectives. Correlation vs. Regression. In this chapter, you learn:

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