An Indian Journal FULL PAPER ABSTRACT KEYWORDS. Trade Science Inc.

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1 [Type tet] [Type tet] [Type tet] ISSN : Volume Issue 9 BoTechology 4 A Ida Joural FULL PAPER BTAIJ, (9), 4 [37-35] Grey correlato degree-based CBA basetball game techques fluece factors study Chule Zhag Physcal Educato Departmet, Chagchu Uversty of Scece ad Techology, Chagchu, 3, JL, (CHINA) ABSTRACT I recet years, basetball games are costatly popular; varous people partcpate basetball games, so the paper goes deeper research basetball games. Based o documets lterature, regresso aalyss, grey correlato aalyss, the paper maes quattatve aalyss of recet fve sessos CBA league matches champos teams, o ths bass, t costructs dcators grey correlato sequece ad regresso model. By researchg, t aalyzes champos teams wg fluece factors that clude feldgoal percetage, free throw percetage; three-pot shot percetage, assst, defese ad others e ds of factors. Ad the by aalyzg the e ds of fluece factors, t gets games scores fluetal relatve sgfcat dcators, fally t maes summary ad provdes suggestos for teams trag. KEYWORDS CBA; Techcal dcator; Grey correlato; Regresso aalyss; Champo team. Trade Scece Ic.

2 38 Grey correlato degree-based CBA basetball game techques fluece factors study BTAIJ, (9) 4 INTRODUCTION Basetball was orgated Amerca 89,t was veted by Amerca physcal educato teacher Dr.James Nasmth. I the begg, Nasmth respectvely stalled two basets that used to put pears guard bar of both sdes corrdor of secod floor school gym, basetball upper sde was 3.5m hgher from groud, used football as games tool, played games the way of throwg to baset. Now basetball evet s hot, Natoal Basetball Assocato (NBA) s of great cocers of every basetball fa. Chese basetball games are also uprecedeted hot, CBA games become dspesble tal whe every youth that s fod of basetball at lesure. Basetball s a d of techologcal evet, basetball techques are essetal codtos to decde games performaces, the paper carres o research ad aalyss of basetball games each dcator techque by grey correlato method; by stepwse regresso model, t solves scores correlated sgfcat dcators ad verfes. RESEARCH OBJECTS AND METHODS Research objects CBA league matches recet fve years champos teams that seaso 9-,seaso -,seaso -,seaso -3 ad seaso 3-4 champos teams. Utlze Chese basetball assocato offcal webste obtaed CBA league matches recet fve years champos teams all games data as research objects, ad meawhle carry o quattatve aalyss []. Research methods Documets lterature: O the bass of cosultg umerous relatve basetball sports techques, basetball tactcs, basetball defese techques tme factors, correlato test ad other aspects lterature formato, the paper focuses o researchg relatve formato of them; by detaled searchg ad cosultg teams formato, t gets acowledge CBA league matches champo team. Vdeo observatoal method: Watch games vdeos by Cha teret TV stato, ad observe appled sports techques, tactcs statstcal method by vdeo, mae statstcs of champos teams feld goal percetage, reboud, fault ad other techcal dcators. Data statstcs method: ()By hadlg wth CBA league matches recet fve seasos all teams data, mae statstcs of every seaso champo team scores status, cout each tem techcal dcator ad game scores correlatos, use EXCEL software to mae statstcs of basetball techcal dcators, ad mae classfcato of dcators ad draw []. ()The core of grey correlato aalyss s utlzg sequece curve geometrc shape appromate degree to judge whether ts coectos are compact or ot, curve geometrc shape gets more smlar, the correspodg sequeces correlato degree wll be bgger, o the cotrary, t gets smaller. It s well ow that all tme sequece data, horzotal sequece data ad dcator sequece data ca be used to mae correlato aalyss. Due to CBA champo team attac ad defese data ad wg rate are oe d of horzotal sequece data, therefore, the paper usg correlato aalyss s reasoable ad feasble. (3)Grey correlato aalyss applcato rage [3]. Whe solve correlato degree, t uses dcators every pot correlato coeffcet average value. Whe correlato coeffcet dstrbuto s dscrete, the t wll produce oe clato that pot wth bg correlato coeffcet umerc value decdes overall correlato degree. Therefore, case sub sequece gets closer to ma sequece correspodg elemets, results obtaed by grey correlato degree s obtaed by lttle dscrete degree correlato coeffcet average value, ow average value ca reflect correlato coeffcet overall commetary, therefore t s relable. (4)Calculate basetball game s all techcal dcators (that are fluece factors)ad game result correlato degree, cocrete calculato process s )frstly defe referece sequece ad comparso sequece; )mae orgal data trasformato of sequece, ad the solve absolute dfferece sequece;

3 BTAIJ, (9) 4 Chule Zhag 39 3)calculate correlato coeffcet, correlato degree; 4) ra correlato sequeced, get correlato matr ad mae advatage aalyss. (5)Utlze regresso aalyss method to hadle wth research objects recet fve years partcpated all games (total 4 games) data, ad the costruct regresso model test [4]. RESULT AND ANALYSIS Data aalyss Mae table ad sort out data et s data as TABLE shows, t s clear that champo teams games performace status the fve years show ustable tedecy as frst stable ad the declg, teams performaces are gradually declg after 9 seaso, whch shows teams fal scores levels have declato. I recet fve seasos perod, ecept for Zhejag team s every champo team feld goal percetage has t had fercely fluctuato that amog 5%-5%. It dcates every champo team ecept for Zhejag team,ts feld-goal percetage eeps stable state, fluctuato s o more tha two percetage, of course eclude 3-4 seaso. From the table, t s clear that recet two years seaso s free throw percetages are hghest; t shows teams have mproved free throw aspect. Threepot shot percetage also always eeps amog.3-.37, t s relatve stable but the declg tred. 3-4 seasos Zhejag team free throw shot percetage s the hghest, 9- ad - these two seasos champos are Guagdog team, whle Sha team s the champo -ad -3 the two seasos. Ad 3-4 seaso champos are Zhejag team, whch dcates 3 seaso, both Guagdog team ad Sha team performace decle. But Guagdog team reboud umber eeps uchaged, t shows Guagdog delegato s relatve sllful ad has stable bass the techcal dcator. By TABLE data, t s clear that amout of steals are relatve stable the fve seasos perod, o bg chages, from whch steal amout s largest 9- seaso; fault amout chages are larger,whch represets frst reduce ad the crease, ad9- seaso fault amouts are stll largest, therefore the paper studed teams focus o fault reducto, gve ther ormal performace to play; free throw percetage ad scores have larger correlatos, so research objects should more strct wth free throw trag, mprove ther ht rates; amout of bloc shot chages are larger the fve seasos, t presets ustable tedecy, ad acheve hghest records -3 seaso ;amout of foul chages get closer to creasg fucto, durg the fve seasos, t shows creasg by seaso, whch dcates research objects should put emphass o competto rules, ad uderstad competto rules ther hearts, they should tae more cultvato ad trag ey techques at ordary tmes, so that ca get good results compettos;amout of asssts are relatve stable, these fve seasos, o ecessve creases or decreases appear, but asssts are least - seaso. TABLE : Recet fve seasos champos teams fluece factors ad competto scores status Seaso Champo team Score Feld goal percetage Free throw percetage Three-pot shot percetage Bloc shot Total reboudsassst Foul StealFault 9-Guagdog Guagdog Sha Sha Zhejag Correlato aalyss By correl fucto,mae correlato coeffcet calculato of TABLE every fluece factor ad competto score, t gets TABLE.

4 3 Grey correlato degree-based CBA basetball game techques fluece factors study BTAIJ, (9) 4 TABLE : Correlato coeffcet Feld goal percetage Three-pot shot percetagefree throw percetagetotal reboudsassst Steal Bloc shotfaultfoul From TABLE, t s clear that competto score mamum correlato factor s feld goal percetage. Amog them, free throw percetage, three-pot shot percetage, foul ad steal have sgfcat correlatos by comparg to other techcal dcators, ad have bgger dffereces wth other techcal dcators correlato coeffcets. It shows that f oe team has obvous advatages above aspects, the team scores compettos are hgher, so fally probablty that ws the compettos smlarly wll be bgger. Therefore,CBA league matches all coaches, athletes deserve to focus o these techcal dcators aspects trag, cultvato ad mprovemets, so that possess tatve competto, ad have best chace of wg. But t does t mea the rest techcal dcators are ot mportat, every fluece factors basetball feld caot be gored. It always occurs that strog team s defeated by wea team. I addto, coaches, athletes should also stregthe psychologcal qualtes trag ad cultvato, whch s beefcal to gve ther best performace to play. Grey correlato degree aalyss As a developmet ad chagg system, correlato aalyss actually s quatzato comparatve aalyss of dyamc process developmet tred. So-called developmet tred comparso, s also system each perod relatve statstcal data s geometrc relatoshp comparso. By grey system theory, t s clear that fact every champo team game score s a grey system project. Accordg to every champo team fluece factors ad games scores grey correlato degree aalyss, reflect every score fluetal techcal dcators ad games scores fluece ad effects, ad lear ther correlatos. To guaratee establshed model accuracy ad scetfcty, the paper maes trasformato ad hadlg wth orgal data, let t to elmate dmeso ad has comparablty. Data trasformato techque: Defto : Set t has sequeces: = ( ), ), L )), The map: f : y f ( ) = y(, =,, L It s seres to seres y data trasformato. )Whe: f ( ) = = y(, ( ) ) It s called f s tal value trasformato. )Whe f ( ) = = y(, = ) =

5 BTAIJ, (9) 4 Chule Zhag 3 It s called f s average value trasformato. 3)Whe: f ( ) = = y( From whch s some value that above,t s called f s ormalzato trasformato. 4)Whe: m f ( ) = = y( ma It s called f s rage mamum value trasformato. 5)Whe: m f ( ) = = y( ma - m It s called f s terval value trasformato. I the paper basetball competto techcal dcators aalyss, t maes followg trasformato: ) ) = (,, L ) ) ) It s talzato sequece of orgal sequece X. So that we ca mae talzato processg wth TABLE e sequeces ecept for competto performaces. It s worth otg that for prevous seve sequeces, creasg of umerc values meas sports levels advacemet, whle for the post two sequeces, reducto of umerc values meas sports levels advacemet. Therefore, whe do talzato processg wth sequece 9 ad, adopt followg formula: () () () () = (,,,, ), = 8, 9 () (3) (4) (5) Correlato aalyss: Defto : Select referece sequece: = { ( =,, L, } = ( (), (), L, ( )) Amog them, tme s represeted by. Assume that the umber of comparso seres s m : = { ( =,, L, } = ( (), (), L, ( )), =,, L, m The: m m (t) s (t) +ρ ma ma (t) s (t) s t s t = ( ( +ρ ma ma (t) (t) s t ξ () s

6 3 Grey correlato degree-based CBA basetball game techques fluece factors study BTAIJ, (9) 4 Formula () s comparso sequece to referece sequece the momet correlato coeffcet,from whch resoluto coeffcet s usg ρ [,] to epress, two-level mmum dfferece ad two-level mamum dfferece respectvely use m m ( t) s ( t), ρ ma ma ( t) s ( t) to s t s t epress. I geeral, resoluto rate ad resoluto coeffcet have same chages. Due to correlato coeffcet s a d of dcator that descrbes comparso sequece ad referece sequece correlato degree at oe momet, but every momet has a correspodg cdece umber, formato s ot so cocetrated ad s bad for comparso. Therefore, we mae followg defto. Defto 3: Call: = ξ ( = r () It s sequece to referece sequece correlato degree. The utlze MATLAB to calculate, t gets correlato degree as TABLE 3. Idcator Normal grey correlato degree TABLE 3 : Each dcator ad scores correlato degree table Feld goal percetage Free throw percetag e Three-pot shot percetage Total rebouds Asss t Fou l Steal.74 Bloc shot Faul t Ra Hadle wth team wg fluetal each d of techcal dcators data, ad by grey correlato aalyss calculatg, t gets fluece factors ad competto scores correlato degree szes relatos: feld goal percetage >fault>foul>total rebouds>assst>steal>bloc shot>three-pot shot percetage>free throw percetage. By the relatoshp, t gets the frst three fluece factors obvously have larger correlato degrees wth scores, relatoshp last two tems have least correlato degrees wth scores, but the two tems are also a d of effectve scorg dcator, so t caot smply gore them. If two teams stregth have o bgger dffereces, whch team s well traed the two aspects, t ca grasp the tatve compettos, ad wg odds wll be larger. Team scores ablty fluece (stepwse) lear regresso aalyss Stepwse regresso s a commo method multple regressos that s used to select depedet varables. The basc thought of the method s:troduce depedet varables to equato oe by oe, codto of troducto s the depedet varable partal regresso square sum should be the largest oe uselected depedet varables (uselected quatty),ad t shows sgfcace by F testg. O the other had, whe troduce a ew varable every tme, t should stepwse carry o F test o prevous selected varables equato (selected quatty), ad remove varables that partal regresso squares sum s the smallest ad have o sgfcace from equato, tll depedet varables beyod equato caot be troduces, ad depedet varables equato caot be removed. Aother oe s bacward method, ts basc thought s: frstly establsh regresso equatos that clude all depedet varables, ad the stepwse remove varables, frstly do F (or t) test o every depedet varable, remove sgfcat varables depedet varable wth mmum partal regresso squares sum, recostruct equato. The, mae stepwse F test o depedet varable out of equato, troduce varable wth mamum partal regresso squares sum ad has sgfcace to equato. Repeat above process, tll equato s all depedet varables have sgfcaces ad

7 BTAIJ, (9) 4 Chule Zhag 33 depedet varables out of equato have o sgfcace. The method s avalable case depedet varables ot so may, especally sgfcat varables are ot so may. Compare to geeral multple regressos, regresso equato that s solved by stepwse regresso method has followg advatages: t cluded depedet varables umbers are lttle ad easy to apply; ts rest stadard devato s also small, equato stablty s better: due to every step wll be tested; t esures equato s all depedet varables to have sgfcaces. LetY to represet champo team every game score, t s related to varable feld goal percetage, free throw percetage, three-pot shot percetage, reboud, steal, foul, assst, bloc shot ad fault e fluece factors, from whch e factors respectvely use X, X, L, X 9 to epress. Assume radom factor fluece ests, eve X, X, L, X 9 are relatve fed, teams rags are also ot all the same. Therefore o the codto affrm that Y has lear correlatos wth X, X, L, X 9,the paper aalyzes the lear relatoshp by two parts. Multple lear regresso model s: Y = β + βx + β X + L + β 9X ε ~ N(, σ ) 9 + ε (3) Amog them, ε s supposed to a radom varable that coforms to ormal dstrbuto, β s costat, each factor Y regresso coeffcet s usg β ( 9) to epress, f ts umerc values get bgger, the t shows mpacts are more sgfcat. Utlze depedet varables that have sgfcat mpacts o Y,costruct regresso model. By data, t carres o stepwse regresso aalyss, gets varables of sgfcat mpacts, ad accordg to correlato szes, so that obtaed decsve factors by prevous correlato aalyss s more covcg ad sgfcat. Iput data to formula (3), t ca be epressed as: Y = Xβ + ε ε ~ N(, σ E ) (4) Amog them, E s order ut matr. Parameters estmato, model s parameters that t should select estmato value βˆ j,let whe β = = (y β β βmm ) = j β, β,, βm L stll use least square estmato method, = βˆ, j =,,, L, m,error sum of squares: Q = ε L (5) Arrve at mmum. Thereupo, let: Q =, j,, L, β j = (6) It gets equato sets, by sortg, t gets: j β β = m = β + β = +β + L + βm m = y = = = +β + β + L + βm m = y = = = = +β m + β m + L + βm m = m = = = = Matr equato set s matr form s: y (7)

8 34 Grey correlato degree-based CBA basetball game techques fluece factors study BTAIJ, (9) 4 T T X Xβ = X Y (8) Whe matr X colum s full ra, X T X s reversble matr, formula (8) soluto s: ˆ T T β = (X X) X Y (9) Substtute βˆ bac to orgal model the ca get Y estmato value, as TABLE 4. TABLE 4 : Regresso model calculato result Parameter Parameter estmato value Parameter cofdece terval β [ ] β 4.7 [ ] β [ ] β 4.7 [ ] β [ ] β [ ] β [ ] β 9.74 [ ] R =.7338 F = P = By stepwse regresso aalyss, t gets two dcators are removed from e fluece dcators that are respectvely steal ad assst. Teams rags relatve mportat fluece factors are feld goal percetage, free throw percetage, rebouds, three-pot shot percetage ad scores. Obvously each fluece factor has very remarable sgfcace. Requred to test s orgal hypothess: H = : β = β = β3 = β4 = β5 = β6 = β7 = β8 β9 If H does t dey, the t shows usage of lear regresso model s approprate. () F test method Model obtaed statstcal quatty F = ,by cosultg F dstrbuto umercal table F.95(,3) =.8, obvously F >. 8, by F test crtero, t s clear cofdece sgfcace level.5,t refuses H that thought X, X 4, X8, X9 ad Y lear relatoshp s sgfcat. () Regresso model correlato coeffcet evaluato Negatve correlato coeffcet betweey ad depedet varable after elmato s R =.667, judgmet coeffcet r = It shows the paper costructed mathematcal model ftess etet belogs to good level, lear correlato s very strog, ad meawhle cofdece sgfcace level. 5,t refuses H. (3) P Value test Obtaed P =. obvously meets P < a =. 5,t dcates regresso varable X ad depedet varable Y lear relatoshp s sgfcat. Above three statstcal ferece method ferred results are cosstet, all th after elmato regresso depedet varable X ad depedet varabley lear relatoshp s sgfcat,t shows regresso model ca bascally reflect X ad Y relatoshp. Therefore, coaches ca get competto

9 BTAIJ, (9) 4 Chule Zhag 35 performace fluece fact ors ad szes accordg to the model, fd out respectve advatages ad dsadvatages, ad purposely carry o techque ad tactcs layout ad adjustmet. CONCLUSION By statstcs ad researches o the fve seasos data, t fds that champos teams feld goal percetage, three-pot shot percetage ad free throw percetage the three techcal dcators performace are very stable sce recet fve seasos, the fluctuato s ot bg. By each fluece Factors dcators ad scores correlato aalyss, t gets that feld goal percetage has largest correlato wth scores, secodly s free throw percetage, three-pot shot percetage, total rebouds, foul ad steal. By data processg ad researchg, t gets free throw percetage ad three-pot shot percetage have least mpacts o competto scores, however geeral, the two fluece factors dcators are commo thought to be most mportat. It dcates that people should correct ther recogto mstaes. REFERENCES [] Che Ja, Yao Sog-pg; Applcato of Coected Aalyss to Aalyss of Statstcal Data of Basetball Techque. Joural of Shagha Physcal Educato Isttute, 33(5), (9). [] Wag Lug et al.; Developmet of a Computerzed System for O-the-spot Techcal Statstcs Basetball Matches. Cha Sport Scece, 9(3), 37-4 (999). [3] Mao Je, Sha Shuguag; Basetball Techology Statstcal Software Developmet. Joural of Wuha Isttute of Physcal Educato, 46(), 7-73, 87 (). [4] Zhag Le; Aalyss o Foul Ma's Basetball Fal Phase th Natoal Games. Cha Sport Scece ad Techology, 4(), 5-5 (6). [5] Fu Fa-fe, Yu Zhe-feg, Zhag Qua-g; Aalyss of offesve turover perod of me's basetball fal matches at th Natoal Games. Shadog Sports Scece & Techology, 8(), 4-5 (6). [6] Wag Lug et al.; Developmet of a Computerzed System for O-the-spot Techcal Statstcs Basetball Matches. Cha Sport Scece, 9(3), 37-4 (999). [7] L J-hu; Research o the Curret Stuato ad Developg Strategy of Chese Trac ad Feld Coaches. Joural of Sheyag Sport Uversty, 5(), (6). [8] Yag Yue-qg, Rao Ha-fu, Le J-la; A Study o the Improvemet of Computer Statstc Software for Basetball Games. Joural of Hube Sports Scece, (), 4-5 (3).