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

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1 [Type text] [Type text] [Type text] ISSN : Volume Issue 9 BoTechnology An Indan Journal FULL PAPER BTAIJ, (9), [333-3] Matlab mult-dmensonal model-based - 3 Chnese football assocaton super league football teams strength research Yngcheng Zhang Northeast Normal Unversty, Changchun, Jln, (CHINA) ABSTRACT In order to make comprehensve evaluaton on Chnese football teams strength, the paper analyzes Chnese football teams performances n year -3natonal football frst dvson team league matches, establshes four models from smple to complex, from rough to relatve accurate, frstly successve calculate each team total score, and meanwhle make statstcs of each team number of games, rank total score /number of games, obtaned result can approxmately be used as each team rankng. Secondly, accordng to game data, establsh a dgtal matrx A =(a ), use C++ programmng, nput obtaned matrx, solve Hamlton openng path, and rank t. In the followng, use three-pont to calculate any team and team ( ) score rato b, from whch b =, and get score matrx B =(b ), solve score matrx maxmum feature value, and solve correspondng feature vector. Compare component vector sze that can solve rankng. Fnally use analytc herarchy process, take average score, number of goal dfference and rato between wnnng games numbers and partcpaton games numbers as crteron layer nfluence factors, accordng to ther proportonal relatonshps, construct postve recprocal matrx (nverse matrx), by solvng maxmum feature value and ts feature vector, and then solve rankng. KEYWORDS Football team strength; Graph theory model; Score matrx; Analytc herarchy process. Trade Scence Inc.

2 33 Matlab mult-dmensonal model-based -3 Chnese football assocaton super league football teams strength BTAIJ, (9) INTRODUCTION In recent decades, football such sports event s relatve popular n Chna, s favored by lots of ball fans, more and more large-scale football games have been organzed n domestc, from whch natonal football league match s a relatve formal game organzaton wth relatve precse game requrements. Score prncples beng ust, far and open s partcularly mportant. In modern football technques, tactcs analyss and evaluaton, t often adopts ball controllng percentage, pass number and other orgnal data to make analyss and evaluaton, n fact, orgnal data and game result nconsstency possblty s larger. Wang Ka, Lv Xao-We, He Jang-Chuan [] ()adopted factor analyss method, establshed year 9 season Chnese football assocaton super league team matches four commonalty factors nfluental score standardzaton lneal combnaton estmaton formulas and factor total score standardzaton lnear combnaton estmaton formula, computed and got year 9season Chnese football assocaton super league team matches 6 teams factor scores season evaluaton rankngs, made analytc dscusson on ther dfferences, and provded evdence for scentfc and effectve pre-season tranng control and performance predcton; They establshed a set of new evaluaton system. Xu Le [] (3)appled mathematcal statstcs, sum of ranks rato comprehensve evaluaton method to make quanttatve analyss of season partcpated Chnese football assocaton super league sxteen teams attack and defense ndcators data, made varance analyss and multple comparsons of analyss results, and appled rank correlaton method to detect analyss result, mplemented quantzaton evaluaton on technques and tactcs abltes of Chnese football assocaton super league teams, so as to pursut obectve and realstc reflectng partcpated teams comprehensve technques and tactcs abltes. But lteratures that study from multple perspectves are lttle, the paper tres to apply multple methods to establsh team strength evaluaton model and ranks the teams. EVALUATION MODEL ESTABLISHMENTS Average score method model Accordng to natonal football league matches rule, wn a game wll get three ponts, draw gets one pont, lose a game doesn t get pont. The paper s used symbols llustraton: a the team total number of games; a the team wnnng number of games; a the team draw number of games; a 3 the team losng number of games; w the team total score; ϕ the team average score; Successvely compute every team total score and average score: Obectve functon: ϕ = w a w Constrant condton: = 3 a 3 = a + = a a Graph theory model Establsh a dgtal matrx A = (a ), whent defeatst, make marks a = ;when the two draw or the two have no games, don t make any marks ;whent s defeated byt, mark a = ; Accordng to obtaned matrx, make statstcs of sum total that every lne as that every team defeats opponents numbers, record as a vector α =,a,a,a,a,a,a,a,a,a,a,a ) ; (a

3 BTAIJ, (9) Yngcheng Zhang 335 If vectors have same elements as a = a, then respectvely solve sum total of all teams a that are defeated by T from to (that s N), and use them as new vector () () () () () () () () () () () () β = (a,a,)a,a,a,a,a,a,a,a,a,a ) a value, t gets new vector β ;f t stll has same elements, then randomly let one party to be, the other to be accordng to prncple of drawng lots, fnally t gets - matrx; Accordng to obtaned matrx, execute n well compled C++ programmng, and get Hamlton openng path; Every Hamlton path s a knd of rankng result, but ts dependence on matrx s too strong, whch needs us to further analyze comprehensve data, and get fnal rankng result. Score matrx method model For Model one average score method, t has ts rrevocable rratonalty; when compute game scores, t doesn t consder opponents are strong or weak. Such as, strong team wns strong team, t gets three ponts, and strong team wns weak team, t smlar gets three ponts. So adopt score rato matrx smlarly s use three-pont to compute any team and tme ( s not equal to ) score rato b, from whch b = Accordng to score matrx B = ( b ) (from whch b s team average score and team average score rato), solve score matrx maxmum feature value, and further get correspondng feature vector. Compare component vector sze that can solve rankng. Analytc herarchy process model In the model, we adopt analytc herarchy process. In the topc, we thought team rankng nfluences are manly as followng three factors: average score, goal dfference, wn/ total. Accordng to analytc herarchy process, we establsh followng herarchcal relatonshp Fgure. () Fgure : Herarchcal relaton Each factor x, x, x 3, mportance wth respect to target y (from whch y = w x + w x + w3 x ) uses followng TABLE numercal values to express. TABLE : Importance x / x Equal Relatve strong Strong Very strong Absolute strong a If t s between above two, then take,, 6, 8 [5].

4 336 Matlab mult-dmensonal model-based -3 Chnese football assocaton super league football teams strength BTAIJ, (9) By three factors mpacts on rankng, t construct matrx C, from whch C = ( c ) 3* 3 = ( x / x ) 3* 3, for above data we can wrte matrxc, and then solve maxmum feature value and ts correspondng feature vector. Make normalzaton processng wth feature vectors, then t can get w, w, w 3 values and we can solve rankng. Average score method model soluton Computed result s as TABLE shows: MODEL SOLUTIONS TABLE : Each team game data Team Total score Number of games Average score T T 5. T T T T T T8 7.9 T T 7.8 T T 9. Rankng result: T7 -T3 -T 9 -T8 6 5 Model expanson: For any N team, by competton obtaned data, we can rank accordng to average score, n case average scores are the same, t can consder rank on goal dfference, total goal rate and so on, f these factors are stll the same, only rank on these consderable equal level teams by drawng lots. Graph theory model soluton Establsh matrx

5 BTAIJ, (9) Yngcheng Zhang 337 = A It gets,,) = (,3,7,,,,7,,5,5 α Step two: = A It gets,,,) = (8,7,,,,,,, β. From above,, we stll cannot decde wnnng or losng between T and T, 6 T and T, by prncple of drawng lots, we assume that T s defeated by T, T s defeated by 6 T, fnally perfect matrx : = A By Model one, t can get: 3 T and 7 T team strength are strongest, whle T and T strength are relatve weakest.

6 338 Matlab mult-dmensonal model-based -3 Chnese football assocaton super league football teams strength BTAIJ, (9) From program runnng result, t selects Hamlton openng path wth T3 andt 7 as ntals, result s as TABLE 3 and TABLE shows. TABLE 3 : T 3 team Hamlton openng path TABLE : T 7 team Hamlton openng path Data analyss : () From above two tables, t gets that T 6, T, T 5, T, T are surely the bottom fve; ()Rank T, T, T 8, T 9, T : Combne wth vectorαand β, rank them and get T 9 8 Fnal rankng: T7 -T3 -T Score matrx model soluton Score matrx:

7 BTAIJ, (9) Yngcheng Zhang B = Use matlab software, t can solve B maxmum feature value and ts correspondng feature vector, t can get matrx B maxmum feature value as., ts correspondng feature vector s: [ ] T So we get each team rankng result as: T T6 -T5 Analytc herarchy process model soluton We can get each team average score, goal dfference, wn/total, as TABLE 5 shows. TABLE 5 : Each team game data processng result Team Average score Goal dfference Wn/Total T /9 T. /3 T /5 T /9 T /9 T6. - /5 T /7 T8.9 6/7 T /7 T.8-6/7 T /9 T. -3 /9 We can wrte matrx C = / 3 / 3 / In Matlab software, t can solve C maxmum feature value as λ max = 3.9, feature value λ max

8 3 Matlab mult-dmensonal model-based -3 Chnese football assocaton super league football teams strength BTAIJ, (9) correspondng feature vector as , normalze t and get vector.63, We can see average score proporton s larger, so when we rank teams, we frstly consder average score, when average score s about the same, we then calculate wnnng number of games and the number of games rato. Therefore, we get each team rankng as : T T6 -T5 MODEL TEST Adopt computer smulaton method to do model test. Specfc method s as followng: set t has n peces of teams to attend the games, adopt random functon to generate n peces of number n the nterval [, ] respectvely record them as M, t shows the n teams overall strength level, rank the n numbers from bg to small then can get n each team rankng. Accordng to generated n numbers, t can generate a group of game data, for any T and T, frstly use random functon to generate ther number of games b (value as one among,,, 3), t should also note number of games selecton should ensure graph connectvty that for any T, t should play one game wth other teams at least. Then, generate game data, t mght as well set T s stronger than T, we get a game result probablty experence formula by consultng nformaton [ ] : P{ T wn} = M M P{ T wn} =.3.3 M M P { dogfall} = - P{T wn} - P{T wn} =. -. M - M Record above three formulas probablty respectvely as P, P, P 3. Accordng to above probablty algorthm, t can respectve dvde nterval [, ] nto three segments accordng to above probablty sze to use as computer random smulaton game result. Fnally we smulate every game score, set T and T the q game score s a : b, then T w ns that s when random number X drops nto [, P ] b = rand()%3, a = b + + rand()%(n t)( + (M - M )) Tw ns, that s when random number X drops nto [ P, P + P ] a = rand()%3, b = a ++ rand()% Draw, that s when random number X drops nto [ P + P, ] a = b = rand()%5 After model fnshng, t can get any group data, carry on smple screenng on data then can select some rough data to test, analyze and evaluate establshed model.

9 BTAIJ, (9) Yngcheng Zhang 3 Record random generated rankng order s ( =,,..., n ). We adopted test formula s Q ( =,,..., n ), model generated rankng order s q E = ( Q q ) n n Obvously E gets small, t shows model s more reasonable, n order to elmnate random factors mpacts on model testng, we smulate enough more data to test, and E takes average level. When n =, due to data amount s very bg, we only take fve groups of data to carry on smple testng, test result s as followng TABLE 6. TABLE 6 : Test result Model Model one Model two Model three Model four E average value From TABLE 6, t s clear that model three E average value s smaller. To model usage condton, we need to further consder varance and so on. CONCLUSION The paper establshes four models from smple to complex, from rough to relatve accurate; ther respectve advantages are as followng: () Computaton s smple, operaton s convenent; () From operaton result, t can dstngush every team rough strength range n short tme, and dstngush them between dfferent levels; (3) It can relatve comprehensve and comprehensve compare each sub team strength level; () Consder multple factors mpacts on result; REFERENCES [] Wang Ka, Lu Xao-we, He Jang-chuan; Multvarate Statstcal Analyss on Tactcal and Techncal Structural Dfference of 6 Teams n 9 Chna Football Super League[J]. Chna Sport Scence and Technology, 6(5), (). [] L Qang, Zheng Chang-Jang; The Factor Analyss and Herarchcal Cluster Analyss of Technques Strateges of the last 3 teams n European Champonshp Cup Football In [J]. Journal of Physcal Educaton Insttute of Shanx Teachers Unversty, 7(), (). [3] Zhong Jan-mng, Ja Hong, Yang Xao-hongl; Applcaton Study on the Factors Affectng Teams' Score from Multvarate Statstcs n the FIFA World Cup[J]. Journal of Guangzhou Physcal Educaton Insttute, 3(3), 69-7 ().

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