Avalable onlne www.ocpr.com Journal of Chemcal and Pharmaceutcal Research, 2014, 6(3):326-332 Research Artcle ISSN : 0975-7384 CODEN(USA) : JCPRC5 Research on comprehensve evaluaton model-based NBA schedule nfluences on team performance Dawe Sh Department of Phscal Educaton, Hebe Unverst of Technolog, Tann, Chna ABSTRACT Schedule has dfferent effects on team compettve result to some extent; therefore reasonable and scentfc schedule should not onl reflect equt of competton but also ncrease the splendd degrees of competton. Ths paper makes detaled analss of proper nfluences condtons that NBA regular season schedule affects competton n order to get a reasonable comprehensve evaluaton to schedule through analss and then acheve schedule optmzed scheme. At frst establsh schedule evaluaton comprehensve model through mpact analss of schedule affects team compettveness, then utlze evaluaton model to make comprehensve evaluaton on each team schedule and get evaluaton results, fnall establsh schedule optmzed model through extractng unreasonable factors of schedule based on evaluaton results, and acheve fghtng strateges of eastern conference same secton dfferent regons compettons to provde theoretcal bass for NBA schedule and schedule aspect orentaton for NBA season reform. Ke words: Comprehensve evaluaton model, optmzaton desgn, mpact weght, NBA schedule INTRODUCTION In 1873 badmnton movement was born n England; after 100 ears of vgorous development, badmnton has become a ver popular sports proect n the world; badmnton can full exercse the bod and enhance functons of the human bod. Whether t's a regular badmnton game or as a general ftness actvt, the should conduct footwork, ump, twst and swng on the ground wthout break [1, 2]; ratonal use of varous httng technques and the footwork to strke the ball back and force on the court, thereb ncreasng strength of the arms, legs and wast muscles, acceleratng the sstemc blood crculaton of the exercse, enhancng the functon. NBA competton s one of worldwde basketball fans favorte compettons. To NBA such a enormous competton, t s a ver complcated thng to comple a completed and equtable schedule to each team as far as possble. Schedule has a certan effect on team strength plang and standngs, therefore as whole world basketball fans cared NBA regular season, reasonable schedule arrangements of fond teams are expected. To show schedule equt and fght splendd, ths paper analzes schedule that affects team compettveness plang so as to get reasonable schedule evaluaton model and schedule optmzed model and provde orentaton and theoretcal bass for NBA schedule reform [3-6]. For NBA schedule evaluaton and optmzaton research, lots of people have made efforts, thoughts and results that the put forward are contnuousl verfng b NBA compettons. Among them, Xu Jng(2009) Adopts analtc herarch process to sstematcall analss of NBA2008-2009 seasons competton equt ssues, brngs nto schedule pros and cons comprehensve ndex to measure pros and cons that schedule affects each team, and desgns relatve scentfc competton schemes[1]; Zeng Yu-Hua(2009) Makes analss and evaluaton on NBA schedule b combnng wth natonal college students mathematcal modelng competton queston D, puts forward a set of new method as tpe matchng for NBA schedule partcpatng three courts secondar teams all condtons b achevng 326
man factors that affect competton wth statstcs analss and fttng methods[2]; Zhang Yu-Lan(2011)Accordng to seasons schedule and competton result, takes comprehensve consderatons of teams strength wde gap degree, home and guest courts, scores dfference between two teams total 3 factors, puts forward teams scheme and algorthm of selectng 3 courts n one season, and acheve specfc competton scheme through programmng soluton wth language C [3]. NBA s an enormous competton, and schedule has a certan effect on teams strength plang and standngs, therefore t s a ver complcated thng to make completed and equal schedule so as to elmnate plaers, coaches and medas complans to schedule. Ths paper based on prevous studes, makes analss of NBA schedule nfluences on plaers and team, explores schedule evaluaton model based on one team, and establsh NBA schedule comprehensve evaluaton model n order to put forward more reasonable and scentfc NBA schedule plannng through model analss and provde data bass and research obects for season optmzaton desgn. NBA SCHEDULE ANALYSIS AND EVALUATION METHODS The purpose of analze NBA schedule s to elmnate nequalt of competton and mprove splendd degree of competton. To analze schedule pros and cons to one team, man factors should be consdered. If these factors can be extracted and used to convert schedule nto quanttatve ndex that easer for mathematcal handlng, t would provde great help for schedule evaluaton. Ths paper summarzes sx tpcal condtons and analzes them accordngl so as to acheve purpose of NBA schedule analss [4]. NBA schedule analss Adacent games nterval tme: Basketball game s an event dfferent from other sport ones, ts phscal output bascall ust second to that of football game; Whle one event as NBA whch s ver normal and has global coverage, not onl should provde audence the most wonderful game, but also should ensure plaers have a reasonable rest tme and phscal adust tme after court. However, there are two dsputes exstng on rest tme plannng, one s so long rest tme that ratng books and economc benefts are affected ; the other s so short rest tme that plaers can not show audence a wonderful game. Due to above two condtons constrants, balance ponts between the two should be acqured n schedule so as not favor one over another [5]. Home or guest court mpacts on competton: In NBA basketball competton, home or guest court plas a role n teams competton. The home court advantage refers to that plaers pla wth other teams n the ct that ts team belongs to so that gets rd of tolng awa b long ourne, sleepng late wakng up earl before competton as well as troubles lke nconvenent eatng and lodgng; Meanwhle, competton court s the place wth whch the themselves most famlar and even take tranng, ther adaptaton n spot, lght hoop, clmate and scene atmosphere have advantages over the opponents. To sum up, above factors ndcates that fght n home or guest court plas a certan role n team competton, therefore n schedule of regular seasons should consder whch team frst plas n home court whch team frst plas n guest court, tmes of home and guest courts and so on [7]. Analss of ntervals between home and guest court: Intervals between home and guest court refers to plaers rest tme; Due to regular season has a fxed startng and endng tme n competton, and each team must complete 82 compettons n gven tme, therefore lmted tme should be made full use for lettng plaers phscal qualt get best rest and adust as much as possble. Intervals between home and guest court means plaer s should change competton court, n ths case tred ourne and pschologcal nfluence s nvarable generated, so ntervals between home and guest court would also be regarded one of mportant ndcators to evaluate schedule [8]. Analss of compettons n same secton dfferent regons: There are two plang methods for same secton but dfferent regons team, one s to pla 3 courts, and the other s to pla 4 courts. Manl concerns n choosng whether 3 courts or 4 courts plang s such team phscal strength condton, ten teams wll carr out 36 courts compettons, partal teams would pla 3 courts whle others pla 4 courts, whle numbers of comng across strong teams n competton s one mportant factor that affect teams standngs, ever team would hope tself comes across weak team as much as possble so as to ncrease ther team probablt of enterng plaoffs. Snce ever team would pla respectvel 2 courts wth teams n dfferent secton and pla 4 courts wth teams n same regons, such two plang method are fxed, onl n same secton but dfferent regons such stage the can have pla wth weak team as much as possble, therefore the schedule allocaton of same secton dfferent regons drectl mpacts on them whether can enter nto plaoffs or not. Analss of partcpatng team strength: The strength o teams s one mportant factors that affects ther development ; In ever stage, NBA would rank the teams, teams rankngs pla a specal mportant role n teams development, but based on the lmts of teams strength, teams wthout stronger strength should make efforts to schedule so as to acheve better regular season rankng. Because n regular season, t s requred to pla wth ever team from whole 327
allance, teams would hope the themselves come across stronger team as less as possble, whle pla wth weaker team as more as possble. So evaluate schedule pros and cons to some team, frst should consder such team overall strength and then thnk about excellent plaers strength n the team. Analss of back to back plang: Back to Back s a regular plang n NBA, due to ever team geographcal dstrbuton causes, usuall one team would on the game n other ctes. In order to reduce plaers nconvenences that led b court transferrng as much as possble, the regular back-to-back plang as home-guest-guest-home and guest-home-home-guest are appled. Such applcaton s to reduce team court transferrng tmes so that can ncrease rest tme and mprove competton qualt. NBA schedule evaluaton methods NBA s a compettve event; team s plaoffs entr s an mportant factor that affects team development, normall plaoff selecton s depend on regular season performance rankng, whle regular season rankng method s accordng to each team vctor and fal courts n regular season, n case that vctor and fal court are the same, scores, loss and gap between scores and loss as well as ever home and guest court standngs should be consdered to make comprehensve evaluaton to get each team rankng, fnall select out teams that enter nto plaoff. To ever team, t frst should to pla respectvel n one home one guest total courts compettons wth 15 teams from dfferent sectons, then carres out two homes and two guests wth 4 teams from dfferent regons total 16 courts compettons, such two tems total 46 courts compettons s fxed. For above 46 courts compettons, onl need to consder whch part frst plas n home court and team tself strength such two factors, whle the rest 36 courts competton need to make groups assembl.due to 4 courts and 3 courts plang occur to same secton dfferent regons compettons, accordng to calculaton, t s got that all allance would have 6 teams to pla 4 courts compettons and 4 teams to pla 3 court compettons. To 4 courts compettons and 3 courts compettons, ts own sde comes across strong teams numbers should be taken nto full consderaton, then the two start pla games and get merts of teams b schedule arrangements. Accordng to calculaton, t s got that 6 teams pla 3 courts and 4 teams pla 4 courts n same secton dfferent regons schedule. Ths paper selects as varables from 0 to 1, when comes across strong team, takes 1, on the contrar takes 0.In the teams that selected to pla 4 courts, assume that a teams are stronger than tself n strength, whle b teams are stronger than tself n strength n teams to pla 3 courts, then relatonshp s as formula (1) shows. a 6 1, b 4 1 (1) If make comparson n numbers of strong teams that comes across n 3 courts compettons and 4 courts compettons, then take tmes of comng across strong team and teams numbers n plang 3 courts to evaluate the two rato n 3 courts compettons, get proportons of comng across strong team n 3 court compettons. Smlarl can get proportons of comng across strong team n 4 courts compettons, then let proporton of comng across strong team n 3 courts compettons to mnus that n 4 courts compettons to work out whch teams come across strong team for more tmes so that can get teams merts n the followng compettons development. Use P to represent dfferent value, as formula (2) shows. a b 1 P 6 1 6 4 6 1 4 1 4 In order to get whole allance each team comes across strong teams advantage weght, take weght, as formula (3) shows. Q (2) to represent the Q p 100% p 1 1,2,, (3) Organze each team each competton s rest tme ntervals can work out total rest tme n each competton, then use total rest tme dvdes rest ntervals n competton. Due to ever team has 82 courts compettons, ts rest ntervals s 328
81 tmes, then can use competton total rest tme dvdes rest tmes to get average rest tme n each competton, work out such tme as t 1. 9753 da through calculaton, then wth ths tme ntervals as reference, make comparson wth each rest ntervals n each competton, the more closer that tme ntervals to reference tme, the more beneft that team would be.make superposton of dfferences between team total tme ntervals and reference ntervals can get each team tme ntervals quantt, then accordng to the reference, make rankng on team pros and cons condtons n tme ntervals, ts concrete ndcator F computatonal form s as Formula (4) shows. F x 100% x 1 1,2,, (4) Smlarl can get tme allocaton pros and cons weght M to team based on scene transfer and scene not transfer, S contnuous home court quantt pros and cons weght to team and Frst tme plang n the home court pros K and cons weght to team, as formula (5) shows. From whch, 1,2,,. M m s 41 x 100%, S 100%, K m s 41 x 1 1 1 100% (5) It can be concluded comprehensve evaluaton ndcator formula (6) shows. A Z Z Q F M K S 100% Q F M K S 1 1 100% A that schedule affects competton, ts express s as (6) NBA SCHEDULE OPTIMIZATION DESIGN NBA evaluaton result To make evaluaton of schedule advantages and dsadvantages, frstl should defne wth whch teams each tme plas 3 courts and plas 4 courts, through data handlng and then accordng to ts result make respectve contrastng and lst out whch teams strengths are stronger than own sde team as well as whch teams are weaker than own sde. Brng statstcs results nto formula (3) can get opponent allocaton affects team n 3 courts and 4 courts plang as Table 1 show. Table 1: opponent allocaton nfluences on team standngs based on 3 courts and 4 courts Team Evaluaton Team Evaluaton Team Evaluaton Team Evaluaton Team Evaluaton Celtcs -1.090 Lakers -1.090 Spurs -0.272 Suns -0.363 Magc -0.636 Nuggets 0.1818 Cavalers -0.090 Brave dragons -0.181 76ers -0.181 Hawks 0.0000 Nets 0.2727 Bobcats 0.7272 Knckerbockers 0.8181 Grzzles 0.6363 Supersoncs 1.0909 Pstons -0.909 Hornets -0.909 Rockets -0.909 Jazz 0.0909 Mavercks -0.454 Warrors 0.1818 Wzards -0.454 Tralblazers 0.4545 Kngs 0.4545 Pacers 0.0909 Bulls 0.3636 Bucks 0.6363 Clppers 0.3636 Tmberwolves 1.0909 Heat 1.0909 Team pros and cons based on tme ntervals can be got from formula (4), and ts result as Table (2) show. Table 2: Team pros and cons condtons based on tme ntervals Team Evaluaton Team Evaluaton Team Evaluaton Team Evaluaton Team Evaluaton Celtcs 3.12% Lakers 3.50% Spurs 3.35% Suns 3.20% Magc 3.04% Nuggets 3.35% Cavalers 3.20% Brave dragons 3.35% 76ers 3.80% Hawks 3.65% Nets 3.80% Bobcats 3.27% Knckerbockers 2.74% Grzzles 3.65% Supersoncs 3.35% Pstons 2.74% Hornets 3.50% Rockets 3.50% Jazz 3.42% Mavercks 2.82% Warrors 2.74% Wzards 2.89% Tralblazers 3.12% Kngs 3.50% Pacers 3.50% Bulls 3.37 Bucks 3.73% Clppers 3.50% Tmberwolves 3.65% Heat 3.43% Competton pros and cons condtons based on home and guest courts s as Table 3 shows. 329
Table 3: Competton pros and cons condtons based on home and guest courts Team Total value Weght Team Total value Weght Team Total value Weght Celtcs 144 3.70% Lakers 136 3.50% Spurs 129 3.% Nuggets 108 2.80% Cavalers 118 3.00% Brave dragons 155 4.00% Nets 133 3.40% Bobcats 155 4.00% Knckerbockers 172 4.40% Pstons 131 3.% Hornets 125 3.20% Rockets 125 3.20% Warrors 121 3.10% Wzards 116 3.00% Tralblazers 147 3.80% Bulls 112 2.80% Bucks 95 2.40% Clppers 93 2.40% Suns 183 4.70% Jazz 155 4.00% Magc 131 3.40% 76ers 129 3.% Kngs 119 3.00% Hawks 104 2.70% Grzzles 99 2.50% Tmberwolves 146 3.70% Supersoncs 127 3.20% Mavercks 112 2.80% Pacers 135 3.50% Heat 155 3.90% Competton pros and cons condtons based on frst competton n home court s as Table 4 shows. Table 4: Competton pros and cons condtons based on frst competton n home court Team Weght Team Weght Team Weght Team Weght Team Weght Celtcs 4.02% Lakers 3.83% Spurs 4.06% Suns 2.70% Magc 3.61% Nuggets 3.38% Cavalers 3.61% Brave dragons 2.70% 76ers 2.70% Hawks 2.48% Nets 3.38% Bobcats 4.51% Knckerbockers 3.16% Grzzles 3.16% Supersoncs 3.38% Pstons 3.83% Hornets 3.16% Rockets 2.93% Jazz 3.83% Mavercks 2.93% Warrors 2.25% Wzards 4.06% Tralblazers 2.48% Kngs 3.83% Pacers 2.70% Bulls 2.93% Bucks 1.80% Clppers 3.38% Tmberwolves 3.61% Heat 5.41% Competton pros and cons condtons based on rest tme generated b scene transferrng s as Table 5 shows. Table 5: Competton pros and cons condtons based on scene transferrng Team Weght Team Weght Team Weght Team Weght Team Weght Celtcs 3.56% Lakers 6.18% Spurs 3.56% Suns 4.77% Magc 2.25% Nuggets 5.34% Cavalers -0.43% Brave dragons -6.78% 76ers 5.53% Hawks 3.87% Nets 2.50% Bobcats 3.23% Knckerbockers 3.38% Grzzles 4.21% Supersoncs 1.52% Pstons 2.36% Hornets 6.18% Rockets 5.00% Jazz 1.46% Mavercks 2.77% Warrors 1.89% Wzards 2.37% Tralblazers 5.20% Kngs 5.41% Pacers 3.43% Bulls 1.52% Bucks 6.77% Clppers 5.34% Tmberwolves 3.05% Heat 4.41% Brng 5 tables data nto formula (6) can get schedule pros and cons degree to each team, the smaller the value s the better the team would be, the bgger the value s the worse the team would be, the best and worst teams meet the formula (7). Best mn A, A,, A ; Worst max A, A, A 1 2 1 2, (7) In formula (7), Best shows the best team n schedule, Worst shows the worst team n schedule, overall result s as Table 6 shows. Table 6: Table of schedule comprehensve evaluaton result Team Result Team Result Team Result Team Result Team Result Celtcs -0.9459 Lakers -0.91985 Spurs -0.12927 Suns -0.2093 Magc -0.51597 Nuggets 0.3566 Cavalers 0.006109 Brave dragons -0.15132 76ers -0.0276 Hawks 0.127075 Nets 0.403599 Bobcats 0.877346 Knckerbockers 0.956456 Grzzles 0.771575 Supersoncs 1.205466 Pstons -0.78663 Hornets -0.74855 Rockets -0.76265 Jazz 0.21807 Mavercks -0.34079 Warrors 0.281632 Wzards -0.3277 Tralblazers 0.600599 Kngs 0.611951 Pacers 0.222251 Bulls 0.473457 Bucks 0.783357 Clppers 0.509851 Tmberwolves 1.231075 Heat 1.2558 From fnal result n Table 6, t can be known that schedule s best for Celtcs, whle worst for Heat. NBA schedule optmzaton desgn method In order to make optmzaton desgn of schedule, frstl should analze schedule nfluence factors from competton area overall strength, ever competton area overall strength s depend on each team overall strength; t can be known from comprehensve evaluaton of schedule that average wnnng percentage n ever competton area bascall reman n around 50%, southwest allance team have the hghest wnnng percentage of 58.54%, whle southeast team have the lowest wnnng percentage of 43.64%, other ever competton area overall level has less devaton. It can be concluded that each competton area overall strength has slghtest mpact on schedule, so that t 3
can be gnored. Concentrate research on team strength should take comprehensve consderaton of 5 aspects as wnnng percentage, wnnng dfferences, sub regon wnnng percentage, sub secton wnnng percentage, home and guest courts wnnng percentage, and make quantzaton of them, from whch wnnng percentage entrel can reflect vctor rato wthout consderng an obectve thngs, reflects team last season vctor or defeat condtons; wnnng dfferences reflect team s strength condtons n ts own sub regon; sub regon wnnng percentage reflects such team strength nsde regons, sub secton wnnng percentage reflects vctor or defeat condtons nsde sectons, home and guest courts wnnng percentage reflects team adaptaton ablt as well as other comprehensve qualtes, therefore vctor and defeat tmes are ke factors to measure one team strength. In case that vctor and defeat tmes cannot make ntegrated sequence of team strength, factors as wnnng dfferences, sub regon wnnng percentage, sub secton wnnng percentage as well as home and guest courts wnnng percentage should be used to make strength evaluaton rankng to team. When arranges 3 courts plang schedule, t should take full consderaton of each team overall level that has same secton wth ts own sde but dfferent regons from ts own sde, from whch teams wth the slghtest dfferences n overall levels should be arranged n 3 courts plang as much as possble, meanwhle should also thnk about team level s balance problem. To keep equt among teams, each team quantt and strength such two aspects balance should be remaned and consder constrants of competton courts. In concluson, schedule optmzaton model can be reflected n formula (8). e1 e2 e3 3 n1 mn 5 10 1 5 10 1 5 10 1 5 1 1 1 1 kn 2 3 h h1 a1 b1 a3 b3 a2 b2 e k1 k2 k3 (8) In formula (8), eh shows one regon n same secton, a shows wnnng percentage n one regon, k shows varable from 0 to 1, obectve functon n optmzaton model b shows the rest two regons wnnng percentage, ndcates the strength dfference between ever two teams s the mnmum one, whch s to sa comparable teams pla games that s a close competton whch can meet equt of schedule and also show wonderful confrontaton vews. NBA schedule optmzaton desgn result Utlze optmzaton model n formula (8), t can be got optmzaton desgn scheme of 15 teams n same secton pla 3 courts compettons wth correspondng other two regons two teams as Table 7 shows, take result reference of eastern conference. Table 7: Eastern conference same secton dfferent regons 3 courts plang optmzaton desgn result and fghtng table Celtcs VS Pacers VS Magc VS Bobcats VS Bulls VS Pstons Pstons Magc Cavalers Cavalers Wzard Brave dragons VS 76ers VS Pacers Pacers Bulls Bucks Bulls Bucks Magc Brave dragons Celtcs Wzard 76ers Brave dragons Cavalers VS Pstons VS Celtcs Nets 76ers Nets Knckerbockers Knckerbockers Pstons Pstons Celtcs Pacers Pacers Brave dragons Wzard VS Hawks VS Bulls Bulls Cavalers Bucks Bucks Pacers Brave dragons Wzard Wzard 76ers Hawks Hawks Nets VS Bucks VS Nets Bobcats Bobcats Knckerbockers Heat Heat Magc Magc Celtcs Hawks Hawks 76 人 Knckerbockers VS Heat VS Bobcats Bobcats Nets Heat Heat Knckerbockers 331
CONCLUSION Ths paper made 5 aspects analss of pros and cons that schedule affects team after enterng nto plaoff, and utlzed mathematcal modelng method and mathematcal statstcs method to make quantzaton of each aspect factors. Ths paper establshed comprehensve evaluaton model that schedule nfluences on team, and pros and cons result that schedule affects on partcpatng teams b such model. Through analss pros and cons result and nfluence factors that schedule produced to team, establshed schedule optmzaton desgn model, such model took mnmum dfference between ever fghtng partes as obectve functon wth the purpose of equt reflecton and fghtng whte-hot mprovement, got fghtng plannng schemes of eastern allance same secton dfferent regons after optmzed. REFERENCES [1] Xu Jng. Journal of Kamusze Unverst, 2009, 27(4), 566-569. [2] Zeng Yu-Hua etc. Journal of Chongqng nsttute of technolog, 2009, 11(2), 157-164. [3] Zhang Yu-Lan. Gansu scence and technolog, 2011, 27(2), 42-43. [4] Zhang B.; Feng Y.. Internatonal Journal of Appled Mathematcs and Statstcs, 2013, 40(10), 136-143. [5] Dong Dong-Feng. Journal of Changsha nsttute of communcaton technolog, 2008, 7(2). [6] Zhang B.; Zhang S.; Lu G.. Journal of Chemcal and Pharmaceutcal Research, 2013, 5(9), 256-262. [7] Zhang B.; Internatonal Journal of Appled Mathematcs and Statstcs, 2013, 44(14), 422-4. [8] Zhang B.; Yue H.. Internatonal Journal of Appled Mathematcs and Statstcs, 2013, 40(10), 469-476. 332