2002世界杯足球赛比赛结果预测之研究

2002y G w s§B ¶BK ns O H2002@M y 13w A A i y B g B g b y B W B y B N y B I y B B s y B P B P B y H A h k y G(³B M B t)ªw C k GP k G())75.189.2(311ˆi y +−−+=ept P t k G())75.195.0(3211)ˆˆ(i y +−−+=+e p pi y 1.4578A k w v v F iy p 0.7364A k w t v t v F Y O b A h k w M v t v C w @P 71.2¡A @P 7.8¡A P 21¡A O Somers’D¡G 0.634¡A Gamma¡G 0.802¡A n -a¡G 0.425¡A c¡G 0.817¡C A2002@M y G w n CG y B hp G B A x G Tp q G0927-557630 E-mail¡G t476@B×B s@×@M y H x y A X F p h u A FIFA(¥@ y)´X z v×P W h A H P P F P wa N y A A y w B y P m F@yy a a A B H O X F D O a B Ly C l y P y A O L y B L k C A@P O A A H FIFA W M×A u A L M L k e A@T O o J s C t A T w y t@O y M a P O F@A b X k a A q L O M T w y t A D XX z L A h C A y t w O D D A FM a×A P A i W T w G v T A P M aP A i w T H X z Cb R p k W A w k u O(linear discriminate function)©M k(logistic regression)(³A85)¡A Hosmer, Hosmer P Fisher(1983)«X AX A u O b s W A i p Ap Y t C Press P Wilson(1978)«h X A O s P X A Ak T u O C A s@MO s A H s k R c w@y t Ck O(y)¬G W q(¦p k P k A P A P)¡A Oh(¦p C J B J P J A B L P D)¡A o O q HA N O W q(nominal)©M(ordinal)¶q A L k M c@k Y Ab X¡B Y y b A(Y)¥P(X)¥A u k b q HA O A X A n k F Y(ªL M s A87)¡Cs Y O H q u B M B t v A2002@13wA h k w Cb k m W A(¥85)¥x x@P h zA H G A A t k A w A wv A w T v F77.2¢H(¥T66.2¢H+¥T O11¢H)¡A O vu 5.6¢H A i H P I C(¥87)½s s y AH P A@223W A H P N A kw G logit(p)=-11.36¡0.05׺e y0.03×±y0.46פe0.05¡wC T@P F86.4¢H A@P13.5¢H A s G i m Cw G(©h)ªW q(©)ÅA k i w Pu CG B ss2002@M y13A A i y B g B g b y BW B y B N y B I y B B s y B P B P B y H A@G(³B M B t)ªw CT B su B B t W A p o h t t Ab W p C W A C t A tA A P A P A32yy y A t t p A i CL B sB ss2002 ¥y32y s H A p A32KA C A C T A e W A@16P@qO A A@8P G q O A A@4P M Ai a x A i u x C A2002@M y@32C×8)¡A16O8A8O4A4M2A H @p48(42a x P u x A X p64A C@i A H@128i s CG B p2002@M y s w A p i y(goal scored)(®g i y)B g(shot)(°)B g b y(shot on goal)(®g b y d)B W(foul)(¥P P w H W h)B y(corner kick)(¥X u y o y)B N y(free kick)(¦u W o y)B I y(penalty kick)(»@12X y)¡B(offside)(§e L u)B s y(own goal)(¦uN y i v y)B P(caution)(Äi)B P(expulsion)(ÅX v X)B y(ballpossession %)(±y)B(actual playing time)(¦x y)A¦@¦13(¼e FIFA b@)¡A s D@A NH PK(penalty kick)ªM A H90W D A X p16vs R B vs q B vs B8vs B gvs A@5C13w A H G u B M B t vA h k R w G A H v T O wk CT B Rs HSPSS 10.0128@z p R H u B M B t v T O b 13w W l R A M H SAS 8e h k R ARP B z 128CB G P ×B B B t t2002@M y 128A 45A M 38A t 45AH G b 13t A i W l R A G p G (½g T Y C t )¡A 13u i y B g B g b y M I y t A l 9L t C p T A o b i y W T t A u M (¥t 1.22)¡A u t (¥t 1.78)¥H M u t (¥t 0.56)¡F g W u M (¥t 2.21)¡A u t (¥t 3.84)¡F g b y W u M (¥t 2.19)¡A u t (¥t 3.04)¡F I y W u t (¥t 0.20)¡A M u t (¥t 0.24)¡C b t w A I y t t S @i I y A P P M t A l T t H A M A t C C@z p K nwOt 45 2.22 1.31 M 38 1.00 0.74 i y t 45 0.44 0.69 45 13.24 4.01 M 38 11.03 3.51 gt 45 9.40 3.53 45 7.11 2.21 M 38 4.92 1.78 g b yt 45 4.07 1.97 45 0.20 0.40 M 38 0.24 0.49 I yt45 0 0G B M B t T R K nw t M×F p74.08 2 37.0439.61* 0.0001i y116.89 125 0.94190.97 127334.88 2 167.4412.24* 0.0001g1710.09 12513.682044.97 127220.46 2 110.2327.45* 0.0001g b y502.01 125 4.02722.47 1271.40 2 0.70 5.45* 0.0050I y16.07 125 0.1317.47 127*p<.05T B M B t T K n*p<.05G B h k Rs B(stepwise)¿w A J k w SLENTRY0.01¡A k w n v W J A S w F(SLENTRY<0.01) F P i w A w SLSTAY0.01¡A N O J k wF w(SLSTAY<0.01)¡A P C k w wi y(p)A S L w F J(SLENTRY<0.01)P (SLSTAY<0.01)ªA H k w u i y C(¤@) I P w pu B M B t v T A b h k c k u A P(§Y M P t)ºc@k u A t P t(§Y P M)ºc G k u F i v p k(Maximum Likelihood Estimation)±o I1p-0.61¡A2χ 10.94¡A F F I 2p0.61¡A2χ 10.94¡A F A I1P I2s b p W N q Ct A w P O SCORE p q M w A s13wSCORE p q p F w F p A i y B g b y Bg P I y A SCORE 2χ 47.66¡B32.76¡B15.86 6.59¡C SCORE 2χI J w K n×p2χ pI 1 1 -0.61 0.19 10.94*0.0009I 2 10.00090.61 0.19 10.94**p<.05w SCORE p q K nw×SCORE 2χ pi y 1 47.66 0.0001*g 1 15.86 0.0001*g b y 1 32.76 0.0001*W 1 0.640.42y 1 0.480.49N y 1 0.190.66I y 1 6.590.01*0.411 0.67s y 1 0.090.76P 1 1.390.24P 1 2.310.13y 1 0.070.79y 1 0.010.91*p<.05(¤G) J i y1¡B A X×wb J i y@w A n A X×A p A w w PY A AIC(Akaike Information Criterion)¡B SC(Schwartz Criterion)©M-2log L(-2log Likelihood Statistic)¤T O v(´L A90)¡A F A w PA k O H y A O N q CA X×w K nA X×w I I@pAIC 284.46 213.95 <0.0001*SC 290.17 222.51 <0.0001*-2log L 280.46 207.95 <0.0001**p<.052¡B k Y(£)ªww k Y(£)¡A p C A P T i A v (likelihood ratio)¡BSCORE p q M Wald p q A T 2χ (£=0)¡A k Y O s b CCk Y w K nw ×2χp v 1 72.52 0.0001* SCORE 1 47.66 0.0001* Wald145.76 0.0001**p<.05 3¡B k Rv B k w i y A g i v p R o p (¦p K )¡G I 1-2.89¡A I 2-0.95¡A i y 1.75¡A 2χ 151.26¡A I 29.82A i y 45.76A T F (p<0.05)A Y I M i y s A H s b N q C t A i y (odds Ratio)ÂI p 5.78A N C W @i y A o v W 5.78A i i y v T C t A @i u B M Bt v T k u c A ×v 1.75¡A p i y 0A )ˆ(log 3pit -2.89¡A )ˆˆ(log 32p pit + -0.95¡A ×v N q i y W w W A e CKh k K n×p 2χ pI pI 1 1 -2.89 0.40 51.26 <0.0001* I 2 1 -0.95 0.30 9.82 0.0017* i y1 1.75 0.26 45.76 <0.0001* 5.78*p<.05 H 2002@G w(1)ku p (3ˆp2ˆp 1ˆpt )GP G)(75.189.2)ˆ(log 3i y +−=p itt P t G)(75.10.95)ˆˆ(log 32i y +−=+p p it(2)kH u B M B t v T k A G i X A 01v A i y 0A X P v 0.0527A C X t P t v 0.2789F i y 8A X P H X t P t v 1A i i y W A X u B M B t v v W C k p GP G ())75.189.2(311ˆi y +−−+=e pt P t G())75.195.0(3211)ˆˆ(i y +−−+=+ep pT i A b v 01d A i y W A t v K ×t p A M v K ×W p A v O H i y W W C b T i H t v P M v @I I (cutpoint)A M M v b P v G I I A o u B M B t v A O @w Y C o I I I A 1ˆp 2ˆp i X t 0.7364A 2ˆp3ˆpi X 1.4578A N O i y 1.4578A k w v v F i y p 0.7364A k w t v t v F Y O b A h k w M v t v CK GK G ())75.189.2(311ˆi y +−−+=epM v K ×G 2ˆp ())75.195.0(11i y +−−+e3ˆpt v K ×G 1ˆp13ˆp2ˆp(T ) k M w v A @P (concordant)71.2A @P (discordant)7.8A P (tied)21A N N G T v A @P u C t A A H C Somers’D 0.634A Gamma 0.802A n -a 0.425A c 0.817A T C F n -a A A2002@G w n CB PBs 2002@M y 128s H A y G(B M B t)w A s ×p G(@) 13n p (p )G i y B g b y B g B I y B P B P B B W B y B N y B s y B y y A J k w i y A v T G i y C(G ) k GP k G ())75.189.2(311ˆi y +−−+=e pt P t G())75.195.0(3211)ˆˆ(i y +−−+=+ep p(T ) i y (odds ratio)I p 5.78A N C W @i y A o v W 5.78A i i y v T A i y h A o C () T o BM B t F I I (cut point)A t P M I I 0.7364A M P I I 1.4578A i y 1.4578A k w v v F i y p 0.7364A k w t v t v A Y O b A h k w M v t v C() w @P (concordant)71.2A @P (discordant)7.8A P (tied)21C H A Somers’D 0.634A Gamma 0.802A n -a 0.425A c 0.817C A 2002@G w n CG Bw A b s w W A i P i y A p w a P w t A b e g i 16y A @i i 2.67y A w b e @g i 14y A @i i 2.33y A H a J w w a x t (w t a x )A i 90W v 0.8560A v 0.9764F w 90W v 0.7684A v 0.9580C o v A A O o v @CA P A R k i W T w G v T A M O w g o L G A i T L k T L w A u q C o v A X y R G M a h M P A p i H W e y M H h A w G @A L p y d pB W p (p w n y J (Ballack, M)T )B m N B y B A N h ××A X M a P q X X z P CA Study of Prediction by the Results of Logistic Regression onthe Game in 2002 FIFA World CupHsu Po-YangRepublic of China Sports FederationABSTRACTThe purpose of the study was to construct a prediction model by the results of the game in 2002world cup. The dependence variables were the group of win, draw and losing. The independence variables were including 13 offense-defense indexes (goal scored, shot, shot on goal, foul, corner kick, free kick, penalty kick, offside, own goal, caution, expulsion, ball possession %, actual playing time). Model construction could be analyzed by multiple logistic regression. The results of logistic regression equation wereWin and draw or losing: ())75.189.2(311ˆgoalscored e p+−−+=Losing and win or draw: ())75.195.0(3211)ˆˆ(goalscored ep p+−−+=+If the goals scored were more then 1.4578, the probability of win was more then draw or losing inregression prediction model. If the goals scored were less then 0.7364, the probability of losing wasmore then win or draw in regression prediction model. If the goals scored were between 1.4578 and 0.7364, the probability of draw was more then win or losing in regression prediction model. The quality of prediction model were percent concordant 71.2, percent discordant 7.8 and percent tied 21. The indexes of prediction model were Somers’D 0.634, Gamma 0.802 n -a 0.425, c 0.817. On the whole, the results of the game had good characteristics in 2002 world cup.Key words: world cup, multiple logistic regression.mH(86)G L p P p R C x G E CL(90)G SAS P p R C x G L q C(87)G s s y X C M×p e C p e s G NSC 88-2413-H-179-007C³°°¶©úµ¥(85)¡G¤@-Ó¹w´úªì¶-¸¦æª²{¤§Ã¦N´µ¼¦¡C A43 1A385-394CªL²M¤s(87)G¦h¤¸Ã¹¦N¦¡°jÂk«Y¼Æª³Ì¤j¥i¯à©Ê¦-p¡BÅãH h Nk R A X×C A451A181-200CAgresti, A. (1996). An introduction to categorical data analysis. New York: John Wiley & Sons Inc.. New York: John Wiley Hosmer, D. W. & Lemeshow, S. (1989). Applied logistic regression& Sons Inc.Hosmer, T. A., Hosmer, D. W. & Fisher, L.(1983). A Comparison of three methods of estimating the logistic regression coefficient, Communication statistics computation, 12, 727-751.Press, S. J. & Wilson, S. (1978). 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