1 2015 J ( 2 ) a a 2014 12 12 2015 J 2 3 4 5 62%, 35%, 3%( 3.4) µ±1.2σ 16 (18 ) 2 1 1 J1 2015 ( ) [1]. 1993 J 2004 2 + 2005 [2] [3] a 1-501 konaka@meijo-u.ac.jp
J [4]. 2 1 2 1 5 *1 20 5 J 08 128 12 9 3000 119 14 10 2 ( ) 4 NFL MLB NBA NHL [7] (NPB) 2007 ( ) ( ) J J *2 ( ) 2 *1 [5][6] *2 2
2 2015 J 2015 J 2014 2 25 [1] 18 2 1 17 153 306 4 1 1 2 3 1 W1 W2 ( ) Y1 Y3 W1 Y3 W2 Y2 1 1 2 Y1 Y1 W1, W2, Y2, Y3 W1 W2 Y1 2 1 5 J 1 8 3 5 2 9 4 Y4-3
1 The postseason tournament of J1 League from 2015 season 1 Overlap cases case # overlap(s) teams 1 null 5 2 (Y3, W1) 4 3 (Y2, W1) 4 4 (Y2, W1), (Y3, W2) 3 5 (Y1, W1) 4 6 (Y1, W1), (Y3, W2) 3 7 (Y1, W1), (Y2, W2) 3 8 (Y1, W1), (Y1, W2) 3 2 Overlap case #1 3 1 (W1 W2) 3.1 i j 4
3 Overlap case #2 4 Overlap case #3 5 Overlap case #4 6 Overlap case #5 λ ALL 1 λ i,gf i 1 (Goals For). λ i,ga i 1 (Goals Against). λ i,gf,h λ i,ga,h i 1 λ i,gf,a λ i,ga,a X i i 1 Po(λ) λ. 5
7 Overlap case #6 8 Overlap case #7 9 Overlap case #8 3.2 1 [8]. 10 2013 J1 1 M1: X i Po(λ ALL ) p(x) = e λallλx ALL,x = 0,1,. (1) x! P(X i = x,x j = y) = p(x)p(y). (2) M2: X i Po(λ i,gf ) p i (x) = e λi,gf λx i,gf x! 6,x = 0,1,. (3)
0.4 0.35 Observed Poisson 0.3 Frequency 0.25 0.2 0.15 0.1 0.05 0 0 1 2 3 4 5 6 7 8 9 10 Goals 10 Distribution of goals par game P(X i = x,x j = y) = p i (x)p j (y). (4) ( ) λi,gf +λ j,ga M3: i,j X i Po 2 p i,j (x) = e µx µi,j i,j,x = 0,1,. (5) x! µ i,j = λ i,gf +λ j,ga 2 (6) P(X i = x,x j = y) = p i,j (x)p j,i (y). (7) ( ) λi,gf,h +λ j,ga,a M4: i j X i Po 2 p i,j (x) = e µx µi,j i,j,x = 0,1,. (8) x! µ i,j = λ i,gf,h +λ j,ga,a 2 (9) P(X i = x,x j = y) = p i,j (x)p j,i (y). (10) M5: i j i g (λ i,gf,λ j,ga,g) 7
(λ i,gf,λ j,ga ) 0.4 30 ( ) µ i,j µ(λ i,gf,λ j,ga ) = a 1 λ i,gf +a 2 λ j,ga +a 3 (11) i,j X i Po(µ i,j ) p i,j (x) = e µx µi,j i,j,x = 0,1,. (12) x! P(X i = x,x j = y) = p i,j (x)p j,i (y). (13) λ i,gf, λ i,ga J 3.3 10 5 M5 4 (2010 2013) r 2 = 0.8721 2 3 2 The number of teams reached the postseason Teams M1 M2 M3 M4 M5 case # 3 0.4320 0.5912 0.5196 0.5676 0.6173 4, 6, 7, 8 4 0.4876 0.3740 0.4282 0.3916 0.3519 2, 3, 5 5 0.0804 0.0348 0.0522 0.0408 0.0308 1 mean 3.6485 3.4466 3.5327 3.4372 3.4134 3.4 2 5 10 30 1 M1 M4 11 2013 (63) M2 M4 ( 48.705,54.686,48.797 10 15 ) 8
3 Probability of each overlap cases Teams M1 M2 M3 M4 M5 case # 5 0.0804 0.0348 0.0522 0.0408 0.0308 1 4 0.0754 0.0496 0.0606 0.0527 0.0459 2 4 0.1205 0.0865 0.1016 0.0898 0.0809 3 3 0.0530 0.0549 0.0539 0.0513 0.0550 4 4 0.2917 0.2379 0.2660 0.2491 0.2251 5 3 0.1168 0.1399 0.1328 0.1353 0.1448 6 3 0.2063 0.2766 0.2456 0.2639 0.2864 7 3 0.0559 0.1198 0.0873 0.1172 0.1311 8 3.5 4 x 104 3 M2 M3 M4 Frequency 2.5 2 1.5 1 0.5 0 0 20 40 60 80 100 Points 11 Distribution of points per season M5 4 (Pts) (Mean) (Err) (Std) (Err/Std) 18 16 µ±1.2σ 2 M1 M4 1 2 3 4 [1] 3 4 ( ) 9
4 Simulation result with model M5 (total points) Standing Pts Mean Err Std Err/Std 1 63 60.86 2.14 7.32 0.292 2 62 58.22 3.78 7.37 0.512 3 60 54.64 5.36 7.67 0.698 4 59 59.92 0.92 7.39 0.124 5 59 51.28 7.72 7.63 1.011 6 58 52.24 5.76 7.71 0.747 7 55 50.41 4.59 7.53 0.609 8 54 54.86 0.86 7.63 0.112 9 50 41.67 8.33 7.47 1.115 10 48 45.16 2.84 7.63 0.372 11 47 46.12 0.88 7.52 0.117 12 46 41.85 4.15 7.55 0.549 13 45 48.65 3.65 7.41 0.492 14 45 44.90 0.10 7.47 0.013 15 37 39.43 2.43 7.10 0.342 16 25 30.72 5.72 6.90 0.828 17 23 37.37 14.37 7.22 1.990 18 14 26.62 12.62 6.55 1.926 *3 2015 J 18 2 1 17 153 306 3 (Y1 Y3) Y1 ( 12) 4 3 (W1) 4 (W2) W2 1 *3 [5][6] 10
12 Basic format of postseason W1 Y2 Y3 W1 1 W2 1 ( 13(a)) W1 Y1 W2 1 Y2 Y3 1 ( 13(b)) 13 One stage winner reaches postseason as repechage 4 2 (W1, W2) 1 1 Y2 W2 Y3 W1 4 Y1 ( 14) 14 Two stage winners reach postseason as repechage 11
1 ( 2 ) 2015 J1 1 2 2 2 2015 J 3 3 1 2 3 2 4 2015 J 2 1 [1] J League.. http://www.j-league.or.jp/release/000/00005661.html, Feb. 2014. referred in 2014/11. [2] Jupiler Pro League. Formule de championnat. http://www.sport.be/fr/jupilerproleague/competitieformule/ (in French), 2014. referred in 2014/11. [3] Scottich Professional Football League. The rules of the Scottich Professional Football League. http://spfl.co.uk/docs/067 324 therulesofthescottishprofessionalfootballleagueasat11september 2014 1411980004.pdf, Sep. 2014. referred in 2014/11. [4] ( ). [ ] 2. http://number.bunshun.jp/articles/-/724962, Oct. 2013. referred in 2014/11. 12
[5] MSN.. http://sankei.jp.msn.com/sports/news/131030/scr13103019190009-n1.htm, Oct. 2013. refered in 2014/11. [6] J League. 10 30. http://www.j-league.or.jp/release/000/00005433.html, Oct. 2013. referred in 2014/11. [7]. 2 http://www.footballchannel.jp/2013/11/15/post12391/ ( issue65 ), Nov. 2013. refered in 2014.11. [8] JohnS. Croucher. Using Statistics to Predict Scores in English Premier League Soccer. In Sergiy Butenko, Jaime Gil-Lafuente, and PanosM. Pardalos, editors, Economics, Management and Optimization in Sports, pages 43 57. Springer Berlin Heidelberg, 2004. 13