arXiv201412_JP.dvi
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1 J ( 2 ) a a J %, 35%, 3%( 3.4) µ±1.2σ 16 (18 ) J ( ) [1] J [2] [3] a [email protected]
![2σ 16 (18 ) 2 1 1 J1 2015 ( ) [1].](/docs-images/51/20155555/images/page_1.jpg "1993 J 2004 2 + 2005 [2] [3] a 1-501")
2 J [4] * J ( ) 4 NFL MLB NBA NHL [7] (NPB) 2007 ( ) ( ) J J *2 ( ) 2 *1 [5][6] *2 2
3 J 2015 J [1] W1 W2 ( ) Y1 Y3 W1 Y3 W2 Y Y1 Y1 W1, W2, Y2, Y3 W1 W2 Y J Y4-3
4 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
5 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
6 7 Overlap case #6 8 Overlap case #7 9 Overlap case # [8] 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)
7 Observed Poisson 0.3 Frequency 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
8 (λ i,gf,λ j,ga ) ( ) 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 M5 4 ( ) r 2 = The number of teams reached the postseason Teams M1 M2 M3 M4 M5 case # , 6, 7, , 3, mean M1 M (63) M2 M4 ( ,54.686, ) 8
9 3 Probability of each overlap cases Teams M1 M2 M3 M4 M5 case # x M2 M3 M4 Frequency Points 11 Distribution of points per season M5 4 (Pts) (Mean) (Err) (Std) (Err/Std) µ±1.2σ 2 M1 M [1] 3 4 ( ) 9
10 4 Simulation result with model M5 (total points) Standing Pts Mean Err Std Err/Std * J (Y1 Y3) Y1 ( 12) 4 3 (W1) 4 (W2) W2 1 *3 [5][6] 10
11 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
12 1 ( 2 ) 2015 J J J 2 1 [1] J League.. Feb referred in 2014/11. [2] Jupiler Pro League. Formule de championnat. (in French), referred in 2014/11. [3] Scottich Professional Football League. The rules of the Scottich Professional Football League therulesofthescottishprofessionalfootballleagueasat11september pdf, Sep referred in 2014/11. [4] ( ). [ ] 2. Oct referred in 2014/11. 12
![[3] Scottich Professional Football League. The rules of the Scottich Professional Football League. http://spfl.co.uk/docs/067 324 therulesofthescottishprofessionalfootballleagueasat11september 2014 1411980004.](/docs-images/51/20155555/images/page_12.jpg "pdf, Sep. 2014. referred in 2014/11. [4] ( ). [ ] 2. http://number.bunshun.jp/articles/-/724962, Oct. 2013. referred in 2014/11. 12")
13 [5] MSN.. Oct refered in 2014/11. [6] J League Oct referred in 2014/11. [7]. 2 ( issue65 ), Nov refered in [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 Springer Berlin Heidelberg,
![jp/2013/11/15/post12391/ ( issue65 ), Nov. 2013. refered in 2014.11. [8] JohnS. Croucher.](/docs-images/51/20155555/images/page_13.jpg "Using Statistics to Predict Scores in English Premier League Soccer. In Sergiy Butenko, Jaime Gil-Lafuente, and PanosM.")
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