( ( )) : 1970 * ID * * 1 sabermetrics 2 Important Data identification *3 1

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1 修士学位論文題名統計的手法によるメジャーリーグ野球の打順最適化モデルの構築指導教員福永力教授平成 30 年 1 月 5 日提出首都大学東京大学院理工学研究科数理情報科学専攻学修番号氏名下木健太

2 ( ( )) : 1970 * ID * * *1 sabermetrics *2 Important Data identification *3 1

3 2 1 1 CPU 2

5 [5] 1990 ID [3] [1][2] [9] 2 [10] D Esopo and Lefkowitz [4] [1][6][7][2] [1][6] 1 1 2

6 *1 *2 2 Retrosheet *3 Retrosheet Retrosheet 2001 NUM GAME ID TEAM AWAY ID INN CT OUTS CT BALLS CT STRIKES CT PITCH SEQ TX 441 ANA SEA X 442 ANA SEA BCCBBX 443 ANA SEA X NUM BAT ID PIT ID BASE1RUN ID BASE2RUN ID BASE3RUN ID EVENT CD RBI CT 441 suzui001 hases001 mclem camem001 hases001 mclem marte001 hases001 camem001 mclem NUM 18 1 NUM= *1 *2 *3 3

7 :suzui001 *4 :hases001 :mclem001 EVENT CD *5 = 2 RBI CT = 0 SeanLahmancom *6 Sean Lahman 1871 SeanLahmancom 2 2 Lahman Batting Master Pitching Salaries School Teams OS Windows 10 Pro RAM 160GB CPU Intel Core i RStudio Version R R *4 *5 EVENT CD 0 24 EVENT CD= 2 EVENT CD= 20 *6 4

8 S S-PLUS Ross Ihaka Robert Gentleman Windows Mac OS R 2 5

9 ,2 1,3 2, ( ) ( ) 4 i P i = (p W, p S, p D, p T, p H, p O ) p W p S p D 2 p T 3 p H p O 2001 Lahman Batting 5 6

10 playerid yearid stint teamid lgid G AB R H 2B 3B HR suzukic SEA AL playerid RBI SB CS BB SO IBB HBP SH SF GIDP suzukic stint stint= 2 1 lgid AL NL 2 G R RBI 2 R RBI AB SB CS SO BB ( ) IBB ( ) HBP SH SF GIDP ( ) ( ) = ( ) + ( ) + ( ) + ( ) + ( ) + ( ) ( ) (= 31) ( ) = ( ) + ( ) + ( ) + ( ) ( ) P i = (p W, p S, p D, p T, p H, p O ) BB + HBP p W = BOX H (2B + 3B + HR) p S = BOX p D = 2B BOX p T = 3B BOX p H = HR BOX p O = 1 (p W + p S + p D + p T + p H ) 7

11 ( ) = ( ) + (2 ) + (3 ) + ( ) ( ) = ( ) {(2 ) + (3 ) + ( )} 22 ( ) * Mariners Bluejays Mariners Bluejays Mariners Bluejays * * *

12 Mariners ( 4 ) playerid p W p S p D p T p H p O 1 suzukic mclemma martied olerujo boonebr camermi guillca bellda wilsoda Mariners Bluejays 6 x y Real Marinerssimulation Real BluejaysSimulation Density Density Density Density Score Score Score Score 1 Mariners Bluejays

13 231 k A 1, A 2,, A k 8 8 A 1 A 2 A k O 1 O 2 O k n p 1 p 2 p k 1 np 1 np 2 np k n E i = np i χ 2 i E i 5 k χ 2 (E i O i ) 2 = (1) E i i=1 k 1 χ 2 *9 i O i E i χ 2 χ H 0 H a 2 α = 01 3 χ Mariners 9 *9 p245-p247 10

14 9 Mariners χ 2 i E i 5 1 E i Mariners (1) 10 χ 2 Mariners χ 2 Mariners = 245 Bluejays χ2 Bluejays =

15 χ 2 (k 1) 2 P T > χ 01 k 1 = 01 χ 2 01 (k 1) χ 2 3 k 1 χ 2 10 (α = 01) χ 2 01(k 1) 11 ( ) χ 2 p Mariners Bluejays i 0 i i i O i 162 p P (T > χ 2 ) T k 1 2 χ 2 p χ 2 x χ 2 Mariners 245 Bluejays 192 χ 2 01(k 1) p k 1 2 χ 2 (t; k 1) (p ) = χ 2 χ 2 (t; k 1)dt p Mariners 0011 Bluejays 0004 α 11 α (p ) χ 2 12

17 ( ) ,2 1,2 1, Retrosheet 12 NUM BAT ID PIT ID BASE1RUN ID BASE2RUN ID BASE3RUN ID EVENT CD RBI CT suzui001 nomoh001 * mclem001 nomoh001 suzui marte001 nomoh001 mclem001 suzui NUM= EVENT CD= 20 EVENT CD EVENT CD= 20 NUM= ,3 NUM= NUM= RUN ID 1 14

18 1, ,2 1,3 2, , , , ,2 1,3 2, , , , * = 1 ( ) 13 1,2 = 1 ( ) 1 2 *10 *11 3 ( 14 ) 15

19 312 2 i P i = (p W, p S, p D, p T, p H, p so, p poor ) p W p H p so p poor p so p poor p so = SO BOX p poor = 1 (p W + p S + p D + p T + p H + p so ) 2 ( ) 3 1 ( ) 3 ( ) Retrosheet ,2 1 2,3 1, , # = 1 ( )

20 ,2 1,3 2, # , # , # , # # = 1 ( ) Mariners Bluejays P i = (p W, p S, p D, p T, p H, p O, p so, p poor ) 17 Mariners Mariners ( ) playerid p W p S p D p T p H p so p poor 1 suzukic mclemma martied olerujo boonebr camermi guillca bellda wilsoda

21 2001 Mariners Bluejays 6 Real Marinerssimulation Real BluejaysSimulation Density Density Density Density Score Score Score Score 4 Mariners Bluejays Mariners

22 19 ( ) χ 2 p Mariners Bluejays χ 2 p α (p ) α χ α 19

23 ! foreach R foreach Revolution Analytics * 12 for for ( ) core =4 CPU 413 foreach 4 4! core 3 1 (58 ) 4core 5! 292 x! 292 x! 5! 20 *

24 打順 1~9 番を決める試合数 ( シミュレーション回数 )N を設定並列化する CPU 1~N/4 試合 N/4~2N/4 試合 2N/4~3N/4 試合 3N/4~N 試合コア 1 コア 2 コア 3 コア 4 期待得点を求める 6 [sec] 逐次 core2 core3 core4 スケーラビリティ 7 4! core 9 8! ( 8 ) 42 Mariners 21

25 20 4core 6! 29min 7! 204min 8! 272h 9!( ) 10days ! Mariners ( ) playerid p W p S p D p T p H p so p poor 1 suzukic mclemma martied olerujo boonebr camermi guillca bellda wilsoda (AVG * 13 ) ( ) = ( ) ( ) * 14 3 *13 average *14 (= 31) 22

26 (OBP * 15 ) ( ) = ( ) + ( ) ( ) + ( ) + ( ) (SLG * 16 ) ( ) = ( ) 1 + (2 ) 2 + (3 ) 3 + ( ) 4 ( ) OPS * 17 (OP S) = ( ) + ( ) OPS 1984 OPS 095 [5, p28-29] (OBP) OPS OPS 3 *15 on base percentage *16 slugging percentage *17 on base plus slugging percentage 23

27 8 AVG 24

28 9 OBP 25

29 10 SLG 26

30 11 OPS 27

31 Mariners playerid AVG OBP SLG OPS 1 suzukic mclemma martied olerujo boonebr camermi guillca bellda wilsoda ( 1 1,2 ) ### A B C D E F G H I ( ) (0) ( ) 1 1 1,2 2 1, (1)

32 1 A I = = = 5 1 1,2 6 1 = = = = = D F 2 D = 3 1 (= 24 ) ,2 3 1,3 2, * q 0 24 *

33 09226 < 11661q (1 q 0 ) (2) q 0 > (3) Q = (q 0, q 1, q 2 ) = (07237, 07476, 07179) p steal p steal = SB SB+CS SB CS p steal = Mariners playerid p W p S p D p T p H p so p poor p steal 1 suzukic mclemma martied olerujo boonebr camermi guillca bellda wilsoda Q ( ) 30

34 12 AVG ( ) 31

35 13 OBP ( ) 32

36 14 SLG ( ) 33

37 15 OPS ( ) 34

38 1 3 OPS 4 SLG 2 5 OPS Mariners Mariners OPS OPS

39 36

40 5 37

41 [1] 2015 FA 1939 p [2] (2000) 7 2 p [3] (2008) - [4] D Esopo, DA and Lefkowitz, B, The distributionof runs in the game of baseball, In Optimal Strategies in Sports, 1977 [5] (2014) - [6] p1-14 [7] 2012 D Esopo & Lefkowitz 42 [8] 48 3 p [9] [10] torigoe/ /01sphtml [11] (2014)R [12] JAlbert JBennett(2004) [13] (1991) 38

WPA(Win Probability Added) 1 WPA WPA ( ) WPA WPA WPA WPA WPA

21 4 25 1 31 WPA(Win Probability Added) 1 WPA WPA ( ) WPA WPA WPA WPA WPA 1 1 2 WPA 3 2.1 WPA(Win Probability Added)................................. 3 2.2........................... 3 2.2.1...................................