sito@ism.ac.jp (2012/11/5) 1
(NPB) # # # ACL # - () 2
(NPB) # # # ACL # MLB 3
MLB Regular Season Standings (NPB) # # # ACL # September 29, 2012 E#: Elimination Number... that will eliminate the trailing team from winning the division.... The Elimination Number for the second place team is the Magic Number for the first place team. http://mlb.mlb.com/mlb/standings/ 4
(NPB) # # # ACL # group tournament 5
(NPB) # # # ACL # 6
(NPB) # # # ACL # 1 43 1 1 4 9 43/(4 + 1) = 8... 3 8+1=9 4 7
(NPB) # # # ACL # 2 1 3 A B C D E F 6 1 240 1 1 220 6 A B C D E F 58 48 43 38 20 13 220 (48 + 43 + 38 + 20)/(2 + 1) = 49... 2 49 + 1 = 50 4 8
(NPB) # # # ACL # 9
(NPB) # # # ACL # 2 10
(NPB) # # # ACL # 1996 SF Giants SF Chronicle 2 9 10 Adler et al., Interfaces, 2002) Clinch Avoid Elim Team W L GB GL 1st PS 1st PS Los Angeles 78 63-21 17 17 4 1 San Diego 78 65 1 19 17 17 4 0 Colorado 71 71 7.5 20 * * 11 7 San Francisco 59 81 18.5 22 * * E 19 11
Major League Baseball (MLB) (NPB) # # # ACL # American League West Texas Central Minnesota East Tampa Bay Oakland Chiago New York Los Angels Detroit Boston Seattle Cleaveland Tronto Kansas City Baltimore National League West San Francisco Central Cincinnati East Philadelphia San Diego St. Louis Atlanta Colorado Milwaukee Florida Los Angeles Houston New York Arizona Chicago Washington Pittsburgh 12
(NPB) # # # ACL # J (NPB) (NPB) (MLB) (NPB) (NPB) MLB NPB 13
(NPB) # # # ACL # (1) / (2) (3) (4) 0.5 0.5 (5) (6) + () (1 ) 14
(NPB) (NPB) # # # ACL # 6 1 24 24 1 144 /(+) 3 3 15
(NPB) # # # ACL # チーム a チーム c 120 132 144 132 12 0 0.917 132+1=133 132 132 133 16
CS (NPB) # # # ACL # CS a c 1 c 2 c 3 d 1 d 2 24 3=72 17
CS (NPB) # # # ACL # CS a (72 + 3x) (72 3x) c 1 c 2 72 + (24 x) x 48 c 3 a c 1 c 3 x 4 72 + 3x 144 = 72 + (24 x) 72 + (24 x)+x = 96 x 96 x =16 18
CS (NPB) # # # ACL # CS a 120 24 c 1 c 2 80 16 48 c 3 a 120 24 c i 80 16 48 4 0.833 or 120 CS CS 120 19
(NPB) # # # ACL # i w i, l i w i /(w i + l i ) i, j g ij : 0 g =(g ij )=... 0 20
(NPB) # # # ACL # L n i L w i, l i w i /(w i + l i ) i, j L g ij i, j L g ii =0 g ji = g ij i L j L x ij i L x ii =0 i L j L x ji g ij x ij x ji g, x n 0 0 g =(g ij )=..., x =(x ij )= 0... 0 21
(NPB) # # # ACL # 0 n g x ij + x ji g ij i, j L, i < j x ii =0 i L x ij 0 i, j L, i j x ij Z i, j L, i j x (Z: ) X x X i L w i + x ij j L w i + l i + j L (x ij + x ji ) 22
(NPB) # # # ACL # k k +1 k =1, 2,..., n 1 a L k +1 x X max x X a subject to a a k 23
(NPB) # CS # # # CS # ACL # max x X α A k j L x aj subject to x aj +x ja = g aj j L w a + j Lx aj w a +l a + j L g aj w i + j Lx ij w i +l i + j L (x ij +x ji ) +α i i L, i a A k α i = n k 1, α i {0,1} i L, i a i L i a 24
(NPB) # # # ACL # No Yes x aj j L No k +1 Yes x aj < g aj No j L j L Yes j L x aj +1 k 0 25 j L x aj k +1
MLB vs NPB (NPB) # # # ACL # MLB NPB QCLP 1 n n 2 n n 2 n 2 (g ij +1)(g ij +2) (g ij +1) 2 i<j one-game playoff i<j 26
(NPB) # # # ACL # k +1 k k =1, 2,..., n 1 a L k x X max x X a subject to a a n k 27
(NPB) # # # ACL # 0 k C# = k k E# = k +1 = k +1 k w w +1 k +1 k w 1 w k +1 j L g aj j L x aj 28
CS (NPB) # # # ACL # 29
CS (NPB) # # # ACL # CS ( ) 3 CS ( ) 3 2 CS CS 2 () 6 ( ) 2 ( ) 64 () =1, 536 30
ACL (NPB) # # # ACL # 31
ACL (NPB) # # # ACL # 32
(NPB) # # # ACL # // 56 7 33