{VERSION 4 0 "IBM INTEL NT" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier " 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot " -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 } 3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }3 1 0 0 12 12 1 0 1 0 2 2 19 1 }} {SECT 0 {PARA 18 "" 0 "" {TEXT -1 9 "Batter Up" }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 25 "batter transition matrix" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 186 "#load packages\nrestart;\nwith(linalg):\nwith(plot s):\n\n# set up parameters\nPw := .080527+0.01020; Ps := .1473; Pd := \+ .0475; Pt := 0.00501; Ph := .02945; Po := 1-Pw-Ps-Pd-Pt-Ph;\ncount:=30 ;\n\n" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names nor m and trace have been redefined and unprotected\n" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#PwG$\"&F2*!\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#PsG$\"%t9!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%# PdG$\"$v%!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#PtG$\"$,&!\"&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#PhG$\"%XH!\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#PoG$\"'8+o!\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% &countG\"#I" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 501 "#set up tra nsition matrices\nA := matrix(8,8,[Ph,Ph,Ph,Ph,Ph,Ph,Ph,Ph,\n \+ Ps+Pw,0,Ps,Ps,0,0,Ps,0,\n Pd,0,Pd,Pd,0,0,Pd,0, \n Pt,Pt,Pt,Pt,Pt,Pt,Pt,Pt,\n 0,Ps+Pw, Pw,0,Ps,Ps,0,Ps,\n 0,0,0,Pw,0,0,0,0,\n \+ 0,Pd,0,0,Pd,Pd,0,Pd,\n 0,0,0,0,Pw,Pw,Pw,Pw]);\n\nB := evalm(Po*diag(1,1,1,1,1,1,1,1));\nZ := matrix(8,8,0);\nZ1:= matrix(8, 1,0);\nZ2:= matrix(1,8,0);\nO3 := evalm(Po*matrix(1,8,1));\nAbsorb := \+ matrix(1,1,1);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6# 7*7*$\"%XH!\"&F*F*F*F*F*F*F*7*$\"'F!Q#!\"'\"\"!$\"%t9!\"%F2F1F1F2F17*$ \"$v%F4F1F6F6F1F1F6F17*$\"$,&F,F9F9F9F9F9F9F97*F1F.$\"&F2*F0F1F2F2F1F2 7*F1F1F1F%\"BG-%'matrixG6#7*7*$\"'8+o!\"'$\"\"!F.F-F-F-F-F -F-7*F-F*F-F-F-F-F-F-7*F-F-F*F-F-F-F-F-7*F-F-F-F*F-F-F-F-7*F-F-F-F-F*F -F-F-7*F-F-F-F-F-F*F-F-7*F-F-F-F-F-F-F*F-7*F-F-F-F-F-F-F-F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"ZG-%'matrixG6#7*7*\"\"!F*F*F*F*F*F*F*F)F )F)F)F)F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Z1G-%'matrixG6#7*7# \"\"!F)F)F)F)F)F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Z2G-%'matrix G6#7#7*\"\"!F*F*F*F*F*F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#O3G-% 'matrixG6#7#7*$\"'8+o!\"'F*F*F*F*F*F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'AbsorbG-%'matrixG6#7#7#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 107 "P1 := augment(A,Z,Z,Z1);\nP2 := augment(B,A,Z,Z1);\n P3 := augment(Z,B,A,Z1);\nP4 := augment(Z2,Z2,O3,Absorb);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#P1G-%'matrixG6#7*7;$\"%XH!\"&F*F*F*F*F*F* F*\"\"!F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-7;$\"'F!Q#!\"'F-$\"%t9!\"%F2F-F -F2F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-7;$\"$v%F4F-F6F6F-F-F6F-F-F-F-F -F-F-F-F-F-F-F-F-F-F-F-F-F-7;$\"$,&F,F9F9F9F9F9F9F9F-F-F-F-F-F-F-F-F-F -F-F-F-F-F-F-F-7;F-F/$\"&F2*F1F-F2F2F-F2F-F-F-F-F-F-F-F-F-F-F-F-F-F-F- F-F-7;F-F-F-F%#P2G-%'matri xG6#7*7;$\"'8+o!\"'$\"\"!F.F-F-F-F-F-F-$\"%XH!\"&F/F/F/F/F/F/F/F.F.F.F .F.F.F.F.F.7;F-F*F-F-F-F-F-F-$\"'F!Q#F,F.$\"%t9!\"%F5F.F.F5F.F.F.F.F.F .F.F.F.F.7;F-F-F*F-F-F-F-F-$\"$v%F7F.F9F9F.F.F9F.F.F.F.F.F.F.F.F.F.7;F -F-F-F*F-F-F-F-$\"$,&F1F%#P3G-%'matrixG6#7*7;\"\"!F*F*F*F*F*F*F*$\" '8+o!\"'$F*F*F.F.F.F.F.F.$\"%XH!\"&F/F/F/F/F/F/F/F*7;F*F*F*F*F*F*F*F*F .F+F.F.F.F.F.F.$\"'F!Q#F-F*$\"%t9!\"%F5F*F*F5F*F*7;F*F*F*F*F*F*F*F*F.F .F+F.F.F.F.F.$\"$v%F7F*F9F9F*F*F9F*F*7;F*F*F*F*F*F*F*F*F.F.F.F+F.F.F.F .$\"$,&F1F%#P 4G-%'matrixG6#7#7;\"\"!F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*$\"'8+o!\"'F+F+F+ F+F+F+F+\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "P := stac kmatrix(P1,P2,P3,P4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"PG-%'matr ixG6#7;7;$\"%XH!\"&F*F*F*F*F*F*F*\"\"!F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-F- 7;$\"'F!Q#!\"'F-$\"%t9!\"%F2F-F-F2F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-F- 7;$\"$v%F4F-F6F6F-F-F6F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-7;$\"$,&F,F9 F9F9F9F9F9F9F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-7;F-F/$\"&F2*F1F-F2F2F-F 2F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-7;F-F-F-F " 0 "" {MPLTEXT 1 0 47 "check := matrix(1,25,1);\nevalm(check&*P-check);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%&checkG-%'matrixG6#7#7;\"\"\"F*F*F*F *F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 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"> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 23 "expected number of runs" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 316 "# construct run matrix\nRA := matrix(8,8,[1,2,2,2,3, 3,3,4,\n 0,1,1,1,2,2,2,3, \n 0,1,1,1,2 ,2,2,3,\n 0,1,1,1,2,2,2,3,\n 0,0,0,0,1 ,1,1,2,\n 0,0,0,0,1,1,1,2, \n 0, 0,0,0,1,1,1,2, \n 0,0,0,0,0,0,0,1]); " }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%#RAG-%'matrixG6#7*7*\"\"\"\"\"#F+F+\"\"$F,F,\"\"%7*\"\"!F*F*F*F+F+F+ F,F.F.7*F/F/F/F/F*F*F*F+F0F07*F/F/F/F/F/F/F/F*" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 157 "Z4 := matrix(1,1,0);\nR1 := augment(RA,Z,Z,Z1 );\nR2 := augment(Z,RA,Z,Z1);\nR3 := augment(Z,Z,RA,Z1);\nR4 := augmen t(Z2,Z2,Z2,Z4);\nR := stackmatrix(R1,R2,R3,R4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Z4G-%'matrixG6#7#7#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#R1G-%'matrixG6#7*7;\"\"\"\"\"#F+F+\"\"$F,F,\"\"%\"\" !F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.7;F.F*F*F*F+F+F+F,F.F.F.F.F.F.F.F.F.F .F.F.F.F.F.F.F.F/F/7;F.F.F.F.F*F*F*F+F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F .F0F07;F.F.F.F.F.F.F.F*F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#R2G-%'matrixG6#7*7;\"\"!F*F*F*F*F*F*F*\"\"\" \"\"#F,F,\"\"$F-F-\"\"%F*F*F*F*F*F*F*F*F*7;F*F*F*F*F*F*F*F*F*F+F+F+F,F ,F,F-F*F*F*F*F*F*F*F*F*F/F/7;F*F*F*F*F*F*F*F*F*F*F*F*F+F+F+F,F*F*F*F*F *F*F*F*F*F0F07;F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F+F*F*F*F*F*F*F*F*F*" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#R3G-%'matrixG6#7*7;\"\"!F*F*F*F*F*F *F*F*F*F*F*F*F*F*F*\"\"\"\"\"#F,F,\"\"$F-F-\"\"%F*7;F*F*F*F*F*F*F*F*F* F*F*F*F*F*F*F*F*F+F+F+F,F,F,F-F*F/F/7;F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F* F*F*F*F*F+F+F+F,F*F0F07;F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F* F+F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#R4G-%'matrixG6#7#7;\"\"!F*F *F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RG-%'matrixG6#7;7;\"\"\"\"\"#F+F+\"\"$F,F,\"\"%\"\" !F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.7;F.F*F*F*F+F+F+F,F.F.F.F.F.F.F.F.F.F .F.F.F.F.F.F.F.F/F/7;F.F.F.F.F*F*F*F+F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F .F0F07;F.F.F.F.F.F.F.F*F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.7;F.F.F.F.F.F .F.F.F*F+F+F+F,F,F,F-F.F.F.F.F.F.F.F.F.7;F.F.F.F.F.F.F.F.F.F*F*F*F+F+F +F,F.F.F.F.F.F.F.F.F.F3F37;F.F.F.F.F.F.F.F.F.F.F.F.F*F*F*F+F.F.F.F.F.F .F.F.F.F4F47;F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F*F.F.F.F.F.F.F.F.F.7;F.F.F .F.F.F.F.F.F.F.F.F.F.F.F.F.F*F+F+F+F,F,F,F-F.7;F.F.F.F.F.F.F.F.F.F.F.F .F.F.F.F.F.F*F*F*F+F+F+F,F.F7F77;F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F .F.F*F*F*F+F.F8F87;F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F*F.7 ;F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 308 "# iterative calculation of runs\nENR := \+ 0; \nU0 := matrix(25,1,0):\nU0[1,1] :=1; \nU := copy(U0):\nfor i from \+ 1 to count do\n ENR := ENR+add(add(R[j,k]*P[j,k]*U[k,1],j=1..25),k= 1..25);\n U := evalm(P&*U); \n od:\n# expected number of runs fo r a half inning \nENR;\n# expected number of runs for a game\nENR*9; \+ \n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ENRG\"\"!" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>&%#U0G6$\"\"\"F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#$\"+WfH$y%!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+]j'\\I%!\"*" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "1 0 0" 25 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }