{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 Outpu t" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 } 1 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {SECT 1 {PARA 3 "" 0 "" {TEXT -1 30 "Set up Markov and Run mat rices" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "#load packages\nres tart;\nwith(linalg):\nwith(plots):" }}{PARA 7 "" 1 "" {TEXT -1 80 "War ning, the protected names norm and trace have been redefined and unpro tected\n" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoord s has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 841 " # define a function setting up the Markov matrix given \n# probability of walk+HBP, single, double, triple, home run.\nmarkov:= proc(Pw,Ps, Pd,Pt,Ph) local Po,A,B,Z,Z1,Z2,O3,Absorb,PA,PB,PC,PD,P; \nPo:= 1-Pw-P s-Pd-Pt-Ph;\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]);\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 := mat rix(1,1,1); \nPA := augment(A,Z,Z,Z1); \nPB := augment(B,A,Z,Z1); \nPC := augment(Z,B,A,Z1); \nPD := augment(Z2,Z2,O3,Absorb);\nP := stackma trix(PA,PB,PC,PD); end;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'markovGR 6'%#PwG%#PsG%#PdG%#PtG%#PhG6/%#PoG%\"AG%\"BG%\"ZG%#Z1G%#Z2G%#O3G%'Abso rbG%#PAG%#PBG%#PCG%#PDG%\"PG6\"F:C/>8$,.\"\"\"F?9$!\"\"9%FA9&FA9'FA9(F A>8%-%'matrixG6%\"\")FK7\\oFEFEFEFEFEFEFEFE,&F@F?FBF?\"\"!FBFBFNFNFBFN FCFNFCFCFNFNFCFNFDFDFDFDFDFDFDFDFNFMF@FNFBFBFNFBFNFNFNF@FNFNFNFNFNFCFN FNFCFCFNFCFNFNFNFNF@F@F@F@>8&-%&evalmG6#*&F=F?-%%diagG6*F?F?F?F?F?F?F? F?F?>8'-FI6%FKFKFN>8(-FI6%FKF?FN>8)-FI6%F?FKFN>8*-FR6#*&F=F?-FI6%F?FKF ?F?>8+-FI6%F?F?F?>8,-%(augmentG6&FGFYFYFgn>8--F\\p6&FPFGFYFgn>8.-F\\p6 &FYFPFGFgn>8/-F\\p6&F[oF[oF_oFfo>80-%,stackmatrixG6&FjoF_pFcpFgpF:F:F: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1218 "# construct run matri x\nbuildrunmatrix:= proc () local RA,RB,RC,Z,Z1,Z2,Z4,R1,R2,R3,R4,R; \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]);\nRB := matrix(8,8,[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,\n \+ 0,0,0,0,0,0,0,1, \n 0,0,0,0,0,0,0,1, \n 0,0,0,0,0,0,0,0]);\nRC := matrix(8,8,[0,0, 0,0,1,1,1,2,\n 0,0,0,0,0,0,0,1,\n 0,0, 0,0,0,0,0,1, \n 0,0,0,0,0,0,0,1,\n \+ 0,0,0,0,0,0,0,0,\n 0,0,0,0,0,0,0,0, \n \+ 0,0,0,0,0,0,0,0, \n 0,0,0,0,0,0,0,0] );\nZ := matrix(8,8,0); \nZ1:= matrix(8,1,0); \nZ2:= matrix(1,8,0); \n Z4 := matrix(1,1,0);\nR1 := augment(RA,RB,RC,Z1);\nR2 := augment(Z,RA, RB,Z1);\nR3 := augment(Z,Z,RA,Z1);\nR4 := augment(Z2,Z2,Z2,Z4);\nR := \+ stackmatrix(R1,R2,R3,R4); evalm(R); end;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%/buildrunmatrixGR6\"6.%#RAG%#RBG%#RCG%\"ZG%#Z1G%#Z2G% #Z4G%#R1G%#R2G%#R3G%#R4G%\"RGF&F&C/>8$-%'matrixG6%\"\")F:7\\o\"\"\"\" \"#F=F=\"\"$F>F>\"\"%\"\"!FF@FF@FF@F@F@F@F8%- F86%F:F:7\\oF@FF@F@F@F@F8&-F86%F:F:7\\oF@F@F@F@F8'-F86%F:F:F@>8(-F86%F:F8)-F86%F8*-F86%F8+-%(augm entG6&F6FBFGFP>8,-Fhn6&FLF6FBFP>8--Fhn6&FLFLF6FP>8.-Fhn6&FTFTFTFX>8/-% ,stackmatrixG6&FfnF[oF_oFco-%&evalmG6#FgoF&F&F&" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 " buildrunmatrix():" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 910 "# Set up Markov matrix give n BB+HBP, 1b,2b,3b,HR, plate appearances\nmarkov2:= proc(bb,sng,dbl,t rp,hr,pa) \nlocal Pw,Ps,Pd,Pt,Ph,Po,A,B,Z,Z1,Z2,O3,Absorb,PA,PB,PC,PD, P; \nPw:=evalf(bb/pa); Ps:=evalf(sng/pa); Pd:=evalf(dbl/pa); Pt:=eva lf(trp/pa); Ph:=evalf(hr/pa);\nPo:= 1-Pw-Ps-Pd-Pt-Ph;\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]);\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); \nPA := augmen t(A,Z,Z,Z1); \nPB := augment(B,A,Z,Z1); \nPC := augment(Z,B,A,Z1); \nP D := augment(Z2,Z2,O3,Absorb);\nP := stackmatrix(PA,PB,PC,PD); end;" } }{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(markov2GR6(%#bbG%$sngG%$dblG%$trpG %#hrG%#paG64%#PwG%#PsG%#PdG%#PtG%#PhG%#PoG%\"AG%\"BG%\"ZG%#Z1G%#Z2G%#O 3G%'AbsorbG%#PAG%#PBG%#PCG%#PDG%\"PG6\"F@C4>8$-%&evalfG6#*&9$\"\"\"9)! \"\">8%-FE6#*&9%FIFJFK>8&-FE6#*&9&FIFJFK>8'-FE6#*&9'FIFJFK>8(-FE6#*&9( FIFJFK>8),.FIFIFCFKFMFKFSFKFYFKFinFK>8*-%'matrixG6%\"\")Ffo7\\oFinFinF inFinFinFinFinFin,&FCFIFMFI\"\"!FMFMFioFioFMFioFSFioFSFSFioFioFSFioFYF YFYFYFYFYFYFYFioFhoFCFioFMFMFioFMFioFioFioFCFioFioFioFioFioFSFioFioFSF SFioFSFioFioFioFioFCFCFCFC>8+-%&evalmG6#*&F_oFI-%%diagG6*FIFIFIFIFIFIF IFIFI>8,-Fdo6%FfoFfoFio>8--Fdo6%FfoFIFio>8.-Fdo6%FIFfoFio>8/-F]p6#*&F_ oFI-Fdo6%FIFfoFIFI>80-Fdo6%FIFIFI>81-%(augmentG6&FboFdpFdpFhp>82-F]r6& F[pFboFdpFhp>83-F]r6&FdpF[pFboFhp>84-F]r6&F\\qF\\qF`qFgq>85-%,stackmat rixG6&F[rF`rFdrFhrF@F@F@" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 21 "Set up batting lineup" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 85 "Pavg:=markov( .085274664+.010196705, .154730947, .0 47546856, .005006636, .029446357):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "Pbonds:=markov2( 186, 49,32,2,73,664):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "P1:= Pbonds;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#P1G%'PbondsG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "Ppitcher:=markov2(185,611,117,7,26,5486):" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 37 "for k from 2 to 9 do P||k:= Pavg; od;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#P2G%%PavgG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#P3G%%PavgG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#P4G %%PavgG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#P5G%%PavgG" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%#P6G%%PavgG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%#P7G%%PavgG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#P8G%%PavgG" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#P9G%%PavgG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 30 "Set up \+ more tools for analysis" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 383 " # iterative calculation of expected runs given a batting order\nExprun s:=proc(batorder) local ENR,R,U0,U,i,ii,boi ;\nENR := 0; R:=buildrun matrix(); \nU0 := matrix(25,1,0):\nU0[1,1] :=1; \nU := copy(U0):\nfor \+ ii from 1 to 4 do \nfor i from 1 to 9 do\n boi:=batorder[i];\n E NR := ENR+add(add(R[j,k]*P||boi[j,k]*U[k,1],j=1..25),k=1..25);\n U \+ := evalm((P||i)&*U); \n od: od:\nENR; end;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(ExprunsGR6#%)batorderG6)%$ENRG%\"RG%#U0G%\"UG%\"iG%# iiG%$boiG6\"F0C)>8$\"\"!>8%-%/buildrunmatrixGF0>8&-%'matrixG6%\"#D\"\" \"F4>&F:6$F?F?F?>8'-%%copyG6#F:?(8)F?F?\"\"%%%trueG?(8(F?F?\"\"*FKC%>8 *&9$6#FM>F3,&F3F?-%$addG6$-FX6$*(&F66$%\"jG%\"kGF?&(%\"PGFQFhnF?&FD6$F jnF?F?/Fin;F?F>/FjnFaoF?>FD-%&evalmG6#-%#&*G6$(F]oFMFDF3F0F0F0" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 403 "# iterative calculation of \+ expected runs given a situation and batting order\nSitruns:=proc(sit,b atorder) local ENR,R,U0,U,i,ii,boi ;\nENR := 0; R:=buildrunmatrix(); \nU0 := matrix(25,1,0):\nU0[sit,1] :=1; \nU := copy(U0):\nfor ii from 1 to 4 do \nfor i from 1 to 9 do\n boi:=batorder[i];\n ENR := E NR+add(add(R[j,k]*P||boi[j,k]*U[k,1],j=1..25),k=1..25);\n U := eval m((P||i)&*U); \n od: od:\nENR; end;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(SitrunsGR6$%$sitG%)batorderG6)%$ENRG%\"RG%#U0G%\"UG%\"iG%#iiG %$boiG6\"F1C)>8$\"\"!>8%-%/buildrunmatrixGF1>8&-%'matrixG6%\"#D\"\"\"F 5>&F;6$9$F@F@>8'-%%copyG6#F;?(8)F@F@\"\"%%%trueG?(8(F@F@\"\"*FMC%>8*&9 %6#FO>F4,&F4F@-%$addG6$-FZ6$*(&F76$%\"jG%\"kGF@&(%\"PGFSFjnF@&FF6$F\\o F@F@/F[o;F@F?/F\\oFcoF@>FF-%&evalmG6#-%#&*G6$(F_oFOFFF4F1F1F1" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1444 "# iterative calculation of run distribution for a given batting order.\nERProd := proc (batorder ) local kk,lob,ERP,nub,bok,Pout,U0,U,bf,oot,i,stayt,rval,ii; \nlob:=[0 ,1,1,1,2,2,2,3];\nfor kk from 1 to 36 do ERP[1,kk]:=0: od: for kk from 1 to 10 do nub[bats,kk]:=0: od:\nPout:=[0$9]; print(Pout);\nfor kk f rom 1 to 9 do bok:=batorder[kk]; Pout[kk]:=P||bok[25,24]; od; print(Po ut);\nU0 := matrix(25,1,0):\nU0[1,1] :=1; \nU := copy(U0):\n U:= eval m( P3&*P2&*P1&*U): bf:=3:\nERP[1,1]:= U[25,1]: nub[bats,4]:=U[25,1 ]: oot:=U[25,1]: print( [seq(nub[bats,kk],kk=1..9)], add(nub[bats,kk], kk=1..9),oot);\nfor i from 4 to 9 do \n bf:=bf+1: \n for stayt from 17 to 24 do \n rval:= bf - 3 - lob[stayt-16]: \n if rval>-1 the n ERP[1,rval+1]:=ERP[1,rval+1]+Pout[i]*U[stayt,1]: fi: \n od: \n U:=evalm((P||i)&*U): nub[bats,(bf mod 9)+1]:=U[25,1]-oot: oot: =U[25,1]: print(oot); od: \nfor ii from 2 to 4 do\n for i from 1 to 9 do \n bf:=bf+1: \n for stayt from 17 to 24 do \n rval:= bf - 3 - lob[stayt-16]: \n if rval>-1 then ERP[1,rval+1]:=ERP[1, rval+1]+Pout[i]*U[stayt,1]: fi: \n od: \n U:=evalm((P||i)& *U): nub[bats,(bf mod 9)+1]:=nub[bats,(bf mod 9)+1] + U[25,1]-oot: \+ \n oot:=U[25,1]: od: \n od: \nprint([seq(ERP[1 ,kk],kk=1..36)], add(ERP[1,kk],kk=1..36), U[25,1], add(ERP[1,kk]*(kk -1),kk=1..31)); \nnub[bats,10]:=nub[bats,1]:\nprint( [seq(nub[bats,kk ],kk=1..10)], add(nub[bats,kk],kk=2..10)); end;\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'ERProdGR6#%)batorderG60%#kkG%$lobG%$ERPG%$nubG%$bokG %%PoutG%#U0G%\"UG%#bfG%$ootG%\"iG%&staytG%%rvalG%#iiG6\"F7C7>8%7*\"\"! \"\"\"F=F=\"\"#F>F>\"\"$?(8$F=F=\"#O%%trueG>&8&6$F=FAF &8'6$%%batsGFAF<>8)7#-%\"$G6$F<\"\"*-%&printG6#FP?(FAF=F=FUFCC$>8(&9$6 #FA>&FPFin&(%\"PGFfn6$\"#D\"#CFV>8*-%'matrixG6%F`oF=F<>&Fco6$F=F=F=>8+ -%%copyG6#Fco>F[p-%&evalmG6#-%#&*G6$-Fdp6$-Fdp6$%#P3G%#P2G%#P1GF[p>8,F ?>&FFFio&F[p6$F`oF=>&FL6$FN\"\"%Faq>8-Faq-FW6%7#-%$seqG6$FK/FA;F=FU-%$ addGF^rFhq?(8.FfqF=FUFCC(>F^q,&F^qF=F=F=?(8/\"#80,(F^qF=F?! \"\"&F:6#,&FirF=\"#;F_sF_s@$2F_sF]s>&FF6$F=,&F]sF=F=F=,&FgsF=*&&FP6#Fd rF=&F[p6$FirF=F=F=>F[p-Fap6#-Fdp6$(F^oFdrF[p>&FL6$FN,&-%$modG6$F^qFUF= F=F=,&FaqF=FhqF_s>FhqFaq-FW6#Fhq?(81F>F=FfqFC?(FdrF=F=FUFCC'>F^qFgr?(F irFjrF=FaoFCC$>F]sF^s@$Fes>FgsFjs>F[pFat>Fgt,(FgtF=FaqF=FhqF_s>FhqFaq- FW6&7#-F]r6$FE/FA;F=FB-FbrFcvFaq-Fbr6$*&FEF=,&FAF=F=F_sF=/FA;F=\"#J>&F L6$FNFI&FL6$FNF=-FW6$7#-F]r6$FK/FA;F=FI-Fbr6$FK/FA;F>FIF7F7F7" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1172 "# iterative calculation of run distribution for a given batting order.\nRundist := proc (batorde r) local kk,lob,ERP,nub,bok,Pout,U0,U,bf,oot,i,stayt,rval,ii; \nlob:=[ 0,1,1,1,2,2,2,3];\nfor kk from 1 to 36 do ERP[1,kk]:=0: od: for kk fro m 1 to 10 do nub[bats,kk]:=0: od:\nPout:=[0$9]; \nfor kk from 1 to 9 d o bok:=batorder[kk]; Pout[kk]:=P||bok[25,24]; od; \nU0 := matrix(25,1, 0):\nU0[1,1] :=1; \nU := copy(U0):\n U:= evalm( P3&*P2&*P1&*U): bf: =3:\nERP[1,1]:= U[25,1]: nub[bats,4]:=U[25,1]: oot:=U[25,1]: \nfor i from 4 to 9 do \n bf:=bf+1: \n for stayt from 17 to 24 do \n rv al:= bf - 3 - lob[stayt-16]: \n if rval>-1 then ERP[1,rval+1]:=ERP[ 1,rval+1]+Pout[i]*U[stayt,1]: fi: \n od: \n U:=evalm((P||i)& *U): nub[bats,(bf mod 9)+1]:=U[25,1]-oot: oot:=U[25,1]: od: \nfo r ii from 2 to 4 do\n for i from 1 to 9 do \n bf:=bf+1: \n for stayt from 17 to 24 do \n rval:= bf - 3 - lob[stayt-16]: \n \+ if rval>-1 then ERP[1,rval+1]:=ERP[1,rval+1]+Pout[i]*U[stayt,1]: fi: \n od: \n U:=evalm((P||i)&*U): nub[bats,(bf mod 9)+1]:=n ub[bats,(bf mod 9)+1] + U[25,1]-oot: \n oot:=U[25,1]: od: \+ \n od: \n[seq(ERP[1,kk],kk=1..36)]; end;" }}{PARA 12 " " 1 "" {XPPMATH 20 "6#>%(RundistGR6#%)batorderG60%#kkG%$lobG%$ERPG%$nu bG%$bokG%%PoutG%#U0G%\"UG%#bfG%$ootG%\"iG%&staytG%%rvalG%#iiG6\"F7C2>8 %7*\"\"!\"\"\"F=F=\"\"#F>F>\"\"$?(8$F=F=\"#O%%trueG>&8&6$F=FAF&8'6$%%batsGFAF<>8)7#-%\"$G6$F<\"\"*?(FAF=F=FUFCC$>8(&9$6#FA>& FPFfn&(%\"PGFY6$\"#D\"#C>8*-%'matrixG6%F]oF=F<>&F`o6$F=F=F=>8+-%%copyG 6#F`o>Fho-%&evalmG6#-%#&*G6$-Fap6$-Fap6$%#P3G%#P2G%#P1GFho>8,F?>&FFFfo &Fho6$F]oF=>&FL6$FN\"\"%F^q>8-F^q?(8.FcqF=FUFCC'>F[q,&F[qF=F=F=?(8/\"# 80,(F[qF=F?!\"\"&F:6#,&F\\rF=\"#;FbrFbr@$2FbrF`r>&FF6$F=,&F `rF=F=F=,&FjrF=*&&FP6#FgqF=&Fho6$F\\rF=F=F=>Fho-F^p6#-Fap6$(F[oFgqFho> &FL6$FN,&-%$modG6$F[qFUF=F=F=,&F^qF=FeqFbr>FeqF^q?(81F>F=FcqFC?(FgqF=F =FUFCC'>F[qFjq?(F\\rF]rF=F^oFCC$>F`rFar@$Fhr>FjrF]s>FhoFds>Fjs,(FjsF=F ^qF=FeqFbr>FeqF^q7#-%$seqG6$FE/FA;F=FBF7F7F7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1343 "# iterative calculation of last batter distrib ution with a given batting order.\nLastbat := proc (batorder) \nlocal \+ kk,boi1,boi2,boi3,boi,lob,ERP,nub,bok,Pout,U0,U,bf,oot,i,stayt,rval,ii ; \nlob:=[0,1,1,1,2,2,2,3];\nfor kk from 1 to 36 do ERP[1,kk]:=0: od: \+ for kk from 1 to 10 do nub[bats,kk]:=0: od:\nPout:=[0$9]; \nfor kk fro m 1 to 9 do bok:=batorder[kk]; Pout[kk]:=P||bok[25,24]; od; \nU0 := ma trix(25,1,0):\nU0[1,1] :=1; \nU := copy(U0):\nboi1:=batorder[1]; boi2: =batorder[2]; boi3:=batorder[3];\n U:= evalm( (P||boi3)&*(P||boi2)&* (P||boi1)&*U): bf:=3:\nERP[1,1]:= U[25,1]: nub[bats,4]:=U[25,1]: o ot:=U[25,1]: \nfor i from 4 to 9 do \n bf:=bf+1:\n boi:=batorder[i]; \n for stayt from 17 to 24 do \n rval:= bf - 3 - lob[stayt-16]: \+ \n if rval>-1 then ERP[1,rval+1]:=ERP[1,rval+1]+Pout[boi]*U[stayt,1 ]: fi: \n od: \n U:=evalm((P||boi)&*U): nub[bats,(bf mod 9) +1]:=U[25,1]-oot: oot:=U[25,1]: od: \nfor ii from 2 to 4 do\n fo r i from 1 to 9 do \n bf:=bf+1:\n boi:=batorder[i]; \n for st ayt from 17 to 24 do \n rval:= bf - 3 - lob[stayt-16]: \n if rval>-1 then ERP[1,rval+1]:=ERP[1,rval+1]+Pout[boi]*U[stayt,1]: fi: \+ \n od: \n U:=evalm((P||boi)&*U): nub[bats,(bf mod 9)+1]:= nub[bats,(bf mod 9)+1] + U[25,1]-oot: \n oot:=U[25,1]: od: \+ \n od: \n [seq(nub[bats,kk],kk=2..9),nub[bats,1]]; end; " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(LastbatGR6#%)batorderG64%#kkG%% boi1G%%boi2G%%boi3G%$boiG%$lobG%$ERPG%$nubG%$bokG%%PoutG%#U0G%\"UG%#bf G%$ootG%\"iG%&staytG%%rvalG%#iiG6\"F;C5>8)7*\"\"!\"\"\"FAFA\"\"#FBFB\" \"$?(8$FAFA\"#O%%trueG>&8*6$FAFEF@?(FEFAFA\"#5FG>&8+6$%%batsGFEF@>8-7# -%\"$G6$F@\"\"*?(FEFAFAFYFGC$>8,&9$6#FE>&FTFjn&(%\"PGFgn6$\"#D\"#C>8.- %'matrixG6%FaoFAF@>&Fdo6$FAFAFA>8/-%%copyG6#Fdo>8%&Fin6#FA>8&&Fin6#FB> 8'&Fin6#FC>F\\p-%&evalmG6#-%#&*G6$-Faq6$-Faq6$(F_oFip(F_oFep(F_oFapF\\ p>80FC>&FJFjo&F\\p6$FaoFA>&FP6$FR\"\"%F^r>81F^r?(82FcrFAFYFGC(>F[r,&F[ rFAFAFA>8(&Fin6#Fgr?(83\"#84,(F[rFAFC!\"\"&F>6#,&F`sFA\"#;F fsFfs@$2FfsFds>&FJ6$FA,&FdsFAFAFA,&F^tFA*&&FT6#F\\sFA&F\\p6$F`sFAFAFA> F\\p-F^q6#-Faq6$(F_oF\\sF\\p>&FP6$FR,&-%$modG6$F[rFYFAFAFA,&F^rFAFerFf s>FerF^r?(85FBFAFcrFG?(FgrFAFAFYFGC(>F[rFjr>F\\sF]s?(F`sFasFAFboFGC$>F dsFes@$F\\t>F^tFat>F\\pFht>F^u,(F^uFAF^rFAFerFfs>FerF^r7$-%$seqG6$FO/F E;FBFY&FP6$FRFAF;F;F;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 145 "# rotate the batting order to begin at a different place.\nRot:= proc ( listt,k) local kk;\n[seq(listt[kk],kk=k+1..9),seq(listt[kk],kk=1..k)] ; end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$RotGR6$%&listtG%\"kG6#%#k kG6\"F+7$-%$seqG6$&9$6#8$/F3;,&9%\"\"\"F8F8\"\"*-F.6$F0/F3;F8F7F+F+F+ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1172 "# iterative calculati on of expected runs using run distribution.\nExpruns2 := proc (batorde r) local kk,lob,ERP,nub,bok,Pout,U0,U,bf,oot,i,stayt,rval,ii; \nlob:=[ 0,1,1,1,2,2,2,3];\nfor kk from 1 to 36 do ERP[1,kk]:=0: od: for kk fro m 1 to 10 do nub[bats,kk]:=0: od:\nPout:=[0$9]; \nfor kk from 1 to 9 d o bok:=batorder[kk]; Pout[kk]:=P||bok[25,24]; od; \nU0 := matrix(25,1, 0):\nU0[1,1] :=1; \nU := copy(U0):\n U:= evalm( P3&*P2&*P1&*U): bf: =3:\nERP[1,1]:= U[25,1]: nub[bats,4]:=U[25,1]: oot:=U[25,1]: \nfor i from 4 to 9 do \n bf:=bf+1: \n for stayt from 17 to 24 do \n rv al:= bf - 3 - lob[stayt-16]: \n if rval>-1 then ERP[1,rval+1]:=ERP[ 1,rval+1]+Pout[i]*U[stayt,1]: fi: \n od: \n U:=evalm((P||i)& *U): nub[bats,(bf mod 9)+1]:=U[25,1]-oot: oot:=U[25,1]: od: \nfo r ii from 2 to 4 do\n for i from 1 to 9 do \n bf:=bf+1: \n for stayt from 17 to 24 do \n rval:= bf - 3 - lob[stayt-16]: \n \+ if rval>-1 then ERP[1,rval+1]:=ERP[1,rval+1]+Pout[i]*U[stayt,1]: fi: \n od: \n U:=evalm((P||i)&*U): nub[bats,(bf mod 9)+1]:=n ub[bats,(bf mod 9)+1] + U[25,1]-oot: \n oot:=U[25,1]: od: \+ \n od: \nadd(ERP[1,kk]*(kk-1),kk=1..36); end;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%)Expruns2GR6#%)batorderG60%#kkG%$lobG%$ERP G%$nubG%$bokG%%PoutG%#U0G%\"UG%#bfG%$ootG%\"iG%&staytG%%rvalG%#iiG6\"F 7C2>8%7*\"\"!\"\"\"F=F=\"\"#F>F>\"\"$?(8$F=F=\"#O%%trueG>&8&6$F=FAF&8'6$%%batsGFAF<>8)7#-%\"$G6$F<\"\"*?(FAF=F=FUFCC$>8(&9$6 #FA>&FPFfn&(%\"PGFY6$\"#D\"#C>8*-%'matrixG6%F]oF=F<>&F`o6$F=F=F=>8+-%% copyG6#F`o>Fho-%&evalmG6#-%#&*G6$-Fap6$-Fap6$%#P3G%#P2G%#P1GFho>8,F?>& FFFfo&Fho6$F]oF=>&FL6$FN\"\"%F^q>8-F^q?(8.FcqF=FUFCC'>F[q,&F[qF=F=F=?( 8/\"#80,(F[qF=F?!\"\"&F:6#,&F\\rF=\"#;FbrFbr@$2FbrF`r>&FF6$ F=,&F`rF=F=F=,&FjrF=*&&FP6#FgqF=&Fho6$F\\rF=F=F=>Fho-F^p6#-Fap6$(F[oFg qFho>&FL6$FN,&-%$modG6$F[qFUF=F=F=,&F^qF=FeqFbr>FeqF^q?(81F>F=FcqFC?(F gqF=F=FUFCC'>F[qFjq?(F\\rF]rF=F^oFCC$>F`rFar@$Fhr>FjrF]s>FhoFds>Fjs,(F jsF=F^qF=FeqFbr>FeqF^q-%$addG6$*&FEF=,&FAF=F=FbrF=/FA;F=FBF7F7F7" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1345 "#Expected number of runs i n a game for a given batting order\nExprung:= proc (batorder) local EX PR,numb,kk,jj,lb,bo,LO,LU,leadoff,batter,inning,EINN; \nEXPR:= [0$9] : EXPR[1]:=Expruns(batorder);\nnumb:= matrix(9,9,0):\nlb:=Lastbat(bat order);\nfor kk from 1 to 9 do numb[1,kk]:=lb[kk]; od; \nfor jj from 1 to 9 do \n bo:= Rot(batorder,jj-1); \n EXPR[jj]:= Expruns(bo);\n \+ lb:=Lastbat(bo);\n for kk from 1 to 9 do numb[jj,kk]:=lb[kk]; od;\n \+ od:\nprint(EXPR); \n# numb is last batter probability 9x9 matrix rows \+ are rotations of order.\nprint(evalm(numb));\n# expected number of run s with Bonds leading off \nLO:=matrix(9,1,0): LU:= matrix(9,1,0): lead off:=matrix(9,9,0): \n LO[1,1]:=1: leadoff[1,1]:=1: \nleadoff[2,1]:=n umb[1,9]: \nfor batter from 2 to 9 do leadoff[2,batter]:=numb[1,batter -1]; od:\nfor inning from 3 to 9 do \nleadoff[inning,1]:=add(leadoff[i nning-1,kk]*numb[kk,10-kk],kk=1..9):\n for batter from 2 to 9 do \n \+ leadoff[inning,batter]:=add(leadoff[inning-1,kk]*numb[kk,batter-kk],k k=1..batter-1)+ add(leadoff[inning-1,kk]*numb[kk,9+batter-kk],kk=batte r..9):\n od:\nod: \nprint(evalm(leadoff));\nfor inning from 1 to 9 do EINN[inning]:=EXPR[1]*leadoff[inning,1] + add(EXPR[kk]*leadoff[inn ing,11-kk],kk=2..9): od:\n# to see exp.runs inning by inning use [se q(EINN[kk],kk=1..9)]; \nprint( [seq(EINN[kk],kk=1..9)] ); \nadd(EINN[ kk],kk=1..9); end;\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(ExprungGR6# %)batorderG6.%%EXPRG%%numbG%#kkG%#jjG%#lbG%#boG%#LOG%#LUG%(leadoffG%'b atterG%'inningG%%EINNG6\"F5C6>8$7#-%\"$G6$\"\"!\"\"*>&F86#\"\"\"-%(Exp runsG6#9$>8%-%'matrixG6%F>F>F=>8(-%(LastbatGFE?(8&FBFBF>%%trueG>&FH6$F BFQ&FM6#FQ?(8'FBFBF>FRC&>8)-%$RotG6$FF,&FYFBFB!\"\">&F86#FY-FD6#Ffn>FM -FOF`o?(FQFBFBF>FR>&FH6$FYFQFV-%&printG6#F8-Fho6#-%&evalmG6#FH>8*-FJ6% F>FBF=>8+Fap>8,FI>&F`p6$FBFBFB>&FfpFipFB>&Ffp6$\"\"#FB&FH6$FBF>?(8-F_q FBF>FR>&Ffp6$F_qFcq&FH6$FB,&FcqFBFBF[o?(8.\"\"$FBF>FRC$>&Ffp6$F[rFB-%$ addG6$*&&Ffp6$,&F[rFBFBF[oFQFB&FH6$FQ,&\"#5FBFQF[oFB/FQ;FBF>?(FcqF_qFB F>FR>&Ffp6$F[rFcq,&-Fbr6$*&FerFB&FH6$FQ,&FcqFBFQF[oFB/FQ;FBFiqFB-Fbr6$ *&FerFB&FH6$FQ,(F>FBFcqFBFQF[oFB/FQ;FcqF>FB-Fho6#-F]p6#Ffp?(F[rFBFBF>F R>&8/6#F[r,&*&F@FBF_rFBFB-Fbr6$*&&F8FWFB&Ffp6$F[r,&\"#6FBFQF[oFB/FQ;F_ qF>FB-Fho6#7#-%$seqG6$&FjtFWF\\s-FbrF]vF5F5F5" }}}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 20 "Examp le calculations" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "# compute expected runs in an inning for a batting order\nExpruns([1,2,3,4,5,6, 7,8,9]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+:DBJo!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "Expruns([2,1,3,4,5,6,7,8,9]);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+B,V,r!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "# compute expected runs for a particular situati on\nSitruns(1,[1,2,3,4,5,6,7,8,9]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #$\"+:DBJo!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "Sitruns(8, [1,2,3,4,5,6,7,8,9]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+U4N3E!\"* " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "# compute run distribu tion (prob 0 runs, 1 run, etc.) in inning for a batting order\nRundist ([1,2,3,4,5,6,7,8,9]);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7F$\"+(ppLV' !#5$\"+.No\\=F&$\"+T)zcy)!#6$\"+'y=i_%F+$\"+hu=A@F+$\"+X`;t'*!#7$\"+8g WwPF2$\"+3N=u;F2$\"++N=\"\\\"F2$\"+s>ChY!#8$\"+4nwt;F;$\"+lr4vk!#9$\"+ e=t5DF@$\"+uJy2&*!#:$\"+1+?OOFE$\"+<51K7FE$\"+(fZz\"\\!#;$\"+z.27WFL$ \"+B*[)=6FL$\"+O*4\"QQ!#<$\"+\"z\"R*R\"FS$\"+h\"pX5&!#=$\"+Hj2L=FX$\"+ VA/wm!#>$\"+w5&f;#Fgn$\"+/h0\\$)!#?$\"+tm85vF\\o$\"+kP$ov\"F\\o$\"+keS [f!#@$\"+Z0q7@Fco$\"+-t([](!#A$\"+6,3aDFho$\"+m2)eS'!#B$\"+7#\\iG\"F]p \"\"!F`p" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "Rundist([2,1,3, 4,5,6,7,8,9]);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7F$\"+(ppLV'!#5$\"+. No\\=F&$\"+T)zcy)!#6$\"+'y=i_%F+$\"+VwHf@F+$\"+m`x?5F+$\"+R6z)z$!#7$\" +;/<2ChY!#8$\"+4nwt;F;$\"+lr4vk!#9$\"+e=t5DF@$\" +*)z_G'*!#:$\"+\\#fU\"QFE$\"+^+b\\7FE$\"+\\%eK1&!#;$\"+oePbPFL$\"+B*[) =6FL$\"+O*4\"QQ!#<$\"+\"z\"R*R\"FS$\"+h\"pX5&!#=$\"+#>_U&=FX$\"+S\\`!* p!#>$\"+^>7-AFgn$\"+]xLC')!#?$\"+*4RzO'F\\o$\"+kP$ov\"F\\o$\"+keS[f!#@ $\"+Z0q7@Fco$\"+-t([](!#A$\"+6,3aDFho$\"+m2)eS'!#B$\"+7#\\iG\"F]p\"\"! F`p" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "# find prob. distrib ution of the last batter in the inning.\nLastbat([1,2,3,4,5,6,7,8,9]); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7+$\")'yVv%!#5$\")jR$z$F&$\"+hEOy@ F&$\"*JIr(H!\"*$\"*2 " 0 "" {MPLTEXT 1 0 29 "Lastbat([2,1,3,4,5,6,7,8,9 ]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7+$\").8Zl!#5$\"(X1+#!\"*$\"*mi $y@F)$\"*KIr(HF)$\"*2 " 0 "" {MPLTEXT 1 0 29 "Lastbat([2,3,4,1,5,6,7,8, 9]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7+$\")08Zl!#5$\")h.bFF&$\"*ix$ *)H!\"*$\"*Xr&e@F+$\"*2 " 0 "" {MPLTEXT 1 0 54 "# Rotate the batting or der\nRot([1,2,3,4,5,6,7,8,9],1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7+ \"\"#\"\"$\"\"%\"\"&\"\"'\"\"(\"\")\"\"*\"\"\"" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 28 "Rot( [2,1,3,4,5,6,7,8,9],4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7+\"\"&\"\"'\"\"(\"\")\"\"*\"\"#\"\"\"\"\"$\"\"%" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "# compute run distributions with annotations\nERProd( [1,2,3,4,5,6,7,8,9]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7+\"\"!F$F$F$F$F$F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7+$\"+\"f(R\\[!#5$\"*Nyzn'!\"*F'F'F'F'F'F'F'" }}{PARA 11 "" 1 " " {XPPMATH 20 "6%7+\"\"!F$F$$\"+.!3E;#!#5F$F$F$F$F$F%F%" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#$\"+%**RL8&!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#$\"+.d+yt!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+bM!3r)!#5" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+'zO[S*!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+29bP(*!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+=? 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