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Win ratio その2

Win ratio その2

Win ratioの問題点と、それに対してどのように考えて、使うのか、一つの例を解説しています。

Shuntaro Sato

August 28, 2023
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  1. ঺հ͢Δ࿦จ 2 ࿦จλΠτϧ 'BMMBDJFTPG6TJOHUIF8JO3BUJPJO$BSEJPWBTDVMBS5SJBMT $IBMMFOHFTBOE4PMVUJPOT ஶऀ໊ɺܝࡌδϟʔφϧɺग़൛೥ &[JNBNBLB"KVGP FUBM +"$$#BTJDUP 5SBOTMBUJPOBM4DJFODF

     ݚڀσβΠϯ ํ๏࿦ʹର͢Δҙݟ࿦จ "KVGP&[JNBNBLB /BZBL"EJUJ .FISB.BOEFFQ3'BMMBDJFTPG6TJOHUIF8JO3BUJPJO$BSEJPWBTDVMBS5SJBMT+"$$#BTJDUP5SBOTMBUJPOBM 4DJFODFr
  2. ෳ߹ΤϯυϙΠϯτͷ໰୊఺ 5 'FSSFJSB(PO[ÂMF[* #VTTF+8 )FFMT"OTEFMM% .POUPSJ7. "LM&" #SZBOU%. FUBM 


    1SPCMFNTXJUIVTFPGDPNQPTJUFFOEQPJOUTJODBSEJPWBTDVMBSUSJBMTTZTUFNBUJDSFWJFXPGSBOEPNJTFEDPOUSPMMFEUSJBMT#.+"QS  ͷ'JHVSF ᶃ %FBUI ᶄ $SJUJDBM 4USPLF  ᶅ .BKPS /POGBUBM.*  ᶆ .PEFSBUF )PTQJUBMJ[BUJPO  ᶇ .JOPS $IBOHFJOCMPPEQSFTTVSF w ॏ঱౓͕ߴ͍ΤϯυϙΠϯτ͸ɺ 
 ޮՌ͕খ͍͞ w ॏ঱౓͕௿͍ΤϯυϙΠϯτ͸ɺ 
 ޮՌ͕େ͖͍ w ॏ঱౓͕௿͍ΤϯυϙΠϯτ͸ߴ͍ΤϯυϙΠϯτΑΓɺΠϕϯτΛൃੜ͠΍͍͢ w ෳ߹ΤϯυϙΠϯτ͸ɺUJNFUP fi STUFWFOUͷ৘ใΛ༻͍Δ ॏ঱౓͕ߴ͍ΤϯυϙΠϯτͷ৽نͷ࣏ྍޮՌΛద੾ʹධՁͰ͖͍ͯͳ͍͔΋͠Εͳ͍ ৽ن࣏ྍ͸ෳ߹ΤϯυϙΠϯτͷൃੜස౓Λม͑ͨ ϛεϦʔσΟϯά
  3. ΞϧΰϦζϜɹᶃϖΞΛ࡞Δ 6 5IFNBUDIFEQBJSTBQQSPBDI 5IFVONBUDIFEQBJSTBQQSPBDI 3JTLTDPSF    ಉ͡ϦεΫΛ࣋ͭਓಉ࢜ΛϖΞʹ͢Δ ࣏ྍ܈

    ରর܈ w ϞσϧʹΑΓɺҰਓҰਓͷ3JTLTDPSFΛܭࢉ͢Δඞཁ w ݪஶ࿦จͰ͸નΊΒΕ͍͕ͯͨ w ࣮༻తͰͳ͍ͱɺஶऀΒࣗ਎΋೥ޙͷ࿦จͰݴٴ 3FEGPST# (SFHTPO+ $SPXMFZ" .D"OESFX5 #FO:FIVEB0 4UPOF(8 FUBM5IF XJOSBUJPBQQSPBDIGPSDPNQPTJUFFOEQPJOUTQSBDUJDBMHVJEBODFCBTFEPOQSFWJPVT FYQFSJFODF&VS)FBSU+%FD  r ͢΂ͯͷ૊Έ߹ΘͤΛϖΞʹ͢Δ ࣏ྍ܈ /5 ରর܈ /$ w 3JTLTDPSF͸ෆཁ w ݩͷϦεΫ͕ۃ୺ʹ཭Ε͍ͯΔਓಉ࢜ΛϖΞʹ ͍ͯ͠Δ w ࣮༻త ϖΞͷ਺ /5º/$
  4. ΞϧΰϦζϜɹᶅᶆ࣏ྍ܈ͷ8JO -PTF 5JFͷ൑ఆ 8 ྫɿ$7EFBUI)PTQJUBMJ[BUJPOͰߏ੒͞Εͨෳ߹Ξ΢τΧϜ  $7EFBUIͰ࣏ྍ܈ͷ8JO͕ܾ·Δύλʔϯ ଧͪ੾Γ ࣏ྍ ରর

    ࣏ྍ ରর ࣏ྍ ରর ࣏ྍ͸ରরΑΓ΋ૣ͘ )PTQJUBMJ[BUJPOΛى͍ͯ͜͠Δ͕ɺ ༏ઌॱҐ͕ߴ͍$7EFBUIΛධՁͯ͠ ͍ΔͨΊແࢹ w ͲͪΒ΋$7EFBUIΛى͍ͯ͜͠ͳ͍৔߹ɺ 
 ੜଘظ͕ؒશ͘ಉ͡৔߹ɺ  )PTQJUBMJ[BUJPOͷධՁ΁ w ؍࡯ظؒΛ୹͍ํʹͦΖ͑ͨͱ͖ʹɺͦͷ࣌఺ʹ$7EFBUIΛ ى͍ͯ͜͠ͳ͚Ε͹ɺ  )PTQJUBMJ[BUJPOͷධՁ΁ ࣏ྍ ରর ଧͪ੾Γ  )PTQJUBMJ[BUJPOͰ࣏ྍ܈ͷ8JO͕ܾ·Δύλʔϯ ଧͪ੾Γ ࣏ྍ ରর ࣏ྍ ରর ࣏ྍ ରর ࣏ྍ܈͸$7EFBUIΛى͍ͯ͜͠Δ͕ɺ 
 ؍࡯ظؒΛͦΖ͑ͨ৔߹ɺ 
 Ҿ͖෼͚ʹͳΓɺ  Ͱ൑ఆ͢Δύλʔϯ w ͲͪΒ΋)PTQJUBMJ[BJPOΛى͍ͯ͜͠ͳ͍৔߹ɺ 
 ൃੜظ͕ؒશ͘ಉ͡৔߹ɺ5JFʢҾ͖෼͚ʣ൑ఆ w ؍࡯ظؒΛ୹͍ํʹͦΖ͑ͨͱ͖ʹɺͦͷ࣌఺ʹ )PTQJUBMJ[BUJPOΛى͍ͯ͜͠ͳ͚Ε͹ɺ5JFʢҾ͖෼͚ʣ൑ఆ ࣏ྍ ରর 1PDPDL4+ "SJUJ$" $PMMJFS5+ 8BOH%5IFXJOSBUJPBOFXBQQSPBDIUPUIFBOBMZTJTPGDPNQPTJUFFOEQPJOUTJODMJOJDBMUSJBMTCBTFEPODMJOJDBMQSJPSJUJFT&VS)FBSU+ +BO  rͷ'JHVSFΛࢀߟ
  5. ΞϧΰϦζϜɹᶇ8JOSBUJPͷܭࢉ 9 ࣏ྍ܈ /5 ରর܈ /$ ਓ ਓ 300 ×

    312 = 94224 ϖΞ 5JFT / 8JOT /8 -PTTFT /- 5JFT / 8JOT /8 -PTTFT /-  $7EFBUI  )PTQJUBMJ[BUJPO 5PUBMXJOT 5PUBMMPTTFT 27060 + 15270 = 42330 18532 + 7745 = 26277 8JOSBUJP 5PUBMXJOT 5PUBMMPTTFT       $*UP 1 3FEGPST# (SFHTPO+ $SPXMFZ" .D"OESFX5 #FO:FIVEB0 4UPOF(8 FUBM5IFXJOSBUJPBQQSPBDIGPSDPNQPTJUFFOEQPJOUTQSBDUJDBMHVJEBODFCBTFEPOQSFWJPVTFYQFSJFODF &VS)FBSU+%FD  rͷ'JHVSFΛࢀߟ
  6. ޡղᶃɿ8JOSBUJP͸ɺ૯߹తͳ࣏ྍޮՌΛද͢)3ͷΑ͏ʹղऍͰ͖Δ 11 Ҿ͖෼͚ϖΞΛ࢖Θͳ͍ˠඪతूஂ͕มΘΔ ඪతूஂ ແࢹ ղऍ $PYൺྫϋβʔυϞσϧ )3͕ͷ৔߹ɺ 
 ඪతूஂʹ͓͍ͯɺରর܈ͱൺֱͯ͠

    
 ࣏ྍ܈ͷΠϕϯτൃੜ཰͕ݮগͨ͠ 
 ͜ͱΛࣔ͢ 8JOSBUJP 83͕ͷ৔߹ɺҾ͖෼͚ͷϖΞ͸ແࢹ͞ Εͨɺ୯७ʹউ͔ͭෛ͚Δ͔ʹ෼ผͰ͖Δɺ ΑΓখ͞ͳαϒάϧʔϓͷதͰɺ 
 ࣏ྍ܈ͷউͭ֬཰͕ෛ͚Δ֬཰ΑΓେ͖ ͍͜ͱΛࣔ͢
  7. ޡղᶄɿউͭ͜ͱ͸ɺ͢ͳΘͪྟচతʹ༗ҙٛͰ͋Δ͜ͱΛࣔ͢ 12 "KVGP&[JNBNBLB /BZBL"EJUJ .FISB.BOEFFQ3'BMMBDJFTPG6TJOHUIF8JO3BUJPJO$BSEJPWBTDVMBS5SJBMT+"$$#BTJDUP5SBOTMBUJPOBM4DJFODFrͷਤΑΓ ࣏ྍޮՌʹ 
 Ұ؏ੑ͕͋Δ͔ʁ ॏཁͳΠϕϯτͰ͸͕ࠩ ͔ͭͣɺൺֱతྟচతʹ

    ҙຯͷऑ͍߲໨Ͱ͕ࠩͭ ͍ͯͳ͍͔ʁ ࣏ྍ ରর ࣏ྍ ରর ࣏ྍ ରর w Πϕϯτͷൃੜස౓͸ಉ਺ w ൃੜ೔͕Θ͔ͣʹ୹͍͚ͩ w 8JOSBUJP͸࣏ྍ͕উͭ͜ͱΛࣔ͢ ͜ΕͰ͍͍ͷ͔ʁ ঱ީੑॏ঱ࡾઑหด࠯ෆશ঱ʹର͢ΔܦΧςʔςϧతFEHFUPFEHFम෮ज़ͱༀ෺ྍ๏ͷӨڹΛධՁͨ͠53*-6.*/"5&ࢼݧ
  8. ޡղᶅɿױऀใࠂΞ΢τΧϜ͸ɺ83ʹ͓͍ͯద੾ʹධՁͰ͖͍ͯΔ 13 "KVGP&[JNBNBLB /BZBL"EJUJ .FISB.BOEFFQ3'BMMBDJFTPG6TJOHUIF8JO3BUJPJO$BSEJPWBTDVMBS5SJBMT+"$$#BTJDUP5SBOTMBUJPOBM 4DJFODFrͷਤ w 20-Ͱେ͖ͳ͕͍͍ࠩͭͯΔ w ໡ݕԽͰ͖͍ͯͳ͍

    20-ͷࠩ͸ɺ࣏ྍޮՌʁ 
 ࣏ྍͨ͜͠ͱʹΑΔޮՌʁ ঱ީੑॏ঱ࡾઑหด࠯ෆશ঱ʹର͢ΔܦΧςʔςϧతFEHFUPFEHFम෮ज़ͱༀ෺ྍ๏ͷӨڹΛධՁͨ͠53*-6.*/"5&ࢼݧ w ໡ݕԽ͢Δ w ϓϥηϘʢTIBNʣΛ࢖͏
  9. ޡղᶆɿ֤ϖΞͷϦεΫϓϩϑΝΠϧ͸όϥϯεͱΕ͍ͯΔ 14 5IFVONBUDIFEQBJSTBQQSPBDI ͢΂ͯͷ૊Έ߹ΘͤΛϖΞʹ͢Δ ࣏ྍ܈ /5 ରর܈ /$ ϖΞͷ਺ /5º/$

    ࡀͷঁੑͱࡀͷஉੑͱ͍ͬͨϖΞ΋Ͱ͖Δ 
 ɹˠϦεΫ͸ҧ͏ 4USBUJ fi FE8JOSBUJPBQQSPBDI ط஌ͷϦεΫҼࢠͰ૚Λ࡞Γɺ 
 ͦͷதͰVONBUDIFEQBJSTBQQSPBDIΛ͓͜ͳ͏ ࣬ױײडੑҨ఻ࢠ͋ΓʢHʣ ࣬ױײडੑҨ఻ࢠͳ͠ʢHʣ 83H 83H TUSBUJ fi FE83
  10. ޡղᶇɿҾ͖෼͚͸݁࿦ʹӨڹ͠ͳ͍ 15 Ҿ͖෼͚Λແࢹ͢Δͱɺ࣏ྍޮՌͷաେධՁʹͭͳ͕Δ 8JOPEETʢҾ͖෼͚΋ߟྀ͢Δʣ 8JOTJOUSFBUNFUHSPVQ + 1/2PGBMMUJFT -PTTFTJOUSFBUNFUHSPVQ + 1/2PGBMMUJFT

    "KVGP&[JNBNBLB /BZBL"EJUJ .FISB.BOEFFQ3'BMMBDJFTPG6TJOHUIF8JO3BUJPJO$BSEJPWBTDVMBS5SJBMT+"$$#BTJDUP5SBOTMBUJPOBM 4DJFODFrͷද
  11. ྟচࢼݧʹ͓͍ͯ8JOSBUJP͸ɺͲͷΑ͏ʹղऍ͢΂͖͔ʁ 16 "KVGP&[JNBNBLB /BZBL"EJUJ .FISB.BOEFFQ3'BMMBDJFTPG6TJOHUIF8JO3BUJPJO$BSEJPWBTDVMBS5SJBMT+"$$#BTJDUP5SBOTMBUJPOBM 4DJFODFrͷਤΛҰ෦೔ຊޠԽ 8JOSBUJP͸ɺࢲͨͪʹԿΛڭ͑ͯ͘ΕΔ͔ʁ w Ҿ͖෼͚͕ͳ͍ϖΞʹ͓͍ͯɺ5&&3࣏ྍ܈ͷ֬཰͸ ߴ͍

    Ҿ͖෼͚Λແࢹ͢Δ͜ͱ͸ɺͲͷΑ͏ͳ݁࿦Λಋ͔͘ʁ w Ҿ͖෼͚ϖΞ͸Ͱ͋Δɻ͜ΕΒΛແࢹ͢Δ͜ͱ ͸ޮՌͷେ͖͞ͷա৒ਪఆʹͭͳ͕Δ ͲͷΤϯυϙΠϯτ͕༗ҙͳ8JOSBUJPʹد༩͔ͨ͠ʁ w ࣏ྍޮՌ͸ɺױऀใࠂΞ΢τΧϜʢ,$$2TDPSFʣʹ ΑͬͯͷΈઆ໌͞ΕΔ ͜ͷݚڀ͸ͲͷΑ͏ʹղऍ͢΂͖͔ʁ w ͜ͷඇ໡ݕࢼݧͷ5&&3͕উͬͨͱ͍͏݁Ռ͸ɺ 
 ϋʔυΤϯυϙΠϯτͰ͸ͳ͘ɺױऀใࠂΞ΢τΧϜ ͷ݁ՌͷΈʹجͮ͘΋ͷͰ͋Δ w ૯߹తͳΤϏσϯεͷղऍʹ͸ɺϓϥηϘޮՌͷཱূ ΋ඞཁͰ͋Δ
  12. 8JOSBUJPͷ՝୊ʹର͢Δղܾ๏ 17 "KVGP&[JNBNBLB /BZBL"EJUJ .FISB.BOEFFQ3'BMMBDJFTPG6TJOHUIF8JO3BUJPJO$BSEJPWBTDVMBS5SJBMT+"$$#BTJDUP5SBOTMBUJPOBM 4DJFODFrͷ$FOUSBM*MMVTUSBUJPOΛҰ෦೔ຊޠԽ 8JOPEETͰҾ͖෼͚Λߟྀ Ҿ͖෼͚਺͕͘͝গ਺Ͱ͋Δͱ͖Λআ͍ͯɺৗʹ ʮ8JOPEETʯΛܭࢉ͢Δ ඪ४తͳίϯηϯαεͷ։ൃ

    ෳ਺ͷεςʔΫϗϧμʔʹΑΔɺෳ߹Τ ϯυϙΠϯτͷߏ੒ཁૉɺ༏ઌॱҐɺଌ ఆఆٛɺ࣌ؒґଘੑͷҙຯʹؔ͢ΔΨΠ υϥΠϯΛ࡞Δ ม਺ͷΞϯόϥϯεʹରͯ͠૚ผղੳ ϦεΫҼࢠͷόϥϯε͕ͱΕ͍ͯͳ͍ 
 ࢼݧ΍ඇϥϯμϜԽࢼݧͷ৔߹ɺ 
 ૚ผ8JOSBUJP๏Λਪ঑͢Δ ױऀใࠂΞ΢τΧϜ·ͨ͸ 
 ػೳతΞ΢τΧϜͷͨΊʹ໡ݕԽ ෳ߹ΤϯυϙΠϯτʹɺ130΍ػೳతΞ ΢τΧϜΛؚΉࢼݧ͸ɺϓϥηϘ·ͨ͸ TIBNΛରরʹ͢΂͖ ֤ߏ੒ཁૉͷ෼ੳ݁ՌͷใࠂΛٛ຿Խ w ֤ཁૉͷXJOSBUJPΛܭࢉ w ϋʔυΤϯυϙΠϯτʹରͯ࣌ؒ͠Λར༻ ͨ͠ղੳ w /VNCFSOFFEFEUPUSFBUPSIBSN΋ਪఆ ྟচతՁ஋ͱܦࡁతՁ஋Λ૊ΈࠐΉ ཧ૝తʹ͸ɺඅ༻ରޮՌධՁ෼ੳΛ͓͜ͳ͏