ϨʔςΟϯάͷ ͍ɾΖɾ͸ ὑ ~υϥΰϯϘʔϧΛఴ͑ͯ~ Sports Analyst Meetup #3 kur0cky

• ࠇ໦ ༟ୋ / Kuroki Yutaka • Twitterɿ@kur0cky_y • ࢓ࣄɿ͕͠ͳ͍େֶӃੜ (M2) • ઐ໳ɿࣗ෼Ͱ΋෼͔ͬͯͳ͍ • झຯ ɿԻָɾөըɾञɾσʔλ෼ੳ ɾkaggle(ऑ͍) • εϙʔπɿݟΔઐɺϠΫϧτϑΝϯ ࣗݾ঺հ ਤ1ɿσʔλ෼ੳͯ͠Δͱ͖ͷࢲ ͦͷޙ

ϨʔςΟϯά ͬͯͳʔʹʁ ਤ2ɿಥ೗΍͖ͬͯͨλεΫ

• ͋Δʮ֓೦ʯʹؔ͢ΔॱংԽɺ਺஋Խɻ ‣ ڧ͞ͷ਺஋Խ͸ਓͷ৺Λૡཱ͖ͯΔɻ εΧ΢λʔ • εϙʔπҎ֎ʹ΋༷ʑͳԠ༻ ‣ өը, Webϖʔδ, ޿ࠂ, ͓͢͢Ίॱ, etc… • 1࣍ݩ΁ͷʮ௚઀ղऍՄೳͳࣹӨʯͱ͍͑Δ • ϨʔςΟϯάΛιʔτ͢ΔͱϥϯΩϯά͕࡞ΕΔ ϨʔςΟϯά ϨʔςΟϯά ϥϯΩϯά ˚ ○

• Elo ϨʔςΟϯά (Elo, 1978) - ಈతͳߋ৽ɻνΣεൃ঵ɻશମͷฏۉ͕ৗʹ1500 • Massey (1997) - Ϩʔτ͕ࠩಘ఺ࠩʹͳΔͱ͠ɺ࠷খೋ৐๏ɻ - Offense ྗɾDefense ྗͷϨʔςΟϯά΋ՄɻͳΜͱम࢜࿦จʂ • Page Rank (Brin & Page, 1998) - ݴΘͣͱ஌ΕͨGoogleͷ΍ͭ - ഊऀ͔Βউऀ΁ͷ౤ථɻϚϧίϑ࿈࠯ͷఆৗ֬཰ʹ஫໨ • Colley (2002) - ΞΠσΞɿLaplace’s Law of Succession. উ཰Λ (উར਺ + 1) / (ࢼ߹਺ + 2) Ͱิਖ਼ جຊతͳ ϨʔςΟϯάɾΞϧΰϦζϜ

• EloϨʔςΟϯάʹ͍ͭͯ͸લճͷ spoana Ͱ΋͋ͬͨɻ • @konakalab ઌੜʹΑΔൃද → spoana #2 ʹͯ https://speakerdeck.com/konakalab/spoana-number-2-unified-prediction-model-for-rio2016

ϨʔςΟϯάͷൺֱɾྑ͠ѱ͠ ਤ3ɿൃදޙͷઌੜํͷίϝϯτ

• ʮͲͷΞϧΰϦζϜ͕ࣅͨ݁ՌΛग़͔͢ʯʹண໨ ‣ ྨࣅ౓͸ɺ֨෇͚ͳͲͷղऍʹ΋༗༻ (ۚ༥, ϒϥϯυ, ϗςϧ, etc) • ୯७ͳͷ͸ɺॱҐ૬ؔ܎਺ (Spearman, Kendall) ͳͲ ‣ 2νʔϜͷॱংʹ஫໨ • Kendall ɿ−1 ≤ (Ұக਺) − (ෆҰக਺) (૊Έ߹Θͤ૯਺) ≤ 1 ϨʔςΟϯάͷྨࣅ౓

• ط஌ͷج४ͱͷൺֱ ‣ ط஌ͷج४͕ઈରతʹਖ਼͍͠ͱԾఆ ‣ ਺஋γϛϡϨʔγϣϯͳͲͰ༗ޮ • ༧ଌਫ਼౓ͰଌΔ ‣ εϙʔπͰ͸ςετσʔλ͕গͳ͘ͳΓ͕ͪͳ͜ͱʹ஫ҙ ‣ ࣌ܥྻΛҙࣝ͠ͳ͚Ε͹ͳΒͳ͍͜ͱʹ஫ҙ → ϩʔϦϯάͳͲ͕༗ޮ • ΞϧΰϦζϜͷݡ͞ΛݟΔ ‣ ༧ଌ͕ਖ਼ղ͢ΔΑ͏ʹͳΔ·Ͱͷ୹͞ ‣ ಈతʹύϑΥʔϚϯεͷਪҠΛݟΔ ϨʔςΟϯάͷධՁ

ϨʔςΟϯάͷ౷߹ ਤ4ɿԿނ͔ൟ๩ظʹདྷΔλεΫ

• ػցֶशͷΞϯαϯϒϧʹ΋௨ͮΔ ‣ ʮͨ͘͞ΜͷϨʔςΟϯάͰڧ͍ϨʔςΟϯάΛ࡞Δʯ • ֤ΞϧΰϦζϜ͝ͱʹ εέʔϧΛ߹ΘͤΔඞཁ ‣ ਖ਼نԽ ‣ Box-Coxม׵ ‣ Yeo-Johnsonม׵ • جຊతͳϨʔςΟϯά౷߹ ‣ (ॏΈ෇͖) ฏۉ ‣ উഊ΍఺ࠩͳͲΛઆ໌͢ΔϩδεςΟοΫճؼ ‣ Page Rank ౷߹ɿΞϧΰϦζϜ͝ͱͷϨʔτࠩΛ౤ථͱΈͳ͢ ϨʔςΟϯάͷ౷߹

Massey ͷϨʔςΟϯά ͜ͷ··ऴΘΔͷ΋ຯؾͳ͍ͷͰ

• શνʔϜͷϨʔςΟϯάϕΫτϧ ɿ • ఺͕ࠩϨʔτࠩʹ༝དྷ͢ΔͱԾఆ ɿ ‣ : ࢼ߹ index • Ϛονϯάߦྻ Λ༻͍ͯ 3νʔϜͷྫɿ r = (r1 , r2 , …, rm )′ yk = ri − rj k X Massey ͷϨʔςΟϯάɾجຊ Xr = y r1 − r2 = 4 r2 − r3 = − 7 r1 − r3 = 2 r1 − r2 = − 3 1 −1 0 0 1 −1 1 0 −1 1 −1 0 r1 r2 r3 = 4 −7 2 −3 ࠷খೋ৐๏Ͱཅʹਪఆ

• લϖʔδ͸ಉνʔϜͷࢼ߹Λશͯू໿ͯ͠΋ྑ͍ • ͜͜Ͱɺ ͸νʔϜͷରઓ਺Λද͢ର֯ߦྻ ͱɺϚονϯάΛද͢
 ඇର֯ߦྻ ʹ෼ղͰ͖Δ M T P Massey ͷϨʔςΟϯάɾجຊ ( 3 −2 −1 −2 3 −1 −1 −1 2 ) r1 r2 r3 = 3 −8 5 Mr = p (T − P)r = p ( 3 0 0 0 3 0 0 0 2 ) − ( 0 2 1 2 0 1 1 1 0 ) r1 r2 r3 = 3 −8 5

Offenseྗ, Defenseྗ ͷਪఆ • Offenseྗ, Defenseྗ ͷϕΫτϧɿ • ͱԾఆ • νʔϜ ͷྦྷੵಘ఺ɺྦྷੵࣦ఺Λ ͱ͢Δͱ o = (o1 , …, om )′, d = (d1 , …, dm )′ oi + di = ri i fi , ai Massey ͷϨʔςΟϯάɾԠ༻ Mr = p (T − P)r = p (T − P)(o + d) = f − a (To − Pd) − (Td − Po) = f − a

Offenseྗ, Defenseྗ ͷਪఆ • Offenseྗ, Defenseྗ ͷϕΫτϧɿ • ͱԾఆ • νʔϜ ͷྦྷੵಘ఺ɺྦྷੵࣦ఺Λ ͱ͢Δͱ o = (o1 , …, om )′, d = (d1 , …, dm )′ oi + di = ri i fi , ai Massey ͷϨʔςΟϯάɾԠ༻ Mr = p (T − P)r = p (T − P)(o + d) = f − a (To − Pd) − (Td − Po) = f − a ߈ܸ - ఢͷ๷ޚ = ಘ఺ ๷ޚ - ఢͷ߈ܸ = ࣦ఺ ͷԾఆͱɺલ߲ͷ r Λ༩͑ͯղ͚Δ

• ϨʔςΟϯάͷ جຊͷʮΩʯΛ঺հͨ͠ • ༏ΕͨεΧ΢λʔΛ୳ٻ͍͖͍ͯͨ͠ • ڧ͘ͳΓ͍ͨ • ݸਓతʹɺ͜Ε͔Β͸εΧ΢λʔશ੝ͷ࣌୅ͩͱࢥ͍ͬͯ·͢ • ৴༻είΞϦϯά • اۀͷESG֨෇͚ ·ͱΊɾײ૝

1) Elo, A. E. (1978). The rating of chessplayers, past and present. Arco Pub.. 2) Massey, K. (1997). Statistical models applied to the rating of sports teams. Bluefield College. 3) Brin, S., & Page, L. (1998). The anatomy of a large-scale hypertextual web search engine. Computer networks and ISDN systems, 30(1-7), 107-117. 4) Colley, W. N. (2002). Colley’s bias free college football ranking method: The Colley matrix explained. Princeton University, Princeton. ࢀߟจݙ

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