rating_introduction

9c42c4bc1d91c409d754da88c91cb2ef?s=47 kur0cky
June 30, 2019

 rating_introduction

Sports Analyst Meetup #3 LT資料

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kur0cky

June 30, 2019
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  1. ϨʔςΟϯάͷ ͍ɾΖɾ͸ ὑ ~υϥΰϯϘʔϧΛఴ͑ͯ~ Sports Analyst Meetup #3 kur0cky

  2. • ࠇ໦ ༟ୋ / Kuroki Yutaka • Twitterɿ@kur0cky_y • ࢓ࣄɿ͕͠ͳ͍େֶӃੜ

    (M2) • ઐ໳ɿࣗ෼Ͱ΋෼͔ͬͯͳ͍ • झຯ ɿԻָɾөըɾञɾσʔλ෼ੳ ɾkaggle(ऑ͍) • εϙʔπɿݟΔઐɺϠΫϧτϑΝϯ ࣗݾ঺հ ਤ1ɿσʔλ෼ੳͯ͠Δͱ͖ͷࢲ ͦͷޙ
  3. ϨʔςΟϯά ͬͯͳʔʹʁ ਤ2ɿಥ೗΍͖ͬͯͨλεΫ

  4. • ͋Δʮ֓೦ʯʹؔ͢ΔॱংԽɺ਺஋Խɻ ‣ ڧ͞ͷ਺஋Խ͸ਓͷ৺Λૡཱ͖ͯΔɻ εΧ΢λʔ • εϙʔπҎ֎ʹ΋༷ʑͳԠ༻ ‣ өը, Webϖʔδ,

    ޿ࠂ, ͓͢͢Ίॱ, etc… • 1࣍ݩ΁ͷʮ௚઀ղऍՄೳͳࣹӨʯͱ͍͑Δ • ϨʔςΟϯάΛιʔτ͢ΔͱϥϯΩϯά͕࡞ΕΔ ϨʔςΟϯά ϨʔςΟϯά ϥϯΩϯά ˚ ◦
  5. • 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
  6. • EloϨʔςΟϯάʹ͍ͭͯ͸લճͷ spoana Ͱ΋͋ͬͨɻ • @konakalab ઌੜʹΑΔൃද → spoana #2

    ʹͯ https://speakerdeck.com/konakalab/spoana-number-2-unified-prediction-model-for-rio2016
  7. ϨʔςΟϯάͷൺֱɾྑ͠ѱ͠ ਤ3ɿൃදޙͷઌੜํͷίϝϯτ

  8. • ʮͲͷΞϧΰϦζϜ͕ࣅͨ݁ՌΛग़͔͢ʯʹண໨ ‣ ྨࣅ౓͸ɺ֨෇͚ͳͲͷղऍʹ΋༗༻ (ۚ༥, ϒϥϯυ, ϗςϧ, etc) • ୯७ͳͷ͸ɺॱҐ૬ؔ܎਺

    (Spearman, Kendall) ͳͲ ‣ 2νʔϜͷॱংʹ஫໨ • Kendall ɿ−1 ≤ (Ұக਺) − (ෆҰக਺) (૊Έ߹Θͤ૯਺) ≤ 1 ϨʔςΟϯάͷྨࣅ౓
  9. • ط஌ͷج४ͱͷൺֱ ‣ ط஌ͷج४͕ઈରతʹਖ਼͍͠ͱԾఆ ‣ ਺஋γϛϡϨʔγϣϯͳͲͰ༗ޮ • ༧ଌਫ਼౓ͰଌΔ ‣ εϙʔπͰ͸ςετσʔλ͕গͳ͘ͳΓ͕ͪͳ͜ͱʹ஫ҙ

    ‣ ࣌ܥྻΛҙࣝ͠ͳ͚Ε͹ͳΒͳ͍͜ͱʹ஫ҙ → ϩʔϦϯάͳͲ͕༗ޮ • ΞϧΰϦζϜͷݡ͞ΛݟΔ ‣ ༧ଌ͕ਖ਼ղ͢ΔΑ͏ʹͳΔ·Ͱͷ୹͞ ‣ ಈతʹύϑΥʔϚϯεͷਪҠΛݟΔ ϨʔςΟϯάͷධՁ
  10. ϨʔςΟϯάͷ౷߹ ਤ4ɿԿނ͔ൟ๩ظʹདྷΔλεΫ

  11. • ػցֶशͷΞϯαϯϒϧʹ΋௨ͮΔ ‣ ʮͨ͘͞ΜͷϨʔςΟϯάͰڧ͍ϨʔςΟϯάΛ࡞Δʯ • ֤ΞϧΰϦζϜ͝ͱʹ εέʔϧΛ߹ΘͤΔඞཁ ‣ ਖ਼نԽ ‣

    Box-Coxม׵ ‣ Yeo-Johnsonม׵ • جຊతͳϨʔςΟϯά౷߹ ‣ (ॏΈ෇͖) ฏۉ ‣ উഊ΍఺ࠩͳͲΛઆ໌͢ΔϩδεςΟοΫճؼ ‣ Page Rank ౷߹ɿΞϧΰϦζϜ͝ͱͷϨʔτࠩΛ౤ථͱΈͳ͢ ϨʔςΟϯάͷ౷߹
  12. Massey ͷϨʔςΟϯά ͜ͷ··ऴΘΔͷ΋ຯؾͳ͍ͷͰ

  13. • 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
  14. • 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
  15. 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
  16. 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
  17. • ϨʔςΟϯάͷ جຊͷʮΩʯΛ঺հͨ͠ • ༏ΕͨεΧ΢λʔΛ୳ٻ͍͖͍ͯͨ͠ • ڧ͘ͳΓ͍ͨ • ݸਓతʹɺ͜Ε͔Β͸εΧ΢λʔશ੝ͷ࣌୅ͩͱࢥ͍ͬͯ·͢ •

    ৴༻είΞϦϯά • اۀͷESG֨෇͚ ·ͱΊɾײ૝
  18. 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
  19. Enjoy