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rating_introduction

kur0cky
June 30, 2019

 rating_introduction

Sports Analyst Meetup #3 LT資料

kur0cky

June 30, 2019
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  1. • ࠇ໦ ༟ୋ / Kuroki Yutaka • Twitterɿ@kur0cky_y • ࢓ࣄɿ͕͠ͳ͍େֶӃੜ

    (M2) • ઐ໳ɿࣗ෼Ͱ΋෼͔ͬͯͳ͍ • झຯ ɿԻָɾөըɾञɾσʔλ෼ੳ ɾkaggle(ऑ͍) • εϙʔπɿݟΔઐɺϠΫϧτϑΝϯ ࣗݾ঺հ ਤ1ɿσʔλ෼ੳͯ͠Δͱ͖ͷࢲ ͦͷޙ
  2. • ͋Δʮ֓೦ʯʹؔ͢ΔॱংԽɺ਺஋Խɻ ‣ ڧ͞ͷ਺஋Խ͸ਓͷ৺Λૡཱ͖ͯΔɻ εΧ΢λʔ • εϙʔπҎ֎ʹ΋༷ʑͳԠ༻ ‣ өը, Webϖʔδ,

    ޿ࠂ, ͓͢͢Ίॱ, etc… • 1࣍ݩ΁ͷʮ௚઀ղऍՄೳͳࣹӨʯͱ͍͑Δ • ϨʔςΟϯάΛιʔτ͢ΔͱϥϯΩϯά͕࡞ΕΔ ϨʔςΟϯά ϨʔςΟϯά ϥϯΩϯά ˚ ◦
  3. • 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
  4. • EloϨʔςΟϯάʹ͍ͭͯ͸લճͷ spoana Ͱ΋͋ͬͨɻ • @konakalab ઌੜʹΑΔൃද → spoana #2

    ʹͯ https://speakerdeck.com/konakalab/spoana-number-2-unified-prediction-model-for-rio2016
  5. • ʮͲͷΞϧΰϦζϜ͕ࣅͨ݁ՌΛग़͔͢ʯʹண໨ ‣ ྨࣅ౓͸ɺ֨෇͚ͳͲͷղऍʹ΋༗༻ (ۚ༥, ϒϥϯυ, ϗςϧ, etc) • ୯७ͳͷ͸ɺॱҐ૬ؔ܎਺

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

    ‣ ࣌ܥྻΛҙࣝ͠ͳ͚Ε͹ͳΒͳ͍͜ͱʹ஫ҙ → ϩʔϦϯάͳͲ͕༗ޮ • ΞϧΰϦζϜͷݡ͞ΛݟΔ ‣ ༧ଌ͕ਖ਼ղ͢ΔΑ͏ʹͳΔ·Ͱͷ୹͞ ‣ ಈతʹύϑΥʔϚϯεͷਪҠΛݟΔ ϨʔςΟϯάͷධՁ
  7. • ػցֶशͷΞϯαϯϒϧʹ΋௨ͮΔ ‣ ʮͨ͘͞ΜͷϨʔςΟϯάͰڧ͍ϨʔςΟϯάΛ࡞Δʯ • ֤ΞϧΰϦζϜ͝ͱʹ εέʔϧΛ߹ΘͤΔඞཁ ‣ ਖ਼نԽ ‣

    Box-Coxม׵ ‣ Yeo-Johnsonม׵ • جຊతͳϨʔςΟϯά౷߹ ‣ (ॏΈ෇͖) ฏۉ ‣ উഊ΍఺ࠩͳͲΛઆ໌͢ΔϩδεςΟοΫճؼ ‣ Page Rank ౷߹ɿΞϧΰϦζϜ͝ͱͷϨʔτࠩΛ౤ථͱΈͳ͢ ϨʔςΟϯάͷ౷߹
  8. • 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
  9. • 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
  10. 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
  11. 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
  12. 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