Powered by TCPDF (www.tcpdf.org) Title 東京六大学野球リーグ及び東都大学野球リーグを含めた各大学野球連盟における過去 30シーズンの平均競技力の比較研究 Sub Title Comparison of the strengths of Japanese collegiate baseball leagues in past 30 seasons Author 鳥海, 崇 (Toriumi, Takashi) 綿田, 博人 (Watada, Hirohito) Publisher 慶應義塾大学体育研究所 Publication year 2018 Jtitle 体育研究所紀要 (Bulletin of the institute of physical education, Keio university). Vol.57, No.1 (2018. 1),p.43-56 Abstract The Tokyo Big 6 Baseball League (BIG6) and the Tohto University Baseball League (TOHTO) are the top two collegiate baseball leagues in Japan. Both leagues consists of six teams and are highly competitive ; however, there is no opportunity for the teams in the two leagues to compete directly against each other except for the national championships. In this report, we calculate the strengths of six teams across both leagues and compare the superiority of them. Using the Bradley-Terry model and Markov model, we estimate the strengths of each team in both leagues. The Kendall tau rank correlation coefficient of both methods was as high as 0.945. The results indicate that the first team in TOHTO had the highest strength calculated by Bradly-Terry model on the other hand the first team in BIG6 had the highest by Markov model. On comparing the strengths of the same rankings in both leagues, the strengths of every team in TOHTO are higher than those of the corresponding teams in BIG6 in both methods. This is because BIG6 consists of only the same six teams, while TOHTO consists of 21 teams, with the sixth-ranked team playing a replacement game against the first team of the second division every season. Notes 研究資料 Genre Departmental Bulletin Paper URL http://koara.lib.keio.ac.jp/xoonips/modules/xoonips/detail.php?koara_id=an00135710-00570001 -0043
Comparison of the strengths of Japanese Collegiate Baseball Leagues in past 30 seasons Takashi Toriumi 1, Hirohito Watada 2, The Tokyo Big 6 Baseball League (BIG6)and the Tohto University Baseball League (TOHTO)are the top two collegiate baseball leagues in Japan. Both leagues consists of six teams and are highly competitive; however, there is no opportunity for the teams in the two leagues to compete directly against each other except for the national championships. In this report, we calculate the strengths of six teams across both leagues and compare the superiority of them. Using the Bradley- Terry model and Markov model, we estimate the strengths of each team in both leagues. The Kendall tau rank correlation coefficient of both methods was as high as 0.945. The results indicate that the first team in TOHTO had the highest strength calculated by Bradly-Terry model on the other hand the first team in BIG6 had the highest by Markov model. On comparing the strengths of the same rankings in both leagues, the strengths of every team in TOHTO are higher than those of the corresponding teams in BIG6 in both methods. This is because BIG6 consists of only the same six teams, while TOHTO consists of 21 teams, with the sixth-ranked team playing a replacement game against the first team of the second division every season. Ⅰ 1 2626 26 11 1 2017 26 1925 2 6 2017 1931 1 2 43
1 30 1 1990 12 0 0 0 0 2 1990 18 0 0 0 0 3 1991 16 0 1 0 1 4 1969 6 2 10 1 3 5 1991 11 0 0 0 0 6 1952 20 0 2 0 2 7 1993 20 1 1 1 1 8 1952 24 0 3 0 1 9 1925 6 38 23 8 8 10 1931 21 39 32 12 5 11 1964 15 9 12 1 5 12 1949 12 1 3 1 2 13 1949 27 1 1 0 1 14 1975 19 1 0 1 0 15 1968 13 0 0 0 0 16 1982 6 11 15 0 1 17 1982 6 0 3 0 0 18 1955 17 1 0 1 0 19 1948 19 0 0 0 0 20 1950 13 0 0 0 0 21 1967 6 0 1 0 0 22 1974 20 3 0 2 0 23 1949 11 0 0 0 0 24 1957 6 0 0 0 0 25 1971 6 0 1 1 0 26 1952 31 1 0 1 0 381 108 108 30 30 21 4 1 3 6 4 3 24 3 6 14 15 3 5 44
26 26 2 1952 1978 2011 2012 2017 2016 1994 26 Ⅱ 1994 26 1236 2 Ⅲ 1 26 3 45
2017 2 1 1952 i j P ij π i π i p ij π i +π π i j i j π i π j p ij 20172017 2 2 2017 1 0 0 5 3 3 { ππ ii = mm n ij i j m T i i 1 6 m 6 π i 1 6 2 1 π i 2 1 3 2 π i 1 4 2 3 TT ii (1) 1 jj ii nn iiii ππ ii + ππ jj ππ ii = 1 (2) ii=1 π i π i 0 321 0 305 0 145 0 114 0 057 0 057 2 1994 2 0 1 0 5 4 S 1 6 0.00 0.00 0.71 0.00 0.29 0.00 0.67 0.00 0.00 0.00 0.00 0.33 S= 0.21 0.29 0.00 0.21 0.29 0.00 0.31 0.31 0.38 0.00 0.00 0.00 0.25 0.25 0.00 0.25 0.00 0.25 0.25 0.25 0.25 0.25 0.00 0.00 r r S rs rs r n X n y n+1 X n+1 x Pr X n+1 x X n y Pr X n+1 x X n y Pr X n x X n 1 y p ij 0 i n j n p ij Pr X n j X 0 i n- 0<k<n n n (nn) (kk) (nn kk) pp iiii = ppiiii pprrrr rr SS 46
2 2017 13 9 3 1 4 75 0 1 11 8 3 0 4 72 7 2 14 6 6 2 3 50 0 3 12 5 6 1 2 45 5 4 11 3 8 0 1 27 3 5 11 3 8 0 1 27 3 5 3 0 0 2 1 5 2 2 2 9 5 0 0 2 2 2 2 8 2 5 0 0 2 5 0 2 7 0 0 1 5 0 2 2 5 5 1 0 2 0 0 0 3 0 1 0 0 2 0 3 4 2 0 1 0 5 0 0 0 2 5 0 1 0 2 0 0 0 0 1 1 5 2 0 1 5 2 0 2 2 2 5 0 0 0 2 2 0 2 0 2 2 2 2 2 0 0 PPPP(XX nn = jj) = pp rrrr PPPP(XX nn 1 = rr) = p ij r r j 1 r r n n rr SS rr jj = rr ii pp iiii ii SS rs r (nn) pp rrrr PPPP(XX0 = rr) rr SS 1 6 m 6 r i 1 6 2 r1s r2 r2 1 r2 3 r2 r2 S r3 r3 r3 4 rs r r r r 0 252 0 162 0 245 0 110 0 142 0 089 47
2 179 3 4 5 180 1994 3 1 2 1 1 5 1 1 3 2 3 20022017 30 539549 1 29 443539 15521 5 2005 5 1530 1 2 1 26 2 26 1 2 6 3 4 3 1 2 2 1 2 2 6 4 3 2 1 8000 Ⅳ 1 2002 2017 1 2 261000 139 3 126 4 77 9 124 5 123 5 81 6 3 0 945 3 4 6 3 4 6 2 3 4 299 5370 5 468 0 571 8 48
5 20022017 30 521 49
2 6 1 3 126 4 139 3 47 6 2 7 50 4 1 124 5 123 5 2 26 8 9 8 1 30 2 30 50
4 2 3 12 9 4 4 5 6 0 895 3 30 4 30 51
6 1 2 3 4 1 2 3 1 2 4 1 126 4 0 422 126 4 1 139 3 0 376 139 3 2 0 234 70 1 2 0 218 80 7 3 0 156 46 7 3 0 167 61 8 4 0 111 33 4 4 0 113 41 7 5 0 067 20 2 5 0 079 29 2 6 0 010 3 07 6 0 047 17 5 3 299 5 4 370 5 1 2 3 1 2 4 1 124 5 0 266 124 5 1 123 5 0 216 123 5 2 0 227 106 3 2 0 203 116 2 3 0 195 91 3 3 0 185 105 4 4 0 166 77 8 4 0 151 86 4 5 0 116 54 5 5 0 145 83 0 6 0 030 13 9 6 0 099 56 7 3 468 0 4 571 8 7 1 47 6 2 46 5 3 43 0 4 44 5 5 40 9 6 14 9 52
8 2 6 1 139 3 13 31 8 2 126 4 29 2 5 80 7 2 14 28 8 3 77 9 15 26 3 70 1 2 16 25 5 61 8 3 17 21 6 4 59 9 20 2 5 5 56 2 17 5 6 6 51 2 18 17 0 7 47 5 19 16 9 46 7 3 20 16 3 8 45 3 21 15 9 41 7 4 22 15 7 9 40 6 23 15 1 10 36 3 24 11 5 11 34 9 25 6 8 33 4 4 3 1 6 12 32 5 26 2 9 9 2 6 1 124 5 10 40 0 2 123 5 11 36 8 116 1 2 12 33 0 106 3 2 13 28 9 105 4 3 14 25 4 91 3 3 15 24 3 86 4 4 16 23 9 83 0 5 17 22 1 3 81 6 18 18 2 77 8 4 19 15 9 4 67 8 13 9 6 5 59 9 20 13 3 6 58 2 21 12 8 56 7 6 22 12 4 7 54 6 23 8 9 54 5 5 24 8 1 8 49 4 25 8 1 9 44 5 26 3 9 53
Ⅴ 1 26 3 17 16 6 4 1 3 1 4 5 5 4 3 1 15 2 11 11 12 12 13 5 2 1 1994 1 2 2 30 16 17 8 12 1 5 2 6 33 3 126 4 139 3 10 2 47 6 124 5 123 5 2 7 6 14 9 40 947 6 1 47 6 5 40 9 6 2 2 54
3 26 8 9 8 2 3 4 5 9 4 5 4 6 0 895 2 4 3 5 4 1 30 2 3 4 2 1 Ⅵ 26 36 30 26 3 1 26 2 3 4 55
1 2017 2017 72 17 55 82 2 2017 201746 60 3 1952 39 324 345 4 1978 5 2012 57 11 629 638 6 1994 24 1 35 41 7 2016 1990 89 96 8 2017 56 1 45 53 9 2017 2017 357 362 10 2011 42 3232 244 2017 9 15 2017 12 31 56