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2 J A CB B CB J J J J J [], p..
3 Hadley, Ciecka, and Krautmann[]Schmidt and Berri [] MLB J J J J J J J J Competitive Balance CB CB / [], pp. -.
4 Competitive Balance J J J J J J J J [], p. [], p.. [], pp. -. p.. st TBS. NHK.,, / /
5 J & Perform Group J Perform Group J J JSAT & J J J J natural experiment J / [], p.. [], p..
6 Competitive Balance a b st nd st st nd st nd p. / 戸塚 [2013], p.64.
7 / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / ( ) / AFC A
8 Competitive Balance B st nd ( st nd stnd ) Rottenberg [] Uncertainty of Outcome Hypothesis UOH UOH UOH UOH Competitive BalanceCB Uncertainty of Outcome UO UOH CB UO TV 代表的な介入政策としては, 入場料収入の再分配, サラリーキャップ制, 放映権料のリーグ一括管理, 新人選手のドラフト制などが挙げられる. ただしこのような介入政策の多くが, トップリーグに昇格 降格制度のない 閉鎖型 リーグに集中している点は注意を要する. リーグ構造と介入政策の関係については,Ross and Szymanski [2002], および小林 [2015], 第 5 章を参照のこと. Owen [2014], p.42. CB 全般に関してはサーベイ論文である Humphreys and Watanabe [2012] も有益である. Fort and Maxcy [2003].
9 CB Analysis of Competitive BalanceACB CB UO CB a b c UOH ACB ACB CB CB ACB J J J CB CB A CB NAMSI HHI CRICBB CB Kendall CB CB A CB CB NAMSI HHI CRICB Kringstad and Gerrard [2007]. CB 指標の分類に対応して,UO 指標に関しても,a) 各ゲームの不確実性, b)1シーズン全体における結果の不確実性,c) シーズン間の優勝チームの不確実性, という3つに分類することができる (Szymanski [2003]). データは右のJリーグのデータサイトから入手した. Owen [2014], p.43.
10 Competitive Balance NAMSI (National Measure of Seasonal Imbalance) CB NAMSI N w i iw w i,max SD SD lb SD SD ub SD NAMSI NAMSI CB NAMSI CB CB HHI ( Herfindahl Hirschman index) HHI N w i i HHI Herfindahl-Hirschman index HHI lb HHI = N HHI ub HHI =2(2N 1) 3N(N-1) HHI NAMSI HHI Goossens [2006]. 本論文では勝率をもとにNAMSIを算出した. この勝率の計算では, 引き分けを 0.5 勝 として算定した. Depken [], Owen, Ryan and Weatherston [].NAMSIとの違いをみるため, 本論文では勝率ではなく勝ち点をもとにHHI を算出した.
11 CB HHI CB HHI CRICB CR(R)(concentration ratio for the R most teams) CRICB Michie and Oughton [2004].
12 Competitive Balance N R w i i CR(R) CRICB R N NAMSI HHI CRICB CB CB CRICB (C ICB) (CT ICB) (CM ICB) (CB ICB) CB NAMSI HHI.NAMSI HHI CRICB CB C ICB CT ICB CB ICB CM ICB CB B st nd CBst nd CB CB CBNAMSI, HHI, CRICBCB B CM ICB CRICB
13 CB CB B CB Spearman r s Kendall Kendall s coefficient of concordance W Kendall N k k W N k J R i i s R i T Groot [2008], chp 5. Siegel [], pp. -
14 Competitive Balance t j j ~k
15
16 Competitive Balance st-w p <. <. <. <. <. <. <. <. nd-w p <. <. <. <. <. <. <. <. W W W CB W CB CB Kendall CB N H N k H N k st nd CB Siegel [], pp. - Siegel [1956], p.236.
17 NAMSI HHI CB st nd Kendall W. H % k CB A B CB A t t Mann-Whitney U Mann-Whitney U - test U U n n 2 R i n i R i A H CB H CB Siegel [], pp. -
18 Competitive Balance NAMSI HHI* C ICB CT ICB CB ICB n n R R U U- () A. ( %) Mann-Whitney U CB U H st nd CB BA CB Wilcoxon Wilcoxon matched-pairs signed-rank test T T R + + R B H st nd CB Milton [] Siegel [], pp. -
19 NAMSI HHI* C1ICB CT4ICB CB4ICB 標本数 検定統計量 T T- 臨界値 ( 片側 5%) T T- Kendall W H st nd CB BstndCB. CB Wilcoxon TCB T H st nd CB Kendall W Wilcoxon T T H CB st nd acb b st nd CB McCornack [1965].
20 Competitive Balance J JCB CB CB A st nd CB B CB J J CB J ACB CB UOH Brandes and Franck CB J ACB Jissue pp. - Jissue pp. - PHP J
21 issue pp. - J issue pp. - Brandes, L. and E. Franck. [], How fans may improve competitive balance An empirical analysis of the German Bundesliga, Working Paper No., pp. -. Depken, C.A. [], Free-agency and the competitiveness of major league baseball, Review of Industrial Organizations, vol., pp. -. Fort, R. and J. Maxcy. [], Comment : Competitive balance in sports leagues : An introduction, Journal of Sports Economics, vol., pp. -. Goossens, K.[], Competitive balance in European football : Comparison by adapting measures : National measure of seasonal imbalance and top, Rivista di Diritto ed Economia dello Sport,, pp. -. Groot, L. [], Economics, Uncertainty and European Football, Edward Elgar, Cheltenham,UK and Northampton, MA, USA Hadley, L, J. Ciecka, and A.C. Krautmann. [], Competitive balance in the aftermath of the players strike, Journal of Sports Economics, vol., pp. -. Humphreys, B. R. and N. M. Watanabe.[], Competitive balance, in Kahane L. H.and S. Shmanske (eds), The Oxford Handbook of Sports Economics, vol., Oxford University Press, pp. -. Kringstad, M. and B. Gerrard. [], Beyond competitive balance, in Parent, M.M. and T. Slack (eds), International Perspectives on the Management of Sport, Butterworth-Heinemann, Burlington, MA, pp. -. McCornack, R. L.[], Extended tables of the Wilcoxon matched pair signed rank statistic, Journal of the American Statistical Association, vol., pp. -. Michie, J. and C. Oughton. [], Competitive Balance in Football : Trends and Effects, Sports Nexus, London. Milton, R. C. [], An extended table of critical values for the Mann-Whitney (Wilcoxon) two-sample statistic, Journal of the American Statistical Association, vol., pp. -. Owen, P. D. [], Measurement of competitive balance and uncertainty of outcome, in Goddard. J. and P. Sloan (eds), Handbook on the Economics of Professional Football, Edward Elgar, Cheltenham, UK and Northampton, MA, USA, pp. -. Owen, P. D., M, Ryan and C. R. Weatherston. [], Measuring competitive balance in professional team sports using the Herfindahl-Hirschman Index, Review of Industrial Organizations, vol., pp. -. Ross, S. F. and S. Szymanski. [], Open competiton in league sports, Wisconsin Law Review, vol., pp. -. Rottenberg, S. [], The baseball players labor market, Journal of Political Economy, vol., pp. -. Schmidt, M. B. and D. J. Berri. [], Concentration of playing talent : Evolution in major league baseball, Journal of Sports Economics, vol., pp. -. Siegel, S. [], Nonparametric Statistics for the Behavioral Sciences, McGraw-Hill Book Company, Inc, NewYork, Toronto, London. Szymanski, S. [] The economic design of sporting contests Journal of Economic Literature, vol., pp.-.
22 Competitive Balance JJ jleague.jp/release/article-/ J jp/release/post- / JJDAZN DAZN J, J J / J / JJ League Data Sitehttps://data.j-league.or.jp/SFMS / JJ League Data Site /
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