Article
Tournament schedules and incentives in a double round-robin tournament with four teams
László Csató,
Roland Molontay,
József Pintér,
Corresponding Author
László Csató
Research Group of Operations Research and Decision Systems, Laboratory on Engineering and Management Intelligence, HUN-REN Institute for Computer Science and Control (HUN-REN SZTAKI), Kende street 13-17, Budapest, 1111 Hungary
Department of Operations Research and Actuarial Sciences, Institute of Operations and Decision Sciences, Corvinus University of Budapest (BCE), Fővám square 13-15, Budapest, 1093 Hungary
Corresponding author.
Search for more papers by this authorRoland Molontay
Department of Stochastics, Institute of Mathematics, Budapest University of Technology and Economics, Műegyetem rkp. 3, Budapest, 1111 Hungary
ELKH-BME Stochastics Research Group, Műegyetem rkp. 3, Budapest, 1111 Hungary
Search for more papers by this authorJózsef Pintér
Department of Stochastics, Institute of Mathematics, Budapest University of Technology and Economics, Műegyetem rkp. 3, Budapest, 1111 Hungary
ELKH-BME Stochastics Research Group, Műegyetem rkp. 3, Budapest, 1111 Hungary
Search for more papers by this authorLászló Csató,
Roland Molontay,
József Pintér,
Corresponding Author
László Csató
Research Group of Operations Research and Decision Systems, Laboratory on Engineering and Management Intelligence, HUN-REN Institute for Computer Science and Control (HUN-REN SZTAKI), Kende street 13-17, Budapest, 1111 Hungary
Department of Operations Research and Actuarial Sciences, Institute of Operations and Decision Sciences, Corvinus University of Budapest (BCE), Fővám square 13-15, Budapest, 1093 Hungary
Corresponding author.
Search for more papers by this authorRoland Molontay
Department of Stochastics, Institute of Mathematics, Budapest University of Technology and Economics, Műegyetem rkp. 3, Budapest, 1111 Hungary
ELKH-BME Stochastics Research Group, Műegyetem rkp. 3, Budapest, 1111 Hungary
Search for more papers by this authorJózsef Pintér
Department of Stochastics, Institute of Mathematics, Budapest University of Technology and Economics, Műegyetem rkp. 3, Budapest, 1111 Hungary
ELKH-BME Stochastics Research Group, Műegyetem rkp. 3, Budapest, 1111 Hungary
Search for more papers by this authorAbstract
In a round-robin tournament, a team may lack the incentive to win if its final rank does not depend on the outcome of the matches still to be played. This paper introduces a classification scheme to determine these weakly (where one team is indifferent) or strongly (where both teams are indifferent) stakeless matches in a double round-robin contest with four teams. The probability that such matches arise can serve as a novel fairness criterion to compare and evaluate match schedules. Our approach is illustrated by the UEFA Champions League group stage. A simulation model is built to compare the 12 valid schedules for the group matches. Some schedules are shown to be dominated by other schedules. It is found that the strongest team should play at home in the last round against one of the middle teams, depending on the preferences of the tournament organiser. Choosing an optimal sequence of matches with respect to the proposed metric can help to avoid uninteresting matches.
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