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on Sports and Economics |
| By: | Steven J. Brams; Mehmet S. Ismail; D. Marc Kilgour |
| Abstract: | Winning the coin toss at the end of a tied soccer game gives a team the right to choose whether to kick either first or second on all five rounds of penalty kicks, when each team is allowed one kick per round. There is considerable evidence that the right to make this choice, which is usually to kick first, gives a team a significant advantage. To make the outcome of a tied game fairer, we suggest a rule that handicaps the team that kicks first (A), requiring it to succeed on one more penalty kick than the team that kicks second (B). We call this the $m - n$ rule and, more specifically, propose $(m, n)$ = (5, 4): For A to win, it must successfully kick 5 goals before the end of the round in which B kicks its 4th; for B to win, it must succeed on 4 penalty kicks before A succeeds on 5. If both teams reach (5, 4) on the same round -- when they both kick successfully at (4, 3) -- then the game is decided by round-by-round "sudden death, " whereby the winner is the first team to score in a subsequent round when the other team does not. We show that this rule is fair in tending to equalize the ability of each team to win a tied game in a penalty shootout. We also discuss a related rule that precludes the teams from reaching (5, 4) at the same time, obviating the need for sudden death and extra rounds. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.04807&r=spo |
| By: | Gustavo Bergantinos; Juan D. Moreno-Ternero |
| Abstract: | We study the problem of sharing the revenues from broadcasting sports leagues axiomatically. Our key axiom is anonymity, the classical impartiality axiom. Other impartiality axioms already studied in these problems are equal treatment of equals, weak equal treatment of equals and symmetry. We study the relationship between all impartiality axioms. Besides we combine anonymity with other existing axioms in the literature. Some combinations give rise to new characterizations of well-known rules. The family of generalized split rules is characterized with anonymity, additivity and null team. The concede-and-divide rule is characterized with anonymity, additivity and essential team. Others combinations characterize new rules that had not been considered before. We provide three characterizations in which three axioms are the same (anonymity, additivity, and order preservation) the fourth one is different (maximum aspirations, weak upper bound, and non-negativity). Depending on the fourth axiom we obtain three different families of rules. In all of them concede-and-divide plays a central role. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.17897&r=spo |