Abstract
The present paper deals with two-player all pay contests in which a tie is due to slacking, showing that to reduce the likelihood of such an occurrence, slackers should be denied any reward, or even punished. The denial of reward, or the punishment, inflicted on substandard performers, may spur some players to bigger efforts, or induce others to avoid contests in which they are unable to meet standards. However denying any reward to those making small but not substandard efforts, would not raise the proportion of those making the maximum effort, while more competitors would abstain from any effort at all, detracting from overall performance. The point allocation rule suggested by this paper is thus shown to improve on its alternatives. The paper proposes changing the rules of point allocation in soccer, to reduce the incidence of non-scoring draws, often the outcome of bad playing or of extreme risk avoidance, expressed in purely defensive game strategies. Under the new rules, a win would award a team with three points, a scoring draw would entitle the teams to one point each, but neither team would receive any points for non-scoring draws. We show that this change would reduce the numbers of games ending in 0:0, while raising the numbers of goals in other games, thus boosting spectator enjoyment.
Highlights
In winner-takes-all contests, the winner is the one who invested the most in the game and the sole prize receiver, even though all contestants have incurred costs
Cohen and Sela (CS) [8] modeled the points system in soccer (European football) matches using competitions of the “All Pay” type.Like CS, we look at the contest output and deny any prize to low performing teams, even if the teams they have played against have done no better
We show that the CSI model, which adds to the CS model the denial of any points to the teams involved in scoreless draws, will reduce their frequency
Summary
In winner-takes-all contests, the winner is the one who invested the most in the game and the sole prize receiver, even though all contestants have incurred costs. Cohen and Sela (CS) [8] modeled the points system in soccer (European football) matches using competitions of the “All Pay” type (evaluating the optimal prize policy in the case of a draw, as against a win).Like CS, we look at the contest output (rather than at the inputs) and deny any prize to low performing teams, even if the teams they have played against have done no better. The original contribution of the present paper, CSI (Cohen and Schwartz Improvement), is reducing the likelihood of ties due to lack of a serious effort to win on the part of the contestants. We show that to achieve this purpose, slacking teams and those who have played a purely defensive game, failing to take any risks, should be denied any reward whatsoever This denial of reward inflicted on substandard performers, may spur some teams to bigger efforts, while inducing others to avoid contests if they are unwilling or unable to meet minimal standards. Part 3 analyzes the results, offers examples and presents conclusions
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