Fairness in penalty shootouts: Is it worth using dynamic sequences?

Area of Science:

• Sports Science
• Game Theory
• Economics

Background:

• Dynamic team tournaments, like soccer penalty shootouts, involve sequential actions.
• The order of actions (kicking sequence) can create a First Mover Advantage.
• This advantage may distort winning probabilities and reduce overall tournament efficiency.

Purpose of the Study:

• To theoretically compare seven different soccer penalty shootout rules.
• To evaluate the fairness of these rules concerning the First Mover Advantage.
• To analyze the probability of reaching the sudden death stage under various rules.

Main Methods:

• Theoretical analysis of seven distinct penalty shootout rule sets.
• Modeling of the First Mover Advantage in a dynamic tournament context.
• Evaluation of ex-ante winning probabilities and fairness metrics.

Main Results:

• When scoring probabilities are stationary, dynamic rules offer no advantage over static rules.
• The sequence of moves can indeed distort initial winning probabilities.
• Compensating the second-mover by granting them the first move in sudden death is beneficial.

Conclusions:

• Carefully chosen action sequences can lead to fairer outcomes in dynamic tournaments.
• Decision-makers can improve fairness by optimizing the order of actions.
• The findings have implications for designing more equitable tournament structures.