On winning the penalty shoot-out in soccer by Tim McGarry and Ian M. Franks (Patreon)

• The best five ranked penalty takers from the on-field players should be assigned to the first five penalty kicks in their reverse order of ability.
• That is, the fifth best penalty taker should take the first penalty kick, the fourth best penalty taker should take the second penalty kick, and so on.
• In the event of sudden death, the next highest ranked on-field player should be assigned to the next penalty kick until the shoot-out ends.
• For this tactic to be successful, players should be ranked a priori on their penalty-taking ability.
• Similarly, goalkeepers should be ranked a priori on their penalty-stopping ability.
• These findings indicate that the tactical substitution of on-field players for higher ranked penalty takers, including higher ranked penalty stoppers (i.e. goalkeepers), with a view to an impending penalty shoot-out should be given due consideration.

Some practical considerations for winning the penalty shoot-out:

• We recommend that the training of penalties be practised in systematic fashion by each player to improve on p or q'  - the probability of scoring and of not scoring are denoted by p and q respectively (i.e. p + q = 1).
• This undertaking would allow for the coaching staff to identify beforehand an estimate of p or q' for each player on the roster. This can easily be obtained from many practice observations as well from performance in previous competition.
• The best identified players remaining on the field of play at the end of extra-time can then be assigned in their reverse order of ability.
• Furthermore, it is necessary that each player is well practised, since the outfield players at the end of extra-time, from which at least five must be selected, remain uncertain. That the penalty shoot-out has been decided in some cases by the sixth (or higher) penalty taker further emphasizes the importance of a prepared squad.
• Finally, we suggest that the use of substitutes for the express purpose of competing in a shoot-out should be given just consideration should it be appropriate at the time. The simple tactic of substituting players with a view to their known (or expected) penalty-taking ability could make the difference between winning and losing should the game progress to a penalty shoot-out.
• Similarly, the substitution of a goalkeeper late in the game should be given serious thought should the non-elect goalkeeper be considered a better stopper of penalty kicks.

Conclusion

• We suggest that the probability of winning a penalty shoot-out can be increased with systematic practice, both on the part of the penalty takers and on the part of the goalkeeper.
• In addition, we have identified that the optimal line-up order, in general, is to assign the best five penalty takers to the available slots in reverse order.
• This order, however, should not be considered inflexible and a re-arranged order depending on context might be expected to yield favourable results in some instances.
• The intelligent use of substitutions with the express view of an impending penalty shoot-out is also recommended. 
• This tactic should not be restricted to outfield players and the substitution of the goalkeeper may be advised should the non-elect goalkeeper be better at stopping penalty shots.