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From a game theory perspective, I'm trying to find the optimal strategy for selecting penalty kick takers. Anecdotally (and I hope to quantify this relationship later) I've heard that it's always advantageous to shoot first because each player on the second team can face additional pressure coming from behind at each round.

Are managers allowed to adjust their selection of shooters as a result of learning that they will be going first or second?

Do they submit the list immediately following the conclusion of extra time and before the coin flip, or after the coin flip and before the kicks begin?

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Kick takers are selected from the players on the field at the end of the match (either at full time, or if extra time was used, then after extra time). From the IFAB Law 10, with added emphasis on a phrase of special importance,

The referee tosses a coin ... and the team that wins the toss decides whether to take the first or second kick.

With the exception of a substitute for an injured goalkeeper, only players who are on the field of play or are temporarily off the field of play (injury, adjusting equipment, etc.) at the end of the match are eligible to take kicks.

Each team is responsible for selecting from the eligible players the order in which they will take the kicks. The referee is not informed of the order.

Note also in the same Law, with similar emphasis added,

If at the end of the match and before or during the kicks one team has a greater number of players than its opponents, it must reduce its numbers to the same number as its opponents and the referee must be informed of the name and number of each player excluded. ...

There is no requirement to name the order at any point, only to adhere to the conditions outlined in the procedure for kicks from the penalty mark.

However, you could delay selecting the specific player to take a given shot in the sequence until it is time to actually take that shot.

Thus, there is no concern over whether the order will be suboptimal based on the coin toss. Instead, managers are faced with a much more dynamic and complex situation: choosing the most optimal order from this point onwards and before every individual shot.

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    The document this answer references is nearly ten years old and outdated - as a result some of the answers in your question are only partially correct. This source should now be quoted and referenced instead: theifab.com/#!/laws/determining-the-outcome-of-a-match/chapters/… – Reinstate Monica 2331977 Jul 5 '16 at 3:28
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    There are plenty of changes. One change is that teams reduce to equate if a player is sent-off or injured after kicks have begun - previously this was only done at the start of kicks. Secondly, it is now explicitly written that the order of kickers does not need to be provided to the referee at the start of the kicks - in the past competition rules could add such a requirement to the kicks. These are two key changes. – Reinstate Monica 2331977 Jul 5 '16 at 7:24
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    @studro several edits have now been made to reflect the updated Laws. – Nij♦ Aug 28 '16 at 8:50
  • Was just wondering why they would have to submit lists, and your answer seems to address that... they don't. Plus it's good to see that it was changed regarding players removed after kicks start... otherwise I could see a strategy in very vital situations (promotion playoff finals?) where suddenly you have a bunch of "injured" defenders or (even goalies???) (or a sudden rash of sending off offenses). – JeopardyTempest Aug 28 '16 at 20:05

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