  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.
