Game Theory: Team Selection and The Magic of Properly Tanking the FA Cup

In previous posts, I’ve written why it’s rational for teams to field a sub-optimal lineup in the Champions League, despite the fact that it leads to a tragedy of the commons scenario. The short version is that the expected value of resting your top players in cup games and saving them for league fixtures is higher than playing them and trying to win the cup and meet whatever goals you have in the league. The expected value calculations are a little different between the UCL and the FA Cup, but the logic is the same. However, Arsenal’s strategy today made me think that there is one added strategic wrinkle in FA Cup roster selection, and one that Arsene Wenger may not have taken into consideration: the need to avoid a replay.

Arsenal’s lineup yesterday against Sunderland was: Cech, Bellerin, Gabriel, Koscielny, Gibbs, Oxlade-Chamberlain, Chambers, Iwobi, Walcott, Campbell, Giroud.

Wenger clearly chose not to tank the game, placing some value on a possible third straight FA Cup win. This is a strong lineup, with Walcott, Campbell, and Giroud up front, and Oxlade-Chamberlain, Koscielny, Bellerin, and Cech also in Arsenal’s strongest starting XI. However, he didn’t field his strongest lineup, choosing the rest some key players as well.  Notable omissions were Per Mertesacker, Mesut Ozil, and Nacho Monreal. Resting the player who is likely their top defender and their #10  who is one of the best playmakers in the league this season shows that he wasn’t overly concerned about winning either, as these players likely would have featured in a league game. Wenger chose not to tank, but also didn’t necessarily play to win, choosing a “third way” instead.

I’m going to start with a big assumption here: the maximum EV preferences are as follows.

  1. Loss
  2. Win
  3. Draw

Reasonable people can disagree on numbers 1 and 2 – maybe Arsenal gets more value out of winning a third round FA Cup match than I think they do, so maybe they really want to win. However, I think the draw, leading to the replay at The Stadium of Light, was Arsenal’s worst possible option here. The goal then would be to maximize the combined probability of winning and losing while minimizing the probability of a tie. At its extreme, this might look like a 4-2-4 with four defenders, two midfielders, and four strikers: a line-up that will score a lot of goals and concede a lot of goals.1 The odds of this lineup playing to a 0-0 or 1-1 draw are remote.

Wenger did something different: he played his top (available) attackers so maybe he planned on scoring a lot of goals, but he rested the team’s best provider which would potentially limit the number of opportunities they had. He also gave a 19 year old midfielder his first start in midfield, which is good for a lot of reasons but combined with resting Ozil really weakens Arsenal’s midfield.  Wenger didn’t play to win, but he didn’t choose a lineup of youngsters who would likely lose either. He risked a replay, which may have been the worst possible outcome for a team, stretched thin by injuries while trying to mount a title challenge.

Arsenal aside, the FA Cup adds an extra dimension into roster selection strategy that the Champions League doesn’t have. Avoiding a replay should be a priority for any team who hasn’t secured their league goals for the year, which means picking a team that is either going to win or lose, and will do either in convincing fashion. Adding another fixture to an already crowded list, is something all Premier League teams should want to avoid, and should select their teams accordingly.


  1. Like I said, this is extreme. I don’t actually think this would be a valid formation to choose, I only use it as an absurd example to illustrate the idea.

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