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Soccer: Just how damaging is it to get a man sent off?

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We know that it's difficult to play a man down, but what exact impact does it have on a team's ability to score and prevent goals? I went through four seasons of English Premier League games and looked at how shot rates changed for the home and away teams when one of their players took a red card or two yellows.

As you can see, when a team is down a man, a team's shot rate drops somewhat (32% for home teams, 13% for visitors) while shots allowed go way up (42% at home, 73% on the road):

Home Pct of Time Shots For Shots Vs % of Shots
10-10 0.23 12.60 8.31 60.3
10-11 1.71 7.35 14.67 33.4
11-10 2.68 15.36 7.35 67.6
11-11 95.33 10.85 8.47 56.2

Both teams control 2/3 of all shots at 11-10. It's also interesting to note that visiting teams spend 56% more team at 10 men than the home team.

So what's the impact on goal-scoring?

Home Goals For Goals Vs % of Goals Sh% F Sh% A
10-10 0.80 0.54 60.0 6.38 6.45
10-11 0.97 1.84 34.6 13.24 12.53
11-10 2.63 0.76 77.6 17.09 10.34
11-11 1.40 0.99 58.6 12.89 11.66

Interestingly, the home team always has a higher shooting percentage, regardless of the game state. When the home team is a man up, they were almost twice as likely to score as at 11-a-side. The impact of the visitors losing a man for half the game is approximately 0.75 goals - roughly the same as giving up a penalty kick - or at least a 30% increase in the home team's expected winning percentage.