Wednesday 16 November 2011

Red Cards.What To Expect After One is Shown.

Bolton 2-2 Birmingham,EPL August 2010.

When Jussi Jaaskelainen aimed at kick at Birmingham's Roger Johnson and followed it up with a slap around the head a red card was inevitable.Bolton already trailed Birmingham by virtue of Johnson's 4th minute goal and the longterm hole they had dug for themselves got even deeper when they fell further behind just after the break.However,spurred on by a home crowd and the recipients of a couple of generous refereeing decisions they claimed an unlikely point with two late goals.

Newcastle 4-4 Arsenal.EPL February 2011.

This game has been described here.Arsenal had a 4 goal cushion when Diaby was dismissed after 50 minutes,but they weren't quite as resilient as Bolton had been in the previous example and the 10 men Gunners were grateful to return to London with a point.

We have seen that on average a red card reduces a team's in game win probability,but as the two games above demonstrates there is a wide range of possible outcomes that can materialise on the actual matchday.Taken in isolation the Bolton game could be used to justify the often repeated and totally erroneous cliche that "it is (always) harder to play against 10 men than 11".While the Arsenal game dramatically demonstrates the actual real life experience where the numerically reduced side more usually finds scoring and defending much more difficult.

To discover what happens on average it is necessary to take a large number of games and record the scoring patterns of the teams both before and after the red card was shown.I've taken each game during the 2010/11 season where a solitary red card was issued,comprising 45 games in total.The soon to be ten men scored less goals than their opponents in the time prior to the red card being shown,confirming the findings here and here that red cards are more likely to be shown to inferior sides forced to make more defensive challenges or to good sides playing badly and reacting petulantly to this unexpected dip in form.

Scoring and conceding record of red carded sides prior to the red card.EPL 2010/11.

Scored by Red  Carded Side Prior to Card.
Allowed by Red Carded Side Prior to Card.
of Match Goals
Scored by Carded Side.
28 42 40%

In total 70 goals hit the back of the net prior to the dismissal in the 46 games and 40% of them were scored by the team about to see red.

Scoring and conceding record of red carded sides after the red card.EPL 2010/11.

Scored by Red  Carded Side After Card.
Allowed by Red Carded Side After Card.
of Match Goals Scored by Carded Side.
15 36 29%

The average time at which the dismissal occurred was the 64th minute and ranged from numerous injury time cards to Boyata's 5th minute departure from the Man City Arsenal game.With just 21 players on the pitch things became much more difficult for the even numbered side and they now only scored 29% of the total goals scored compared to 40% previously.So although teams who perform heroically in the face of lopsided  numerical odds tend to stick in the memory,usually as a result of inflated media interest,it is the well behaved side who much more often derive the advantage from a dismissal.

The average time of the card also allows us to see how the overall goalscoring differs pre and post dismissal.Some of the games in the sample are mis matches at the start and they will tend to be slightly more goal laden than a more usual English Premiership game.However,overall the sample of games would expect to have just slightly above 2.6 goals scored per game.We know that the average time of the dismissal is the 64th minute and we can fairly easily work out the rate at which goalscoring decays over the course of the game.In a game where an average of 2.6 goals were expected to be scored,we would expect an average of 1.05 goals to be scored after the 64th minute.If we compare the actual total number of goals scored by both teams after the red card we can not only say what proportion of goals will be scored by either team,but also how much more or less goalscoring occurs.

The 45 games produced 51 post card goals at 1.13 goals per game,slightly higher than the pre game expectation for the number of goals that would be scored after the 64th minute in a well behaved game.However,every game starts with a kickoff,but some of the red card "mini" games that lasted on average from the 64th minute onwards started unsurprisingly with a penalty kick and if we allow for these occurrences we can probably say with confidence that games blighted by red cards produce just as many goals as normal games.It's just the scoring distribution that is changed.

So if you're at a game and a red card is shown,you'll still get your money's worth in terms of goals scored,but expect the numerically superior side to do more than their pre game expected share of the scoring.

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