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.

Goals Scored by Red  Carded Side Prior to Card.	Goals Allowed by Red Carded Side Prior to Card.	Percentage 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.

Goals Scored by Red  Carded Side After Card.	Goals Allowed by Red Carded Side After Card.	Percentage 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.

Estonia 0-4 Rep of Ireland,Euro 2012 Playoff.

Estonia 0 Rep of Ireland 4.


Ireland all but guaranteed qualification for Euro 2012 and banished sour memories of William Gallas' controversial goal for France in the same stage of the qualification process for World Cup 2010.For a team as adept at defending as the Irish any lead from the first leg would have been welcome.But clinical finishing from players from such diverse club sides as Stoke,LA Galaxy and Blackburn and an Estonian self destruction mode that prevailed all night means that Tuesday's return leg should be a formality.

Scorers.
0-1,Andrews,13'
0-1,Red Card,Stepanov,34'
0-2,Walters,67'
0-3,Keane,71'
0-3,Red Card,Piiroja,77'
0-4,Keane(pen),88'

Drawing the Wrong Conclusions.Draws in the EPL.

In a case of extreme Karmic Retribution,Bolton inflicted a 5-0 thrashing on Stoke at the Reebok on Sunday.The result may have gone some way to easing the pain their players and fans suffered at Wembley on a very sunny afternoon in April 2011 when The Potters beat The Trotters by the same scoreline to reach the FA Cup Final.It was also equally noteworthy because it extended Bolton's run of games without a draw to 21 league games,more if you include cup ties.The run of non drawn games is certainly unusual,the next longest current run for teams in all games is 13 shared by Nottingham Forest and Peterborough,but is it so unusual that we have to assume that Bolton have a unique (ish) quality that is leading to definite outcomes in games they play?

Bolton don't appear to do Draws. 

There is much less variation in the likelihood of games in the EPL ending all square compared to games ending with say a win.Even when the very best play the very worst there's still around a 20% chance that the game will end deadlocked and in the vast majority of run of the mill match ups that are played the probability of a draw doesn't move much from 26 or 27%.Therefore,we can fairly easily model an extended sequence of games where the odds of a draw is in the region of 27% and the odds of a non draw is 73%.If you enter =rand() into a spreadsheet the cell will return a number between 0 and 1 and if you designate any return below 0.27 as a draw you have your very own,primitive draw generator.In the run of simulated draws I have just done a sequence of 25 consecutive non draws occurred after just 77 games,the next one appeared 700 games later.

So it would seem that although an extended run of non draws is relatively rare,if you look at enough games one such run is bound to occur.Bolton weren't designated as the team to watch for if you wanted a definite outcome before they started their run of non draws and by monitoring the EPL as a whole over a long enough time scale a team with Bolton's unusual sequence of results was bound to appear by chance.It just happened to be The Trotters.

World famous illusionist,Derren Brown does a trick where he tosses a coin to come up heads ten times in a row.It's shot in realtime with no video editing and it happens just as it appears on film.What isn't shown is the probable hours of coin tossing that preceded the run of ten heads.Shown out of context the ten consecutive heads seem remarkable instead of just uncommon and it's the same with Bolton's current run.It's certainly uncommon,but no so remarkable,in the context of 20 EPL teams constantly playing sequences of games,that we have to look for reasons why Bolton don't do draws.Bolton's 25 games without a draw are indistinguishable from a naturally occurring sequence in a much larger sample of games.

If non drawing teams occur largely at random,what about so called draw specialists.We could repeat the simulation on a team by team and season on season basis to see how common an unusually large number of draws were in the simulation,but instead I've taken so called draw specialists and seen how frequently they drew games in their next season in the top flight.If draws were for example a tactically based,repeatable talent we would expect a lot of teams to be able to retain this trait across seasons.A few do,but again this could just be a continuation of the random process,but most do not.Home teams who recorded the most home draws in season N averaged 8.4 draws per 19 games since 1988,but in season N+1 they only averaged 5.6 draws and just 15% of the teams equalled or bettered their previous draw total.Away draw specialists showed similar figures.The average number of home or away draws in the English top flight over that period was 5.3 draws,so draw specialist are most likely random streaks and the teams on average fall back to earth in subsequent seasons.

Average Number of Draws by Venue for the most Draw Prone Teams in the English Top Flight.1988-2011.

Draw Prone Team Type.	Average Number of Draws per Season.	Average Number of Draws Next Season.
Home Teams.	8.4	5.6
Away Teams.	8.8	5.6