Red Cards and the Big Four.

The win probability for each team is tracked on a minute by minute basis throughout each game.At any point in a game a team will have a probability of winning the game outright and an associated probability of drawing the game.By multiplying the probability of winning the game by 3 and the probability of drawing by 1 and adding the results together you will get an expected longterm average for the number of points that team will achieve from that position or Expected Points (EP) for short.

Every football fan can remember games or incidents within games that are especially significant for their club.They usually signify that their team has reached a new high in it's development or plummeted to new and possibly permanent depths of ineptitude.Stoke fans would probably put November 1st 2008 into the former category.The initial 45 minutes of their first EPL season where they shipped a goal every 15 minutes was still a raw and recent memory,but they had partially steadied the ship with wins over Villa,Sunderland and an obliging nine man Tottenham.They occupied 15th place in the EPL,the average finishing spot for promoted teams in their first year in the higher grade,but defeats at the hands of Bolton, Middlesbro', Everton, Chelsea, Man City and Portsmouth meant that the visit of third placed Arsenal to the Britannia was a daunting prospect for the hosts.

Pre game expected points values made the Gunners huge favourites.They would expect to return with an average of 2.34 points from their visit north,while Stoke would be lucky to average half a point a game.

However,today was a day when one of the least favoured scenarios materialised.Fuller's 11th minute strike would rarely have been a decisive first goal and Stoke had to maintain that lead until after the half hour before they became the team favoured to clinch more points on average from that particular game situation.By the 70th minute Stoke still held the advantage and would be expected to gain an average of 2 points per game in such circumstances,but they tightened their grip three minutes later when Olofinjana stumbled his way into the box and bundled a trademark Delap throw over the line.Instant cult status for "Seyi".

Scorers;
1-0,Fuller,11'(Delap assist)
2-0,Olofinjana,73'(Delap assist)
Red Card,van Persie,Arsenal,76'
2-1,Clichy,90'

If Arsenal had been unaware of their underdog status from the half hour mark onwards,they certainly knew their likely fate now and three minutes later their predicament worsened even more.Stoke's keeper Thomas Sorensen deliberately dallied over picking up the ball in his box,inviting the loitering van Persie to participate in a game of cat and mouse where the Dutchman was by far the junior partner.Van Persie's half hearted lunge for the ball was never going to arrive before Sorensen claimed it for himself and what the subsequent shoulder charge lacked in violent intent it certainly made up for in stupidity.Sorensen collapsed in a heap,although he was careful to remain in front of his goal line and Stoke's favourite referring pantomime villain,Rob Styles set van Persie packing with a straight red card.The dismissal left Arsenal in a hole too deep for even a team of their attacking flair to emerge from and Clichy's 90th minute strike was merely a consolation.

The view  from the stands confirmed Stoke as a team who could compete on their own turf with the league's very best,dreams of a European Tour were a few seasons down the road,but the Potters were no longer considered to be a team out of their depth.Regarding the dismissal,it was difficult not to conclude that van Persie had reacted to the situation of trailing and most probably losing to a team who should have been dispatched with the minimum of fuss and in a manner Chelsea had achieved on the same ground a month earlier.It was a clear case of red card bourne out of frustration.

It's easy to attach too much importance to individual events,so to test the theory that the best teams see red when they fail to reach the heights they generally attain,I recorded all games involving the Big Four,Liverpool,Arsenal, ManUtd and Chelsea where a red card was shown to their players. I charted the pre game Expected Point Values and the EP for the team in the minute before their player was dismissed.Games between the big four were removed from the sample.

Games against inferior opposition where the big four received a red card.2004-2011.

Teams.	Number of Red Card Games.	Average EP at Kickoff	Average EP just before Red Card.	Average % fall in EP	% of Games where EP fell before Red Card.
Man Utd.	12	2.02	1.54	24	75
Arsenal.	15	2.09	1.73	17	67
Chelsea.	16	2.29	1.98	14	56
Liverpool.	6	1.83	1.01	45	83
Overall.	49	2.11	1.68	20	67

As can be seen the average Expected Points just prior to the red card are below the average EP at kickoff both for the big four as a group and for each individual team.The EP fell on average by 20% and in about 70% of the games it was below it's starting point.Games numbers are relatively small for each team,so conclusions are necessarily tentative.Liverpool appear to be the most bad tempered of the original big four,5 of their 6 red card games came when the Reds were performing worse than expected.Chelsea were the team who appeared least concerned with the current match position before they saw red.

The figures appear to confirm that teams who are playing badly by their expected standards are likely to compound the problem by having players dismissed.The question now becomes is the effect universal or is it more pronounced when those struggling to perform are the best teams in the division,after all they have more to lose than teams with lower pre match expectations and their under performance will be self-evident to their players.The average fall in EP at the time of the dismissal is around 20%,so in the next part of this series I'll take a representative sample of games not involving the big four and see if the red card situations remain the same.