How Do Red Cards Affect A Football Match?

How much of an impact does a red card have on the result of a football match? Today on the blog Mark Taylor takes a look at how the issuing of red cards affected each of the clubs through the 2011/2012 Premier League season.

Scoring events can run to within touching distance of a thousand in cricket, beyond a hundred in basketball and even comparatively low scoring contests such as American Football, baseball and rugby of both codes regularly breach ten scores per game.

Association football stands virtually alone in championing the cause of low scoring sports contests. Regular viewers of live football will be lucky to see an average of much more than 2.5 goals per game and followers of either the very best or the very worst, where goals are more common should still expect average scoring figures of below three.

While some see low scoring as unappealing it is actually the foundation for much of the drama surrounding the sport. Goals dramatically change the expected course of a match and their very scarcity ensures that the majority of them are meaningful events. Opening goals or goals to break a deadlock or to drag a team to within one score of their opponents are more common than meaningless, late strikes in a comfortable win. So the fear or anticipation of a score in football often pervades the whole game.

The Other Kind Of Game Changing Event

However, not content with one potentially huge game changing event, football has access to a second. Namely, a red card. As with goals, red cards are rare, but potent occurrences. Occasionally, a depleted team will produce a seemingly improved performance by grabbing a draw or an unexpected win, but long term a red card reduces the expected number of points a team would have hoped to gain had they kept eleven men on the pitch.

We can demonstrate this with a basic model that looks at the score lines just prior to each dismissal during the 2011/12 Premiership season and compares the league points each side potentially had at that stage and then again at the final whistle. At 0-0 Arsenal and Liverpool each had a point a piece back in August of 2011, but Frimpong’s 70th minute dismissal saw Liverpool grab all three points with two late goals.

In-running league points immediately before a Red Card and at Fulltime

Match Position	Cumulative Points Total Of Red Carded Teams	Cumulative Points Total Of Their Opponents
Just Prior To Red Card	64	101
End Of Game	36	138

There were over 60 matches featuring a red card last season and the overall share of the league points for the carded side fell from nearly 40% just prior to the card to only 20% at the final whistle. Blackburn turned a 2-1 deficit against Wigan into a 3-3 despite being reduced to ten men after 48 minutes, but this was a rarity overall. A much more typical outcome concerns the fate of the 20 sides which were drawing when one of their players was red carded. 13 went onto lose, six hung on for a draw and one (Blackburn again) managed a win.

So the general case firmly belies the often repeated footballing cliché that playing against ten men is more difficult than when a team faces eleven opponents. It may require a different tactical approach, but the final result is more often a favourable one.

Quantifying The Red Card

We can begin to quantify the cost of a red card if we accumulate data for the margins of victory or defeat we would have expected for a team pre match and compare this to actual values where they received a red card. And as we would expect from the general case above, red carded teams suffer both through scoring less goals than expected after the card and conceding more.

It’s convenient to talk of differences in team quality in terms of goals. An average home side for example will beat an average away team by an average of about 4 tenths of a goal in the long term and the current Chelsea side will beat the current Stoke side by an average of about 1.4 goals at Stamford Bridge. So we’ll use the latter case to illustrate the effect of a red card.

Using data from multiple Premiership seasons and extrapolating across the ninety minutes of a game indicates that a team which sees red in the first minute should expect to see their average goal difference in such matches reduced by about 1.5 goals, both through lack of firepower and an increased tendency to concede. If the card is delayed until half time, the cost to the recipient is 0.85 of a goal and by an hour in it has further fallen to 0.62 of a goal.

So to personalize the data, Chelsea would become marginal underdogs if they saw red in the first minute while still goalless at home to Stoke as the card would take away all of their pre game advantage and a little bit more. Therefore we can deduce that time remaining, the initial difference in quality between the teams and current score line are the critical factors to consider when considering the likely effect of a red card on a match outcome.

Which teams potentially benefited most from Red Cards in 2011/2012?

Using these parameters we can move from the general to the specific and see which teams found themselves in very advantageous positions over the course of the 2011/12 season because of their own good behaviour or the bad behaviour of others.

Every minute of every game has an associated win or draw probability and we can use these figures to predict the average number of points each team should gain from these positions. To take a trivial example, two evenly matched sides at kick off will each have a 38% chance of winning three points and a 28% chance of drawing for one point, leading to an expected average points haul of 1.42 points for each side.

By calculating expected points totals for each team immediately before and immediately after a red card we can see who were the season’s biggest winners and losers. For example when Stoke’s Robert Huth was red carded a minute before halftime in a then stalemated game against Sunderland at the Britannia Stadium the home side’s expected points fell from 1.4 to 0.7 points, while Sunderland saw their expected points rise from 1.2 to 2.0. So Stoke paid a heavy price for neglecting the snowy conditions and Sunderland benefitted to maximum with a single goal victory.

Team	Number Of Red Cards	Number Of Opponent Red Cards	Total Expected Points Cost Of All Reds	Total Expected Points Benefit Of All Reds	Overall Expected Profit/Loss
Fulham	0	4	0	2.1	2.1
Newcastle	2	6	-0.3	1.2	0.9
Tottenham	3	5	-0.6	1.3	0.7
Manchester United	1	6	-0.5	1.0	0.5
Aston Villa	2	4	-0.8	1.3	0.5
Swansea	2	3	-0.5	1.0	0.5
WBA	1	2	-0.1	0.6	0.5
Chelsea	4	3	-0.9	1.4	0.5
Liverpool	5	4	-1.4	1.8	0.4
Sunderland	4	2	-0.8	1.2	0.4
Arsenal	4	7	-1.2	1.5	0.3
Norwich	3	3	-0.9	1.0	0.1
Wigan	3	2	-0.7	0.7	0.0
Everton	1	1	-0.9	0.9	0.0
Stoke	2	3	-1.2	1.1	-0.1
Manchester City	5	2	-1.1	0.9	-0.2
Blackburn	5	2	-1.2	0.6	-0.6
Wolverhampton	4	3	-1.3	0.7	-0.6
Bolton	5	1	-1.9	0.0	-1.9
QPR	9	2	-2.8	0.8	-2.0

Fulham didn’t attract one dismissal all season, while their opponents saw red on four occasions. So red cards were universally welcomed by their fans and Fulham found themselves in advantageous situations that would yield a typical average of 2.1 extra league points directly attributable to the four red cards. Their opponents were carded either early in the game or when the score was either level or within one goal, making each card potentially a big game changer.

To return to our basic earlier model, Fulham changed five points just prior to each red card into nine actual points. So a combination of their talent verses that of their opponents, four helpful cards and short term randomness increased their points total by four points.

Fulham fans were no doubt delighted with their “extra” points, but their success may be an example of the uncertainty of short term events. The Cottagers were remarkably well behaved and their opponents obligingly not, they also undoubtedly took full advantage of their numerical advantage in turning around a 1-0 deficit against Arsenal and beating Liverpool from a late stalemate. These happy accidents may not reoccur to such an extent in subsequent years.

At the bottom of the Premiership, all four struggling teams were either unlucky in how the cards fell or failed to help their own cause with poor discipline. Inferior teams make more tackles in more dangerous and card worthy positions, so red cards do come with the territory, but there was little excuse for QPR’s season high numbers. They were fortunate that an early Chelsea red card, quickly followed by a second made defending a 1-0 lead considerably easier than it may have been. Otherwise their possible concession of nearly 3 points through their nine red cards may have resulted in a very unhappy exit at the end of their season. However, as with Fulham they are unlikely to experience such extremes this term, especially with Barton now gone.

“Luck evens out over a season” appears not to apply to red cards, partly because the worst teams inevitably attract more and partly because of the scarcity of events. Only two teams emerged with equality of opportunity once their red cards had been quantified and counted. A harsh early card in a then stalemated Merseyside derby for Everton was balanced by a similarly timed card for Bolton against the Toffees. And Manchester City came close to parity despite a 5-2 card imbalanced. The Champions profited by seeing red either late in games or while in a comfortable lead and inducing their opponents to concede two cards relatively early in close games.

The real beauty of the red card is that, whereas goals are real and show up on the scoreboard a red card merely presents an opportunity and a challenge to the respective teams. Over many repetitions a team will benefit from facing a diminished opponent, but over a limited trial of a single match there still exists both the need to exploit their advantage and the small possibility that long term expectation will succumb to short term variation.

A red card is a potential game changer, but the game still has to be changed.

 

 

Read more of Mark's work on his The Power Of Goals blog

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