How Do Red Cards Affect A Football Match?
Nov 13th, 2012 - Posted by Mark_Taylor in Football
NFL and football fan. I've seen my two favourite sides, Stoke and the San Diego Chargers play at the new Wembley....and both lost.
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
And follow Mark of Twitter: @MarkTaylor0
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Prizes have been sent Poetik. Let me know if there are any problems and I will handle it.
Valid points tachyon59. I understand the need for a bigger sample in order to be able to make valid inferences. To continue on the Mourinho example, even if trends were to keep on bringing to the fore good results for him, the environment for Mourinho has changed significantly now as the Liga does not really entertain either Real Madrid or Barcelona with much difficulties given the huge gap in quality between them and the rest of the teams. A feature missing in both the Premier League and the Serie A.
Statistics collection and analyses will always help us form better judgment but of course we are unable to take into account every aspect. Attempts can be very good though and help get a clearer picture and eventually a valid betting aid. Thank you for your replies and for a good job Mark.
Hi David,
great discussion. To use the current buzz words, the smaller your sample, the more noise and less signal you have. So a Mourinho type over performance when falling behind or a better than expected team reaction to a red card may just be down to random fluctuations or it may be real, but exaggerated by fewer trials.
The "Special One" certainly got better than expected performances from both Chelsea and Inter when they trailed, but the last time I checked the effect hadn't carried over to well to Real Madrid.
So you have to ask if "x" happens in general, but "y" happens over and above expectations in the case of a particular team or manager, how do we combine "x" and "y". I've always erred on the side of giving alot of weight to the general case and much less to the team specific trait to account for the greater uncertainty.
Of course, the team specific scenario will always be baked into the prediction to some degree, anyway. Man Utd are better equipped to deal with a red card when leading 1-0 after an hour than Stoke would be under the same conditions, because United are the more talented side to begin with.
Mark .
Sorry David, but I have e-mail problems. Maybe you have closer info about previous month prizes for Gamebookers? Thank you for the replace here
Thanks for the reply tachyon59. My main point was that analysing stats over a decade for a club will underestimate the many changes undergone, caused by different 'disrupting' influences. Inter is a case in point, going from the first ever Italian club to register a treble of trophies in one season to changing managers at a very quick rate and affecting results towards a downward spiral reaching is climax at the start of last year. It is a question of personalities and the way those characteristics allow for a reaction, or the absence of it, in adverse situations. Mourinho's work is more than anything else motivational. A leader's role. With the captain gone it was no wonder the team could not amalgamate well with good managers like Benitez and Gasperini. It was a question of will - wanting to adapt to a new system imposed by the new manager. Reactions to a red card, whether this is perceived as unfair or not, depend a lot on personalities on the pitch and that of the manager. With men like Terry, Di Canio, Gattuso and so forth a team may feel compelled to produce a reaction much more than another without such strong leaders on the field. Same goes for the manager. These factors impinge on the possibility of reacting to a perceived injustice or disadvantage - a red card, an unfair goal - or simply going a goal down in a regular manner. Stats still count of course but what I would like to get the attention to is that analyses single out clubs and their records but they fail to take into account individuals whose characteristics impinge on the end result with higher probability.
Hi David,
it's about setting baselines for what may happen. Red cards in the long run are detrimental to a team's chances compared to pregame expectations.
Inter have gained an average of just over 2 points a game in matches were neither side has received red card over the last decade. Pretty much spot on with prematch estimates. When they've seen red, they've gained an average of just over 1.7 points per game, 10% below their pregame expectations and they've also scored less and conceded more in those red card games compared to their non red carded games.
If you feel their red card performance is typical and sustainable and better than how you'd expect an average side to react, then downgrade Inter's chances less after a red compared to an average side.
I'd agree that Mourinho is a case worthy of investigation. His Chelsea side were marginally, but consistently more likely to recover from going behind in games than you might expect compared to the general case. However, individual cases will inevitably have much smaller sample sizes and that often leads to extreme, but non repeatable patterns.
Stephen, you make an excellent point about the over reaction to major events within a match, including red cards. Even without a dismissal, games ebb and flow and periods of dominance for one side are quite natural, but may not be indicative of what will happen for the rest of the game.
Mark
In Spain they know all about the power of red cards with referees often too eager in showing cards and deciding games themselves. Over the weekend we had Rayo Vallecano and Zaragoza turn 0-2 deficits into victories after their opponent was shown a card. Attitudes to a sudden reduction in men on the pitch vary from one league to another and from one team to another though so generally there are no rules you can stick to in betting. A team like Inter would probably react much better given their new system of play, and so has Mourinho on numerous occasions in the past. So this does make for some neat stats but going into what lies beneath will be an unfruitful exercise for betting profits in my opinion.
Very interesting article and thought provoking. I'm sure that sometimes the teams with a numerical advantage chase the game far more, believing they are now "expected" to win, and often lose shape and discipline. Betfair "in-running" prices certainly tend to overreact to a sending off far more than perhaps these statistics show.
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Good article, a red card is always a potential change and there is no two ways about that. The advantage is of course that extra man but of course, it could make things more complicated and one dimensional however, the fans will always have the hope to get that goal or hold out. Never the less, it's about how team approach to change and adapt, I'll put my money on the team who has that extra player will remain undefeated so losing is out of the question. If you look at local derbies match up then usually it's a game changer where more goals will come in and when in english football, a draw is always and a surprise is always on the card. That is sometimes.