The impact of a red card in soccer depends on a number of factors, particularly, team strength, current score and time remaining. You can use these three factors in a Poisson calculation to determine the likelihood of each result following a dismissal, which is especially useful for live bettors.
Is it harder to play against ten men?
One of soccer's oldest clichés is that it's harder to play against ten men, than eleven. Given the rarity a team with a numerical disadvantage win, when they do, it's more memorable than the more frequent matches they lose.
Generally the punitive nature of a dismissal greatly disadvantages a team, and with more extensive data available we can easily debunk the idea that ten men can regularly out-perform eleven.
After 100 EPL games this season, there have been 18 red cards. So far, the team with the numerical advantage has scored 12 goals and conceded just 2 during the period of play where 10 played against 11, compared to conceding ten and scoring just seven whilst team numbers were level.
Two red cards resulted in successfully converted penalty kicks, which would increase the chances of an immediate score, but even this data, which is limited to goals scored or allowed, would appear to refute the suggestion that playing with ten men is no disadvantage.
Every performance indicator we have looked at shows a decline for the team that is red carded
We can analyse how the balance of play is altered by a dismissal by observing the chances created by each team both before, and after a dismissal, taking particular notice in how the expected goals figures for each team alter.
How teams expected goals alter following a red card
The average time a red card has been shown this season is just past 60 minutes - which is typical for the EPL - and as a result, sixteen sides have enjoyed a period of play with a man advantage.
When evenly matched, the side to benefit from the red card, on average made an attempt on goal every 9 and ½ minutes, but this time was halved following the dismissal. Similarly, the carded team shot less frequently than previously.
Goal expectation - by analysing chances created - predicted a goal every 66 minutes for the non- carded team while playing with even numbers, but this improved to an expected goal every 40 minutes after the dismissal.
Therefore every performance indicator we have looked at shows a decline for the team that is red carded. In short, their capacity to score goals is reduced and they are more likely to concede following a dismissal.
These conclusions should be enough to refute the opening cliché that 10 men are difficult to play against, but bettors should be intrigued to know how this affects live betting?
How to use Poisson to calculate live odds following a Red card
The impact of a red card on a game will depend on the relative quality of each team, the current score and the amount of time remaining.
Wider goal based studies show that a team who are reduced to ten men underperform, on average, by 0.6 of a goal compared to pre-game expectations, through scoring fewer and allowing more goals.
Based on pre-game odds that featured a red card since 2002, the Premier League teams who received a red card were expected to win 33% of matches. On average, they were expected to score 0.2 fewer goals per game than they conceded, highlighting that red cards are more often awarded to the weaker teams – which can be expected, given they make riskier challenges.
The effect of the dismissal reduced their overall win percentage from the expected 33% to just below 17%. On average they scored close to a goal, but allowed 1.8, therefore confirming the 0.6 goals per game average previously mentioned.
As stated earlier, the average time for a red card is 60 minutes. So a carded side on average plays for half an hour with ten men and sees its goal difference per game reduced by 0.6 of a goal.
We can therefore use this figure to adjust the live odds of a game to reflect the red card. The 0.6 goals per game underperformance relates to playing the final half hour with ten men. Bettors should understand that this will increase if the red card is shown earlier in the game, or decrease if the dismissal occurs later in the contest.
The impact of a red card on a game will depend on the relative quality of each team, the current score and the amount of time remaining
We therefore need to calculate how the underperformance caused by a red card might change over 90 minutes.
Fewer red cards are shown early in a game, but by using the data that is available and incorporating the rate at which scoring decays over a match, we can estimate that a side immediately reduced to 10 men at the start of a game would underperform by around 1.45 goals.
This average underperformance caused by a red card decays as time elapses in a similar manner to scoring in general.
Everton vs. Swansea – Impact of a red card on live soccer betting
By using the Everton vs. Swansea EPL Week 10 game as an example, we can judge the impact of a red card on live soccer betting.
The average underperformance mentioned above reaches 0.6 of a goal at 60 minutes, however when Swansea were reduced to ten men in the 72nd minute, it had fallen to 0.45 of a goal, while a side reaching the 85th minute before seeing red costs them just 0.2 of a goal.
From a Poisson approach Everton began the game as favourites, and were expected to average 1.8 goals per game to Swansea’s 0.9, giving them a 58% chance of winning the match.
Immediately before the red card, with the game tied at 0-0, Everton's chances of winning had reduced to 34%, and their goal supremacy had fallen to 0.27. The combined total goal expectation for both teams was close to 0.8 for the remaining 20 minutes.
The moment Shelvey was dismissed 0.45 of a goal was added to Everton’s overall supremacy of 0.27, by taking goal expectation from Swansea and adding it to the hosts.
Now with Everton's numerical advantage, an expected supremacy of 0.72 goals and the 0.8 expected goals prior to the red card, we can use a Poisson approach to estimate Everton’s new chances of winning.
The change in circumstances meant Everton were expected to score an average of 0.76 goals to Swansea’s 0.04. But with such little time remaining, the draw was still a significant possibility.
Everton's winning chances increased from 34% to 51%, a boost they were unable to capitalise upon. Despite their numerical advantage, a home win was only slightly more likely than the combined chance of a Swansea win or a draw, due to the time remaining in the game.
There is of course scope for tactical flexibility once one team is reduced in numbers. Swansea, for example, are yet to register a shot at goal whilst playing with ten men this season, perhaps indicating an overtly defensive stance, even for a carded side. Bettors should therefore consider newly generated Poisson odds as a guide, and take into consideration other factors such as tactics and momentum.
This article highlights Poisson's adaptability to go beyond simply calculating pre-match odds, and emphasises its use to calculate the impact of a red card on live soccer odds, giving bettors a powerful tool, when looking for an edge during live betting.
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