Is a Red Card Ever Worth It? The Data Says Yes

Since its inception in 1970, the red card has come to signify the most brutal individual punishment a referee is capable of handing out.  Having a teammate sent off almost always forces a team to fall back into their own half, relying on counterattacks that take advantage of space left by opponents. If they get lucky, maybe they’ll be able to hold on for a draw.

And yet, despite the severe penalty, players are still sent off regularly. The decision is rarely random. Yes, red cards may sometimes be distributed in an ‘unfair’ manner, but more often than not they are the correct decision. They may be handed out when a player prevents a direct goal-scoring opportunity, injures an opponent, or deliberately starts a fight in order to get their target sent off as well. In these scenarios, red card offences are rational decisions taken upon by the player in order to produce a tangible benefit for his or her team. It just so happens these kinds of benefits (disallowing a goal, injury, etc.) are against the rules.

If red card offences were universally unproductive, then they would be exceedingly rare. Hence, the purpose of the red card is to create a negative consequence that invariably outweighs any potential benefit of breaking the rules.

But, like in most cases, the numbers tell a different story. Sometimes, getting a red card really is the best decision, and economists have figured out when that is.

Getting a Red Card – Why Earlier Is Actually Better

In 2009 Jan Vecer, an associate statistics professor at Columbia University, published a paper that analyzes a specific type of red card offense – one that prevents a direct goal scoring opportunity.

Take, for example, the infamous case of Luis Suarez, who shocked the football world when he used his hands to deny a last-minute header by Ghanaian striker Dominic Adiyah. Suarez was sent off, but his red card allowed Uruguay to push through extra-time and eventually win on penalties. Was Luis Suarez smart to play goalkeeper? His absence was certainly missed the following match, a 3-2 semifinal to the Netherlands, but it is exceedingly unlikely that Uruguay would have advanced in the first place had it not been for Suarez’s blatant disregard for the rules and Asamoah Gyan’s subsequent missed penalty.

It doesn’t take an economist to tell you that Suarez made the right choice, but the numbers explain why. Vecer’s paper expands on the findings made in two previous statistical analyses of red card impacts – Down to Ten: Estimating the Effect of a Red Card in Soccer and Consequences of players’ dismissal in professional soccer: A crisis-related analysis of group-size effects. Both studies use pre-game data such as probability of winning or probability of scoring a certain number of goals. Vecer et al. update their work by using newly available in-play betting data to look at the impact of a red card during the game itself. This kind of real-time data is becoming increasingly available to researchers, even outside of corporate partnerships and academic databanks. In-play data allows for nuance and the ability to consider rare effects, such as multiple red cards and card time intervals.

To make his calcualtions, Vecer relies on betting odds from World Cup 2006 and Euro 2008. Luckily, gambling companies suspend betting activities when there is an apparent goal or penalty, giving Vecer a natural way of delineating ‘before’ and ‘after’ betting odds. Vecer takes the difference between these before and after odds after a goal is scored in order to calculate each team’s implied scoring chances.

For example, let’s say the score between Team A and Team B is currently 0-0. Initially, the odds for either team to win can be used to calculate a baseline chance of scoring. Then if Team A scores, the new odds of drawing can actually be used to find the implied chance of Team B scoring a goal. Likewise, the odds of the Team A winning can be used to calculate the implied chance of no further goals, or the implied chance of three or more goals in a match that swing in Team A’s favor. Vecer is able to use scenarios like these to calculate the chance of scoring for both teams at any point in a match.

Now, in order to determine whether or not getting a red card is worth it, Vecer assumes all penalties have a roughly 80% chance of going in. He then compares the difference the scoring chances before and after having a player sent off, and whether or not it’s worth a penalty.

Using betting data, Vecer and his colleagues show that this kind of unsportsmanlike behavior can be optimal to achieve a victory or tie. Previous research has indicated that teams will often choose to commit an illegal offense in order to prevent goal opportunities. Vecer finds that the results depend on two factors: (a) the score-line and (b) whether or not it leads to a penalty. In the right circumstances, getting a red card can actually be desirable.

The following matrices represent the best time to deny a clear goal-scoring opportunity as a function of opponent scoring chances:

Penalty Incurred

1st table

The percentages above represent the threshold at which there *exists* an optimal time. In other words, if the game is tied, there is always an optimal time to stop a goal-scoring chance higher than 80%.When penalties are incurred, there is no single optimal time at which to commit a red card offense. While optimal times exist for individual scoring chances, these can be better thought of as ‘thresholds’ after which it is desirable to commit a red-card offense.

Granted, it’s impossible to time when these kinds of offenses actually happen in a game. But they do provide an important metric: a way of telling what period of time it’s optimal to stop a goal that has a near 100% chance of going in.

This means that in the same tied game, the optimal time threshold for stopping a 100% sure-goal is the 51st minute. For example, if Luis Suarez was going to get sent off, it would have been optimal for it to happen in the 51st minute. But it was still preferable to block Adiyah’s shot in injury time – in fact, it was preferable any time after the 51st minute. Any time before, however, and he would have done well to keep his hands to himself.

second graph

No Penalty Incurred

2nd table
For example, if you’re tied 0-0 and you have the opportunity to stop a goal without giving up a penalty (such as a last-man tackle outside the box) then the scoring threshold is 57.5%. This means that you should always take the chance if the opponent has an estimated 57.5 or higher chance of scoring. As the game progresses, it becomes increasingly optimal to make that kind of tackle at lower scoring chances. After about 60 minutes, the opponent need only a ~17% chance of scoring for it to justify a last-ditch tackle.When penalties are not incurred, things are measured a little differently. The scoring chance thresholds here show the point at which it is *always* preferable to commit a red-card offense. When the opponent chance likelihood dips below these thresholds, then there is only a specific set of times where it is preferable

first graph

So What Does This Mean?

The primary issue is that these chances are calculated by betting odds that are not directly observable in a match by players. Unfortunately, a defender has no practical way of finding out what the precise scoring chances of the opponent is before making a last-ditch tackle.

Nevertheless, the data indicates that, a lot of the time, red cards can be beneficial. Surprisingly, red cards incurred without giving up a penalty are optimal fairly early in the second half. This finding is fairly counterintuitive. After all, shouldn’t it be better to play less time with a man down than more?

As we’re about to see, that isn’t always the case.

Down To 10: Why Less Is Sometimes More

On April 27, Benfica went down to 10 men against Porto in the Portuguese Domestic Cup with sixty minutes left to play. O Clássico, as the match is referred to in Portugal, is known for being one of the most intense in Europe. To play with any sort of disadvantage is no easy task. But Benfica had done it before – ten days earlier they defeated Porto 3-1 in the semi-finals of the Portuguese League Cup after playing with ten men for an hour. And just as they hoped, Benfica went on to beat Porto again, this time winning 4-3 on penalties. Less than a week later Benfica knocked Juventus out of the Europa League at the semi-final stage.  After winning the first leg 2-1 at home, they held out for a 0-0 draw in Turin after going down to ten men in the 67th.

Is this a fluke, or is it possible that playing with 10 men gave Benfica some form of advantage? Most footballing fans would scorn the idea of having their players sent off, but what if it produced strategic benefits that could be gamed?


Arsenal Coach Arsene Wenger after losing to Galatasaray in the 2000 UEFA Cup Final: “It was not a huge advantage for us to have Hagi sent off, sometimes you defend better with 10 men because everybody is focused.”

Mario Mechtel, an economics PhD candidate at University of Trier, Germany, set off to investigate this very effect in 2010. He and his colleagues hypothesized that, given the potential benefits of a red card offense (an illegally stopped goal, for example), losing a player may actually be worth it in some cases.

They found that red cards impact home and away teams differently. If a home team loses a player, they are always disadvantaged. However, for away teams, if the sending-off occurs after the 70th minute of a match, it can actually positively affect the team’s performance and score.

The authors hypothesize that this is the result of several coinciding factors. These can be grouped into three separate categories: The role effect, the substitution effect, and the task effect. They find that all three are relevant to varying degrees.

  1. The Role Effect: A sending-off affects the performance of the penalized team negatively. This is how most football fans might conceive of the red card’s impact. When the 10 remaining players have to compensate for the missing player, they need to not only fulfill their role but an additional one as well. For example, if a defender is sent off, a heavier burden may fall on offensive-minded players to drop deep and defend in addition to their current task. If this effect holds, then the performance of the penalized team will be negative.
  1. The Motivational Effect: a red card affects the performance of the penalized team positively. Social theorists predict that group size is negatively correlated with outside pressure felt by group members. In other words, as a group grows larger, the perceived pressure decreases and effort per member decreases respectively. Imagine if a team is comprised of 11 players, each playing with an effort level of 6, yielding a total group effort of 66. If the team goes down to 10 men and players respond with an effort level of 7, the total group effort increases to 70. By losing a player, players may perceive a greater amount of pressure and respond with higher effort levels, in some cases yielding an improved performance.
  1. The Task Effect: A sending-off has larger negative effects on the performance of the penalized team whenever it is the home team. This hypothesis rests on the notion that away teams play more defensively than home teams. To no surprise, receiving a red card encourages a team to switch to a defensive approach, emphasizing counter-attacking as a primary means of goal scoring. Thus, the theory is that if the away team loses a player, it doesn’t significantly change their tactical approach. On the flipside, a home team whose starting lineup is built around an attacking approach will need to adjust considerably if a player is sent off.

Mechtel and his coauthors indeed observe a stronger red-card effect on home teams than on away teams, indicating the presence of the task effect. However, their results for the motivational effect and role effect are a bit more mixed. By controlling for minutes left until the end of the game, they find that the role effect only begins to offset the motivational effect after the last 20 minutes – in other words, an away team that has a player sent off between minute 71-90 actually experiences a boost to their final score.

The paper is, however, unfortunately riddled with endogeneity problems. Although they repeatedly seek to compensate for these by introducing new controls, these often fall short of being reliable estimators. In particular, Mechtel struggles with finding adequate proxies for team performances and skill. Because he does not have access to the same real-time betting data that Vecer et al. did, he and his colleagues resort to using final league positioning as a substitute. However, league positioning can be unreliable, and in the case of newly promoted teams, he uses previous season standings. To Mechtel, finishing first in the Championship is equivalent to winning the Premiere League. In another test, Mechtel attempts to use numbers of attempts on goal, corner kicks, and yellow cards as an estimator for in-game team performances. While none of these factors drastically change the results, teams that have more yellow cards may be more likely to receive a red card because second yellow offences also count. As a rule of statistics, if you are trying to use a control variable as a proxy for an independent variable (in this case, yellow cards as a proxy for team performance), it should be unrelated to all other independent variables (in this case, red card occurrence). Otherwise, the effect cannot be properly isolated.

These issues should be of concern to the reader, but they should not necessarily jeopardize our consideration of the results. They do suggest that the 70-minute cutoff for receiving a red card is not particularly accurate, but Mechtel went through the effort of repeating his tests with several data sets (one goal-based and one points-based) and found similar results. In all his tests, Mechtel finds the signs on his important coefficients remain the same at a significant level, meaning there’s consistent evidence of a positive effect generated by red cards.

Thus, the results do support a benefit for away teams who go down to 10 minutes late in the game. Ideally, Mechtel’s work could be repeated with a more precise data-set. Maybe Vecer could share his?


Myth Busting: Does Playing the Second Leg at Home Actually Matter?

The Myth

Most football fan will tell you that when it comes to double-legged knockout tournaments, it’s better to play at home in the second leg than away. The idea is simple – the away team has the option (luxury) to play it safe (park the bus), aim for a draw, and then bank on winning the home game. Not the most elegant approach, but an effective one nonetheless.

Proponents of the strategy are not limited to fans and pundits – players and coaches can be just as guilty. Iker Casillas thinks it will give them an advantage over Schalke 04 in the Champions League this February. Dougie Freedman, former Crystal Palace striker, once attributed a victory against Charlton in the second leg of a promotion play-off semi-final to the incredible atmosphere. Patrick Kluivert, former Dutch international, believes it’s better to “make your mistakes in the first leg away from home because there is still time to put things right in the second match.”

"Maybe we have a slight advantage because we are playing the return match at home" - Carlo Ancelotti

“Maybe we have a slight advantage because we are playing the return match at home” – Carlo Ancelotti

But while the story is written by the pundits, the truth is written in the numbers. A 2007 paper by Lionel Page and Katie Page, of the University of Westminster and University of Queensland respectively, looked to find just that. The first academic research of its kind, the study made significant advancements but ultimately fell short of conducting a proper analysis of the phenomenom. It wasn’t until a follow-up study was conducted by three researchers from the Ludwig Maximilian University of Munich that the truth was uncovered: playing the second leg at home is, statistically speaking, irrelevant.

Evidence From the Champions League

It’s not hard to see why this myth has so much traction. On the surface, data from the Champions League fits the narrative: teams play conservatively in the first leg and open up in the second. This is reflected in the increase in goals scored in the return leg.

1st leg goals

2nd leg goals

1st leg goals per game

2nd leg goals per game

2012 (group)





2012 (knockout)





2011 (group)





2011 (knockout)





2010 (group)





2010 (knockout)










Additional calculations by Michael Cox of Zonal Marking for the 2007-2009 Champions Leagues confirm the findings above. That is, with the exception of 2010, more goals are consistently scored in the second leg of CL knockout rounds than in the first.

This phenomenon can work for and against a team playing at home during the second leg. On one hand, the away team is less likely to sit back and park the bus. This lets the home team exploit their home advantage and take control of the deciding match. On the other hand, in a game that’s decidedly more ‘open’, a goal for the away team counts for double. Ideally these two effects would balance out and we would observe a 50-50 chance of advancing, even if more goals are scored in the second leg (e.g. if a team goes 1-0 at home and then loses 1-2 away, the away goal rule would outweigh the home field advantage).

Since we know more goals are being scored, the question becomes: for whom?

The First Study

Between 1994 and 2009, 56 percent of teams which played the second leg of a Champions League tie at home advanced to the next round. On the surface, this suggests home-field advantage frequently outweighs the benefit of the away goal rule.

But these findings are not sufficient. They do not take into consideration that the order of home-away matches for the CL round of 16 is not random.

In fact, group winners first play away, then at home. This was instituted as an added incentive for group winners, based on the very myth itself. This creates a sort of a self-fulfilling prophecy. Seeded teams play at home in the second leg, and it’s not clear if they win because they’re the better team, or because of their home-field advantage.

In their 2007 paper, Lionel Page and Katie Page look examine this specific aspect. Together, they use data from three different European Cup football competitions over 51 years in order to assess the accuracy of the second-leg advantage myth.

One solution they assess is to simply not look at data from the round of 16. Later rounds no longer seed home-away match order, randomizing the process and eliminating possible bias. But they find that this approach considerably reduces the sample size, and makes it harder to obtain meaningful results.

Page and Page instead use team-coefficients to adjust for round of 16 seeding. By controlling for team-quality based on UEFA rankings, they attempt to separate the effect of playing at home in the second leg and the effect of being a better team. Their results produce the following:


This graph shows an overall decrease in second-leg home advantage, both adjusted and unadjusted for team coefficients, over time. Interestingly enough, the decrease in the late 60s in this advantage can be traced to the introduction of the away-goals rule. By increasing away-goal value, the tactic of parking the bus away and winning at home was no longer as effective. For a team playing away, losing wasn’t the end of the world, but scoring an away goal could be the difference that would send them through.

The temporary decrease in advantage between 1984 and 1990 coincides with a five-year ban on English club participation in European competitions as a result of the Heysel Stadium disaster. This suggests that, at the time, English clubs exhibited a more significant second-leg home advantage than their European counterparts. In fact, seven out of eight previous European Cup winners were English. It’s possible that part of this success was the ability to exploit the second-leg home advantage in either the form of favorable refereeing or by employing the ‘defend away, win at home’ strategy.

The Away Goal Rule

At this point, readers would be right to ask: what about the away goal rule? Why does everyone believe there’s an advantage to playing the second leg at home when the away team has the opportunity to play an extra 30 minutes where their goals count double.

Page and Page actually look into this. They analyzed 186 European cup ties which go into extra time and found that the probability of winning the second leg at home is 66.42%. These results are adjusted for team ability, regardless of the fact that ties going into extra time might reflect equally-skilled teams. Page and Page also find that matches that go to penalties on the home ground result in the home team winning 57.33% of the time.

Simply put, the advantage of playing at home for an extra 30 minutes considerably outweighs the advantage of having goals count for double for the same period of time. Note that, whether or not there is an advantage to playing at home first, home advantage is a very real phenomenon.


“Statistically it is not proven. We like to think in our job that to play at home in the second leg is an advantage, but it is not proven at all in the statistics. It is 50:50” – Arsene Wenger

Busting the Myth

Page and Page make one crucial mistake that jeopardizes their conclusion that second leg at home advantage remains today. They only control for team UEFA coefficients, but this is not sufficient to isolate the advantage effect. Think about it this way: In Page and Page’s model, they attempt to separate the following effects:


However, in order for their model to work, the two effects cannot be correlated outside of their impact on the dependent variable (in this case, the round of 16 performance).

If you’re a little confused right now, you should be. This is the same problem Page and Page thought they were solving. But their analysis was rudimentary: you can’t simply control for correlated effects in order to isolate them.

Suppose you have three variables A, B, and C. You hypothesize that A and B both positively affect C. The data shows as much: A, B, and C all rise together. You could jump to conclusions and assume you were right from the beginning. But really, B is positively affecting A and C, giving the illusion your initial hypothesis was correct when in fact A is completely unrelated to C.

For example, imagine that the US government introduces a new anti-smoking campaign. The campaign is a success, and raises the population’s life expectancy. The government also chooses to raise taxes to fund the campaign. One might observe taxes rising and mortality rates decreasing and falsely conclude that paying more taxes means you’ll live longer.

Likewise, Page and Page observe a lot of teams play the second leg at home because they’re good and win their group, and falsely assume that they win the next round because they played the second leg at home. In reality, a better team will have a higher coefficient going into the tournament, and will not only do better in the round of 16, but is also more likely to have the second-leg at home. This leads them to overestimate the effect match order has on the outcome.

Three researchers from the Ludwig Maximilian University of Munich took a closer look at the data, and noticed what Page and Page did. To solve for this issue, they controlled for group stage performance in order to completely isolate the home-away match order effect. Any effect team coefficients have on match order is now funneled into the group stage performance variable, giving them clear results.

The researchers found that, once they controlled for group stage performance, playing the second leg at home had no impact on a team’s chances of success. It turns out that the team that progresses is usually just better than their opponent, contrary to the superstitions of some of football’s greatest minds. Maybe this is the reason Wenger has been so successful – he knows when to listen to the numbers.

Research Roundup Part 1 – The Best Sub Strategy, Will Financial Fair Play Ruin Man City, and Why You Shouldn’t Always Fire Your Coach

Welcome to the first installment of a new Café Futebol series – The Research Roundup. In these posts, we take a long look at the newest and most interesting soccer literature and let you know what’s going on. We walk through the papers and then highlight key insights and concerns we have. 

In the first installment, we’ll take a closer look at research on three major questions:

  1. Is there an optimal substitution strategy?
  2. Will Financial Fair Play be good or bad for your Premier League team?
  3. Does sacking your manager really lead to a temporary increase in performance?

If you have a paper you’d like us to cover, send us an email through the Contact Us page or reach me at @Cafefutebol on twitter!

Is there an optimal substitution strategy?

Paper Information:

  • Title: A Proposed Decision Rule for the Timing of Soccer Substitutions
  • Author, Institution: Bret R. Myers, Villanova University
  • Journal: Journal of Quantitative Analysis in Sports
  • Date of Publication:  March, 2012
  • Link to Paper

The flow of soccer makes it difficult for managers to have a direct impact on the outcome of the match. Once the first whistle blows, the game is, for the most part, decided entirely by the players on the field. The manager is left with only a handful of options should the game go sour. A half-time motivational speech or a slight tactical adjustment may be of importance, but any major changes lie in the substitutions made. These three players remain the manager’s most critical in-game decision for affecting the outcome of a game.

It’s quite surprising then that very little progress has been made on optimal substitution strategy – until now. Bret Myers, an assistant professor of management and operations at the Villanova School of Business, seeks to fill this gap. In his paper, he sets out on inventing the first practical use of academic substitution research for managers’ use. Using data from the major European leagues, the MLS, and the 2010 World Cup, Myers describes his optimal substitution strategy (dubbed the “Decision Rules”):

Proposed Decision Rule:

  • If down at half time
    • Make 1st sub prior to 58th minute
    • Make 2nd sub prior to 73rd minute
    • Make 3rd sub prior to 79th minute
  • If tied or ahead
    • Sub at will

Myers writes:

As the game approaches the first critical point of the 58th minute, a coach should make at least the first substitute if behind. As the game approaches the next critical point of the 73rd minute, if still behind, a coach should make at least the 2nd substitute. If the team is able to equalize or go ahead once the critical point is reached, then it is allowable for the 2nd substitute to be withheld. However, if the team returns to a state of being behind prior to the last critical point of the 79th minute, then a coach should use both the 2nd and 3rd substitution prior to the 79th minute. If a team that was previously tied or ahead falls behind after the 80th minute, there is no specific recommendation on how a coach should use the remaining substitutes if still available.

He concludes that, if a team is in a position to follow the Decision Rule (i.e. if they are behind or tied by half-time), that they can maximize their chance of winning by doing so. He finds that teams that follow his guidelines improve (defined by scoring at least more goal) roughly 36% of the time. The results are less encouraging for teams that are tied or ahead by half-time. In these scenarios, the manager’s substitution timing has little impact on the result of the match.

Additional Charts and Graphs:


Italians were by far the most capable in using their substitutes at maximum capacity, evidenced by their success following Myers’s decision rule. La Liga had the lowest, indicating a league-wide lack of bench depth despite an overall willingness by managers to send in their substitutes before their German or English counterparts. Perhaps La Liga coaches aren’t as afraid to experiment with formations or lineups when behind, even if it doesn’t always work out.


Traditionally, substitution literature has remained largely descriptive in nature, without offering much practical managerial use. Myers’s research is a refreshing initiative towards implementable tools, and regardless of his conclusions, represents an important step in gaining traction in the locker room.

Furthermore, Myers’s results suggest that coaches tend to underestimate the significance of a fresh set of legs on the field. Managers largely “overvalue starters and undervalue the role of substitutes” in a match. If this is one of the few metrics by which we can reasonably evaluate a coach, then further research and application is warranted.


Myers potentially muddles correlation and causation in a manner that might jeopardize his research. Myers believes that early substitutions reduce the effect of player fatigue and lead to an increase in team performance.  However, it is possible that managers are more willing to sub off starters early if they are confident in their replacement. A manager may only be willing to send in a higher quality substitute and a lower quality substitute for 30 and 20 minutes respectively.

For example, Myers notes that, in 2009, Bayern Munich followed his decision rule 5 out of 8 times while Dortmund only did so 2 out of 9 times. Bayern Munich has a much deeper bench than Dortmund. It’s possible that Bayern’s coach simply trusted his substitutes more, leading him to send them in earlier.

If early substitutes are endogenously correlated with higher quality players, then this may be responsible for the observed increase in results. If this is the case, then Myers’s conclusions become more fuddled. Timing is still important – a team with a deeper bench sends in their substitutes early precisely because they are aware of the physical toll on starters – but then the decision rule is no longer universal. It may only apply to teams with a deep bench.

The only substitute you always put in early

There is also a chance that a large score deficit indicates an opportunity to send in youth players for additional experience, knowing that the match has already been decided. Take the case of Barcelona – Bayern Munich 0:3 at the Camp Nou during the 2013 CL semi-finals. Barcelona was down 5-0 on aggregate before Tito sent in his first substitute in the 55th minute: Alexis for Xavi. Ten minutes later, Iniesta was subbed for Thiago Alcantara. No coach in their right mind subs off Xavi and Iniesta when there’s still a chance of winning. In the cases like that of Barcelona, who conceded two more goals following these substitutes, early substitution may be correlated with lower team performance.

Further analysis could isolate this effect by controlling for score deficit and team-season fixed effects based on the quality of the bench in relation to the starting lineup. In the meantime, Myers’s decision rule is insightful, but should be taken with a grain of salt.

What does Financial Fair Play mean for the Premier League?

Paper Information:

  • Title: Vertical restraints in soccer: Financial Fair Play and the English Premier League
  • Author, Institution: Thomas Peeters, University of Antwerp & Stefan Szymanski, University of Michigan
  • Journal: Working Paper from University of Antwerp, Faculty of Applied Economics
  • Date of Publication:  March, 2012
  • Link to Paper

In their paper, Peeters and Szymanski construct a profit model for club teams as a function of their wages, costs, and revenue generated from winning games. Once they have a model and verify it using empirical data, they simulate the effects of FFP. They find that the FFP’s break-even rule has a salary-cap effect similar to the one present in American sports. However, unlike in the US, the rule has not been negotiated as part of a collective bargaining agreement with unions and may not be exempt from competition law in the EU. If the FFP does have a salary-cap effect, it may not be compliant with EU regulations.

The basic premise of their model is that football clubs are not profit maximizing, but are instead constrained by a limited negative profit-line that their owner is willing to cover. In other words – football clubs consistently operate at a loss, only to be bailed out by their wealthy owner. Financial fair play is going to limit the loss any one football club can take. This effectively reduces a club’s budget.

The model of Peeters and Szymanski has three components: revenues, wages, and other costs (stadium maintenance, advertising, etc).  They assume that revenues are already being maximized and that other costs are already being minimized. The only variable that can be cut in order to fit into a smaller budget constraint is player wages.

The next step is to estimate the parameters of the model using data gathered from the top three tiers of English soccer from 1997 to 2008. This allows the researchers to verify that their model holds against real, empirical data, and that it can be explained intuitively. The results are positive – all of the model’s parameters fit their expected values at a statistically significant level. Essentially, the model is well-behaved, suggesting that it can be reasonably used to estimate the impact of a new budget constraint. Finally, Peeters and Szymanski simulate the effects of FFP under their model. They find that the new rules lead to an overall reduction in league player wages over time, although the winners and losers are mixed.

Several major powerhouses will likely remain unaffected. In particular, Manchester United, Arsenal, and Liverpool are all able to “consolidate their position in prediction point totals” due to their high revenue capacity and a statistically strong ability to convert wages to results. On the flip-side, Manchester City and West Ham look to lose considerably more than other teams. Although Chelsea follows a similar strategy to Manchester City in terms of exorbitant spending at the owner’s expense, they have established themselves as a preeminent club and do not “appear to face the same difficulty in sustaining its position under FFP.” The teams set to receive the highest degree of benefit are largely those located at the bottom of the table. They will gain a considerable advantage from the decreased cost of success in terms of player wages.

Additional Charts and Graphs:


You can see for yourself the results of the duo’s FFP simulation. The four scenarios presented correspond to an average accepted deviation of €15m, €10m and €5m per season, and the “final” scenario with a total acceptable deviation of €5m over three seasons. The deviations represent the amount by which clubs are allowed to overspend their budget during the first years of adjusting to FFP. They increase in leniency when read from left to right in the chart above.


Financial Fair Play may not be such a bad rule if you support Liverpool or Arsenal. It will certainly take a hit at relatively wealthy newcomers such as Manchester City, PSG, and Monaco. It’s entirely possible that within a few years of FFP implementation we will see a resurgence of ‘historic’ teams. Tottenham, surprisingly, will still not qualify for the Champions League.

It would be interesting to see how further simulations play out over other European leagues. My guess is that La Liga and the Bundesliga would remain largely intact, while the French league may return to its classic free-for-all.


The profit model constructed leaves out an important factor from the equation: player transfer fees. As these fees increase over time, they become a more significant proportion of club costs and may not be actually be minimized, as Peeters and Szymanski assume. In this scenario, it is entirely possible that tightening a club’s budget will lead to a reduction of player transfer value instead of wages.  It is not surprising this effect is omitted – in Soccernomics Szymanski found that player wages, and not transfer fees, are essential in predicting league success. Nevertheless, when deciding a revenue equation, it is over-simplistic to assume clubs are ‘minimizing’ transfer fees.

Nevertheless, even if transfer fees are reduced instead of wages, it’s unlikely to change the results of the study. Successful, established clubs would remain largely unaffected, given that their prestige and winning-record means the club is attractive enough to entice players without paying inflated prices (i.e. their costs are already minimized). Meanwhile, clubs such as Manchester City would be forced to reduce the payments they can offer for player transfers, and teams at the bottom of the table would face a less inflated player transfer market.

Not Pictured: Wenger on the left, Moyes on the right

It should also be noted that this piece is a working paper and has thus neither been accepted to any academic journal nor officially peer-reviewed. I would normally avoid discussing working papers, but Stefan Szymanski is co-author of Soccernomics and a prominent author in the world of soccer economics and sports management. For this reason, I make an exception.

Does sacking your manager really lead to an increase in performance?

Paper Information:

  • Title: The Effects of Managerial Turnover: Evidence from Coach Dismissals in Italian Soccer Teams
  • Author, Institution: Maria De Paola and Vincenzo Scoppa, University of Calabria, Cosenza
  • Journal: Journal of Sports Economics
  • Date of Publication:  March, 2011
  • Link to Paper

If you follow soccer, you’ve probably heard of the ‘five game bump’. The bump is usually a streak of wins following the sacking of a manager. Players are so shaken by the departure of their coach that, the bump-advocate would argue, they become much more focused in upcoming matches. It is essentially a slap in the face, a well-meaning shake, meant to bring sleeping footballers back to the real world.

Scoppa and De Paola are more skeptical of the phenomenon. They know that positive results observed after a series of losses can be misleading. The new manager could even win more games and still be statistically worse than the last. The two use 1997-2008 Serie A match data to measure the effects of coach changes on team performance, while controlling for two major challenges: the tendency for random data to converge towards its mean and the variation of opponent quality.

The ’regression to the mean’ phenomenon states that if we observe an extreme initial measurement, then a subsequent measurement will tend towards the mean. In a footballing context, if we observe a string of ‘below-average’ club performances, then subsequent performances will tend towards the average, and we will observe an increase in performance. A team could do poorly, fire their coach, and do well, and none of this would be due change in management. Of course, the actual team average performance is unobservable, but if it exists at a higher level than what it takes to get a coach fired, then changing coaches may have no effect at all. Not accounting for this phenomenon could lead to a serious overestimation of managerial impact.

The second issue that Scoppa and De Paola must deal with is that coaches are not fired randomly. Since their dismissals are typically decided after a series of poor performances, weaker teams tend to replace the coach more often. In this case, coach changes are negatively correlated with team quality. This could lead to a serious underestimation of managerial impact.

Gareth “regression to the mean” Bale

In order to compensate for the two, Scoppa and De Paola devise a model based on team and season fixed effects. This model looks at all matches during a given season pre- and post-managerial change. Note that they are not looking at a ‘5-game-bump’, but an entire season. No inter-seasonal managerial changes are recorded since those may actually reflect a good run (good managers are poached by larger clubs). The fixed effect accounts for the fact that the old coach and the new coach do not play against the same opponents. This allows the model to correct for tough schedules and the impact they may have on managerial record.

The results of the analysis are mixed. The model estimates that changing coaches does not positively affect overall team performance, with the exception of number of goals scored. This suggests that firing the coach may not have anything to do with improving team performance, but may be the unfortunate side effect of team boards overestimating their ability to make optimal replacements, or may even serve to brand the coach as a scapegoat. In any case, despite observing an improvement in results post managerial switch, this paper suggests it has little to do with the switch itself.

Additional Charts and Graphs:


In case you were wondering, there is indeed an average increase in points per game following the sacking of a manager. You can see so here! The only thing that’s up for discussion is whether or not it has anything to do with the new manager, or if it’s simply a statistical phenomenon. As it turns out, it’s probably a statistical phenomenon. The data suggests that firing Andre Villas-Boas isn’t going to save Tottenham and that perhaps Manchester United’s board is wise to keep David Moyes on contract despite recent performances.


Although firing the manager doesn’t seem to have any real impact on team performance, it does not mean it’s a completely useless action. Actually, they very fact that firing still occurs indicates that it serves a different purpose entirely. It can relieve pressure on players and on the board of directors. If the board is voted on democratically by club members, or chosen by stock holders in the event that the club is publicly traded (see: Manchester United), it may be in the interest of the board to find a scapegoat. Firing managers also relieves pressure on the managerial side. An incoming manager may find himself with a terrible situation and, often enough, nowhere to go but up. This may make it easier for the new manager to establish his team and methodology without worrying about immediate gratification.


The fixed-effects the authors choose to measure in their paper are confusing and often inconsistent. For example, the authors make a point to consider both rank difference and point differential, despite representing the same implicit factor: a difference in recent performance between teams. Nevertheless, they choose to gauge a team’s quality by their previous year’s rank as opposed to their points per game. It is also unclear as to why the authors choose to use previous-season rankings as an indicator for current form. These can be misleading given inter-season developments including management changes and transfers. A better indicator might be player wages and transfer fees, which previous studies have argued play a major role in determining league performance.

Lastly, there are two additional factors that ought to be addressed: tough scheduling and home field advantage. Although this typically affects higher-quality teams who engage in multiple tournaments, clubs faced with fixtures in a smaller time frame may experience a lag in performance due to stress and lack of adequate rest. It is worth investigating potential effects this has on ‘good’ and ‘bad’ streaks as a consequence of their manager. Additionally, soccer literature largely agrees that home-field advantage is a real phenomenon. If an incoming coach has more home games than away, he may appear to get better results when in fact he is useless. It is not clear whether or not this effect is accounted for in the study due to the vague wording, but I was unable to find any explicit mention of it, so I assume it was overlooked or is endogenous in another variable which was not clearly explained. In any case, it is a simple effect that deserves attention due to the general consensus of its reality.


Thanks for reading!

If you have any questions or comments, send us an email through the Contact Us page or reach me at @Ncholst on twitter.

Why ‘Three Points for a Win’ is a Loss for Football — A Closer Look Into One of the Most Important Rule Changes in Football History

An Introduction to Incentives

Ask an economist how to solve a problem, and he’ll tell you incentives are the answer.1 He wouldn’t be wrong. Punishment and reward are fantastic tools for  exploiting self-interest in the service of the common good. In football, they’re made up of red cards and penalties, trophies and relegation, and always in the interest of preserving the ‘beautiful game’.

But incentives do not always respond the way we expect them to. Take, for example, the infamous 1994 Caribbean Cup match between Barbados and Grenada. In an effort to encourage attacking play during extra-time, tournament officials decided that extra-time golden goals would be worth double for goal difference purposes. A nice idea in theory, but by the end of the match, Grenada found themselves frantically trying to score in either net while Barbados defended both goals. An incredible series of events actually made it in Barbados’ best interest to force an equalizer so that they could score an extra-time goal. You can view a video of the incident below and read about it here.

I feel cheated […] I have never seen this happen before. In football, you are supposed to score against the opponents to win, not for them” – Grenada Manager James Clarkson.2

Even the slightest change to incentives can twist, shape, and decide games in ways we may never anticipate. This is not to say it is an easy task to predict the impact of new incentives – in fact is is often near impossible. However, it is the duty of football officials to review historical data to decide which rules have failed and need updating. In particular, the ‘three points for a win’ rule stands out as a serious offender (from here on the rule will be referred to as 3PW). Despite a growing stack of literature that shows the rule has had the opposite effect from what was intended, it has managed to almost completely fly under FIFA’s radar. It is high time to review the evidence for one of the most important laws of the game. But first let’s rewind.

Football is not a circus”

In October 1980, Stoke City manager Alan Durban, angry at journalists’ criticisms of his tactics in a 0-0 draw against Arsenal, instructed them to “go and watch a bunch of clowns” if they were looking for entertainment. Durban, after all, was simply doing his job, and maybe not such a bad one at that. The “win at home, draw away” philosophy was popular amongst managers and defensive tactics were very much in vogue. Could Durban really take the fall for inverting the pyramid? Perhaps if rapper-cum-actor Ice-T had been present, he could have explained to the crowd of unruly reporters, “Don’t hate the player, hate the game.”

But this wasn’t the only problem. The early 1980s depression had taken its toll on England, and rising ticket prices and television exposure saw match attendance drop to nearly half of its 1950s record-setting numbers. Football fans cried foul: this was not the first time they had felt the beautiful game was under attack.  A generation earlier Herbert Chapman, the legendary former Arsenal manager, remarked:

“It is no longer only necessary for a team to play well. They must get goals, no matter how, and the points. The measure of their skill is, in fact, judged by their position in the League table.”

In comes Jimmy Hill, former chairman of the Professional Footballer’s Association and legendary Coventry manager.3 Hill was not your conventional chairman – in fact, he was a bit of a maverick, famous for leading the charge to scrap the Football League’s £20 maximum wage. He was later known for engineering the Sky Blue Revolution during his tenure as Coventry manager, a club overhaul which would make Assem Allam’s efforts to rebrand Hull City Tigers look amateurish and lazy.

Hill, who “had long thought that soccer had become too defensive and dull” and was concerned that “goals had become rarer with every passing season,”4 proposed a simple revision to the rules: change the reward for winning a match from two points to three points. This would make wins more valuable and incentivize teams to not settle for draws. In 1981, less than a year after Durban’s speech, Hill convinced the FA to introduce his idea of ‘three points for a win’ or 3PW. Thirteen years later, FIFA adopted the system for the upcoming 1994 World Cup in the US, concerned that American fans would be turned off by draws. Sepp Blater hailed the move as “the most important sporting decision taken here, but it rewards attacking soccer”. In 1995, every remaining major football league switched to a three point system.

The Drawing Game

Advocates of 3PW tend to fall back on the result easiest to observe: it reduces the number of draws by increasing the incentives for breaking a draw. Indeed, according to former Football League chairman Brian Mawhinney, draws are still seen as a threat to football’s entertainment factor:

I suggested that for drawn matches each team gets a point and then maybe the team that wins a penalty shoot-out gets an extra point […] We cannot afford to be complacent – people are always talking to be about how we can get more goals and more excitement in football.”5

Some statistics indicate that the rule switch did indeed reduce the number of draws. In the five English First Division seasons leading up to the change, there was an average of 133.0 draws per season. This was twenty more than the average of 113.4 in the first five seasons after.

Data from other countries yield similar results. Evidence from Turkish and German leagues shows a decrease in the number of draws after controlling for number of teams, games played, and cup matches.6,7

But is this a valid metric for measuring entertainment value? Does a reduction in the number of league draws indicate an increase in attacking play?

Scrutinizing England’s data may be the key to answering these questions. The graph below illustrates the number of draws per game over time in England first division football league (no cup games are counted). The value on the left indicates the percentage of matches played that resulted in a draw.


At a first glance, the number of draws per game (DPG) was already in the process of decreasing right before 3PW took effect in 1980 (and has actually been declining since 1970). In fact, it only takes five years for any perceived effects of 3PW to wear off. The reason? Between 1986 and 1988, the number of teams in the league was reduced from 22 to 20. The data indicates that any benefit of 3PW in terms of reducing DPG was negated by the formation of a more competitive league.

This reveals a fundamental problem with looking at draws: the DPG is inversely correlated to league competitiveness. Think about it: if a league is perfectly competitive, then all matches will result in a draw. Take the spike in DPG in 1968, for example, which coincides with the introduction of the substitution. The substitution rule change meant, among other things, that a team would no longer have to play with ten men if one of their players was injured on the pitch. This would naturally lead to fewer unbalanced matches, more draws, and a higher DPG. Indeed, I find a statistically significant inverse correlation between DPG and league competitiveness.

Not only did the rule switch have no noticeable long-term impact on DPG, but the reader must make a subjective judgment on whether they prefer fewer draws, or a more competitive league. If you prefer fewer draws in return for the same old winners and losers, then this rule change may be right for you. I do not however believe this to be the intention of 3PW.

There are other, better metrics, for evaluating the rule’s success. Let us consider them instead.


Regardless of the number of draws, if 3PW encourages attacking play, then it may have served its purpose after all. After all, fans do not watch games to find out the winner – there are plenty of live score feeds online – they watch to see the beautiful game unfold. If the FA is looking to increase stadium attendance, they need to make the experience worth it, most noticeably through an increase in attacking play.

As it turns out, 3PW actually incentivizes defensive play and sabotage (a punishable offence, e.g. purposefully negligent tackling). Researchers looking at card data from England, Spain, and Germany show that teams in a winning position were more likely to commit punishable offences under the 3PW system.8,9

At the core of this issue is the natural tradeoff of offensive play: by increasing your chances of scoring, you are also increasing your chances of conceding a goal. This means that, following the implementation of 3PW, if a team scores and takes the lead, then the expected payoff of playing defensively will increase relative to the expected payoff of playing offensively. In other words, the stakes are so high that a team will not risk giving up a goal. By making wins more valuable, the FA may have succeeded actually made ‘unattractive’ football more common. To quote football statisticians Chris Anderson and David Sally, “three points for a win had not rewarded attacking soccer. It had rewarded cynical soccer”.

Most damning is evidence from a 2005 study by then-University of Chicago economists Luis Garicano and Ignacio Palacios-Huerta. In a discussion paper of theirs, the two analyzed Spanish league data from the 1994-1995 season (when 2PW was last used) and compared it to the 1998-1999 season – the four year gap is so that they do not have to assume an immediate response and change in tactical development. They control league data against cup results, which should remain largely unaffected by the change, to eliminate potential external variables such as referee strictness, injuries, etc.10

Their study also provides evidence that 3PW is ineffective. They show a ~28% increase in the use of starting forwards, but also an increase in the number of defenders and a ~10% increase in both fouls and yellow cards as a result of 3PW. However, despite the increase in forwards, number of goals scored did not go up. This suggests that any attack-minded benefits of 3PW were negated by its less appealing sabotage-effect. The study found that “when ahead, teams became more conservative, increasing their defenders, scoring less goals, and allowing fewer attempts to score by their opponents”.

But more importantly, this study shows that 3PW is actually detrimental to match attendance. They find the incentive change actually decreased attendance for teams who played more defensively and committed more sabotage. By controlling for team popularity and visiting/home factors, Garicano and Palacios-Huerta show a negative correlation between ‘team dirtiness’ and attendance, at a significance level of 1%. This means that, statistically speaking, there’s a 99% chance that a correlation between dirty play and attendance figures exists.


One point that seems to be brought up consistently is that 3PW inspires more league competition, and in particular gives lower-ranked teams a fighting chance to avoid relegation.

The idea is that by increasing points for a win, teams facing relegation at mid-season a given a fighting chance to turn everything around. If true, this would make the league more exciting for supporters of lower-ranked teams.

However, a look at the ten largest comebacks in the top flight of English football tells a different story:


It is striking that only two of the top ten comebacks happened post-1980. In particular, comparing the case of Fulham in 2010 to Ipswich in 1978 reveals the counter-productive effects of 3PW. The Whites lost only one more game during the second half the season than during the first. Their fantastic comeback was due almost entirely to their ability to convert draws into wins. Ipswich, on the other hand lost, only twice in the second half versus eleven times in the first half of the 1978 season, yet managed to advance only a similar number of spots on the league table. The Blues succeeded by converting their losses into wins. It is telling that teams pre-1981 could engineer a comeback by winning against those who beat them, while modern teams can only hope to edge out a win over teams they have already drawn.

We then look at whether or not changing the points system affects which teams are being relegated. If does, because 3PW rewards teams who win more games, teams that win/lose would benefit more than teams that survive by drawing. When the 1976-1980 season tables for the top three tiers of English football are recalculated under 3PW, we get the following:


The evidence suggests that the impact of 3PW is in fact minimal. For teams coming in last or second to last, how you count your points doesn’t change the fact that you don’t have any. Teams in third to last place may sometimes benefit from a new point system, but 80% of the time it would not have made a difference. A fourth to last place team had a 60% chance of staying relegated, but frankly, it’s the third tier of English football. Whether or not the Tranmere Rovers stay up another season is of little concern in this case. Teams that are relegated are not relegated for playing less exciting football, they just aren’t good enough.

So far, it doesn’t look like 3PW has a strong effect on teams’ comeback potential or their chances of being relegated. We still have one more metric to consider, though: league competitiveness. To calculate this metric, we consult a study penned by Kjetil K. Haugen, professor of Logistics and Sport Management at Molde University college. Haugen’s analysis demonstrates that decrease in league-competitiveness following the rule change in the United Kingdom, Norway, and Romania.

By using a tweaked version of his formula, we can calculate the competitiveness level of the bottom-6 teams under 3PW and 2PW systems. These levels are represented on a scale of 0% to 100%, where 0% represents a minimally competitive league, and 100% represents a maximally competitive league.

You can find an explanation for my methodology and full access to my data here.


This graph represents the competitiveness of the bottom six teams during the second half of the season. All pre-1981 season data has been recalculated under 3PW to avoid endogenous distortions (not doing this significantly overestimates the competitiveness of pre-1981 teams). Note that the variance index was able to exceed 100% – it’s because lower-tiered teams consistently over-performed compared to their mid-season rankings. For example, in 1977, the six second-flight teams ranked last in December proceeded to win 186 combined points by June – they were only expected to get 45. This rubric is meant to give us a visualization of competitiveness, not a predictive figure.

At a first glance, it doesn’t look like there is any correlation between 3PW and bottom six. Top-flight competitiveness was already increasing before the change, and data from the other flights doesn’t reveal anything either. A subsequent statistical test shows two things: First, 3PW is a poor indicator of a team’s performance during the second half of a season. Second, on average, a bottom-six team’s performance during the first half of a season is not a great indicator of its performance during the second half.

These results show that, in fact, 3PW doesn’t give losing teams a second wind.


Jimmy Hill’s role in launching 3PW ultimately won him the Contribution to League Football Award at the 2009 Football League Awards. Perhaps if the FLA administrators had done their research, they would have given it to someone else. In most regards, 3PW has been ineffective in accomplishing its goals and, as several studies report, has actually encouraged sabotage and decreased stadium attendance. Further analysis shows that leagues actually become less competitive due to the rule change. This is not to say 3PW affects a league’s inherent quality, but rather that it makes teams’ differences more noticeable in table rankings. If the FA really wants to avoid the same winners and losers each year, then they’ll need to reconsider 3PW.

Points of Interest

  • It is worth nothing that if 3PW encourages team to shed the “win at home, draw away” mentality, then it may have value. Indeed, analysis of Portuguese league data reveals a reduction in home field advantage, albeit at the cost of league competitiveness12. Similar results were obtained by looking at German league data.1113  It’s not a bad metric, but if home field advantage is how we gauge entertainment, then Barcelona is the most boring team in the world.14
  • My analysis, despite its strong results, sometimes comes from a relatively small sample size, ranging from 30 to over 1000 observations depending on the calculations. It would be worth reviewing my conclusions from a larger database, preferably of leagues from outside the UK.
  • All my data is organized and available for download here. Part of the reason I decided to start a blog was to make football data access easier for the general public. It took me months to download everything and organize it, so please don’t waste your time doing the same thing. I highly encourage anyone who found this post interesting to check out my data and see what they can do with it.
  • You can find a more in-depth explanation for my methodology here, along with some cool graphs to consider.
  • Please let me know if you find any mistakes in my approach or if you feel additional data would be of particular value in analyzing the impact of 3PW. You can reach me at
  • Special thanks to Jonathan Wilson of the Guardian for inspiring this post.


1 Ask a FIFA executive how to solve a problem, and he’ll give you previously discredited answer.

2 Gardiner, Simon (2005). Sports Law. London: Routledge Cavendish. pp. 73–74. ISBN 1-85941-894-5.

4 Chris Anderson, David Sally, The Numbers Game: Why Everything You Know About Soccer Is Wrong, 2013

6Bas¸ levent, C., & Tunal (2001). Incentives and outcomes in football: The effect of the three-points system and home advantage on outcomes. Retrieved Febuary 21, 2008, from

7 Dilger, A.,&Geyer, H. (2009). Are three points for a win really better than two? A comparison of german soccer league and cup games. Journal of Sports Economics, 10, 305-318.

8 Julio del Corral & Juan Prieto-Rodriguez & Rob Simmons, 2010. “The Effect of Incentives on Sabotage: The Case of Spanish Football,” Journal of Sports Economics, , vol. 11(3), pages 243-260, June.

9 Dilger, A.,&Geyer, H. (2009). Are three points for a win really better than two? A comparison of german soccer league and cup games. Journal of Sports Economics, 10, 305-318.

10 Garicano, Luis and Palacios-Huerta, Ignacio, Sabotage in Tournaments: Making the Beautiful Game a Bit Less Beautiful (September 2005). CEPR Discussion Paper No. 5231. Available at SSRN:

11 Dewenter, R. (2003). Raising the scores? Empirical evidence on the introduction of the three-point rule in Portuguese football. Discussion Paper, Institute of Economic Policy, University of the Federal Armed Forces, Hamburg.

12 Guedes, J. C., & Machado, F. S. (2002). Changing rewards in contests: Has the three-point-rule brought more offense to soccer? Empirical Economics, 27, 607-630.

13 Amann, E., Dewenter, R., & Namini, J. E. (2004). The Home-Bias Paradox in Football. Discussion Paper, University of Duisburg-Essen, Essen. Dilger, Geyer / A Comparison of German Soccer League and Cup Games