Mathematically Informed Opinions from a Former Referee

The Germany-Sweden World Cup match this past Saturday was one of the most dramatic, most impressive, and most entertaining international soccer matches I’ve seen in years. The tension was incredible, the stakes could not have been any higher in an opening round match, and it served to highlight what is, in my opinion, the absolute worst rule in the entire FIFA Laws of the Game.

When I passed my test to become a FIFA certified “black badge” referee through USSF in 1988, I was the youngest person in the state of Georgia to ever pass the test. I spent the next six years refereeing youth recreational league games, travelling team games (graded “Premier” and “Classic” under the old system), adult league games, and ADASL games, which constitute a kind of an adult “semi-pro” league for our region, with players from colleges and minor leagues sprinkled into the general adult player pool. I logged hundreds of games, in a fantastic variety of situations, and accumulated some stories from the experience that vary from heartwarming to insane. Soccer can be a very passionate, excruciating, competitive, and occasionally quite violent sport. And it was during my tenure that FIFA made a change to their interpretations of the Laws of the Game that took a bad problem, and in my opinion made it worse.

Some Background

Soccer at all levels, but particularly at the professional and international level, had a real problem in the 1980s and prior with something called “professional fouls.” Because goals are hard to come by in soccer, it became common practice for a defender to foul an attacking player who had a clear and obvious goal scoring opportunity, because whatever the punishment for the foul was, it couldn’t be worse than yielding the shot. You see this sort of thing happen in other American sports all the time — fouling someone in the act of shooting to prevent the shot in basketball, or interfering with a pass in football if a defensive back is beaten badly on a route. These are common, but don’t have near the impact in those sports because the scoring is so much higher. This was a big problem in soccer.

Prior to the 1980s, and situationally throughout that decade, the penalty for a professional foul denying an obvious goal scoring opportunity (called “DOGSO”) was a direct free kick from the point of infraction, or a penalty kick if it occurred inside the box, and a caution (“yellow card”) to the offending player. If the player had been cautioned for any offense previously, the caution would be upgraded to an ejection (“red card”) and the team would be forced to play a man short for the remainder of the game. Through the 1980s, leagues individually adopted policies of going straight to a “red card” for professional fouls DOGSO, and in 1990 the interpretation was adopted for World Cup play. It has been effectively a universal ruling in soccer ever since.

The Power of Red

Red Card offenses are the most grievous offenses in soccer, and at the upper levels can severely impact a team’s ability to win a game. This impact is immense, and for numbers driven fans, can actually be calculated. Here’s a fascinating attempt:

There are other attempts at this math, but let’s use that one for argument’s sake, because it’s simple and approachable. Based on Mark Taylor’s statistical analysis at his blog, “The Power Of Goals,” he anticipates for a typical English Premier League game, playing a man down for an entire match means a typical team would score about 0.5 less goals, and the opposing team would score approximately 0.95 more goals. A net difference of 1.45 goals on the match, but amortized. A player getting sent off with 10% of the game remaining (say the 81st minute) might have a net statistical impact of 0.14 goals on the game’s bottom line, but a player sent off 12 minutes in, as should have probably happened this past Saturday when a German defender took a Swedish player down in the box, is basically worth 1.25 goals on the bottom line, to say nothing of the very likely chance (80% or more) that Sweden also scores on the awarded penalty kick.

Here’s the play:

Here is a typical media reaction piece to the play:

Most of the scuttlebutt in the media is about whether the Video Assistant Referee should have overturned the no-call, but I think the media is missing the deeper picture, which is what the referees are thinking. No unbiased soccer aficionado without a vested interest in the outcome of that game will disagree that the correct call, in that situation, puts Germany in a wretched position, and if the red card is issued it basically seals Germany’s fate. And that, I contend, is the actual problem.

The Game from Center

Managing the game as a referee is a tremendous obligation. The field is larger than an American football field, the action never stops except for fouls or when the ball enters touch, (soccer lingo for “out of bounds”) and there is one referee. This “center” referee, is ultimately responsible for every call and every aspect of the game including timekeeping. He or she has two linesmen, now known more politically correctly as “assistant referees,” each of which is primarily responsible for simply informing the referee of out of bounds and offsides on their side of the field. They can also inform the center referee of fouls in the field of play, via flag signals, but their official power on the field is limited to simply an advisory capacity by the architecture of the rules. There’s only one whistle, and that whistle is paramount.

In a properly managed game, the teams and fans both leave the stadium feeling as if the game was fair, and the scales of the outcome of the game were not tipped by the whistle.

That power entails incredible responsibility, not only to ensure that the game is called in an objectively fair manner, but that the game is “managed” properly. Part of game management involves talking to the players, settling them down when necessary, informing them of when their potential “persistent infringement” of the rules may soon provoke a yellow card, managing time wasting tactics, and a variety of other aspects. In a properly managed game, the teams and fans both leave the stadium feeling as if the game was fair, and the scales of the outcome of the game were not tipped by the whistle. Good referees in soccer are constantly talking to the players. And deeply connected soccer fans, as well as referees, can notice this game management incentive leak into the number and nature of fouls called throughout the game. A borderline foul that might not have been whistled in the first half might get called routinely towards the end of the game if the players have started getting more violent and chippy. And in turn, players who perceive unfairness in the calls, might end up getting more violent and chippy out of frustration, so sometimes a sort of feedback loop arises where referees “lose control of the game.” Almost every game with fights or major confrontations exhibits this “loss of control” from the center ref. Managing this control is what separates bad from good referees. Soccer referees are less robots applying the Laws of the Game mechanically, and more artists using the framework of the rules to ensure the game feels fair to all involved, painting a canvas with the rules as their brush, and the players as their palette, while influencing the results as little as possible.

The Failures of “No Tolerance”

As we’ve seen above, the red card is a severe, almost nuclear option for referees, because of the severe benefits a team gains from a permanent man advantage. If a referee drops that nuclear bomb on a team early on, he or she is deciding the game with the whistle. Referees know this, and so do the players. The problem of diving, players attempting to draw weak fouls and make them seem egregious, is driven by this nuclear option. If a player can “simulate” a red card offense and the referee, who is alone on a giant field managing a continuous run of play, can’t differentiate the simulation, then that dive could be worth up to perhaps 1.45 goals in a game outcome that’s not uncommonly decided by one goal or less. If the dive also elicits a penalty kick, let’s go ahead and tack on “0.8 more goals” to the total, by the numbers. A dive can win a game. But in doing so, the referee has dictated the outcome with the whistle, which means the referee has failed in his ultimate duty to facilitate the game that everyone wants to watch and play.

When FIFA opts for a “no tolerance” policy, and attaches such an outcome altering penalty to their no tolerance rule, they tie the referees hands. The ref now must basically choose between two options in the first perhaps two seconds after the incident — decide the outcome of the game with the whistle or let it ride.

When Szymon Marciniak, a very talented center referee from Poland with prior World Cup and UEFA Cup experience, choked on his whistle for that play, it was explicitly the absolute wrong call, whether he issues a yellow or a red card for the offense. But there’s some question about whether it was implicitly the right one, based on the spirit of the incredible task he was assigned, and the weight on his shoulders, with the potential red card implication looming. That call would have assuredly bounced the defending world champion German national squad from the World Cup after only two games in-group — something that has never happened in the history of the Cup. He was put into a terrible position by a decades old bad ruling by FIFA.

A Better Law

Soccer is a deeply international sport, attached intrinsically to traditions in its laws, and is extremely averse to change. Its laws ride heavily on the premise of sportsmanship by all participants. Unsportsmanlike behavior itself is a caution-able (“yellow card”) offense. But when you apply game theory to the laws, and the likely impact of those laws, you see better ways of getting things right. What soccer really needs, to ameliorate these sorts of predicaments, is another card.

But when you apply game theory to the laws, and the likely impact of those laws, you see better ways of getting things right.

Let’s call it an orange card. It’s half way between a yellow and a red. It’s used for DOGSO situations and simulation situations. The player is sent-off, not to return, as with a red card, but the team may replace the offending player after a predetermined duration, perhaps 20 minutes. By our mathematical analysis above, 20 minutes of man advantage is “worth” somewhere around a third of a goal, which combined with the likelihood of Sweden’s penalty kick gives them a clear scoring opportunity commensurate to the opportunity Germany deprived them of, with the foul. Had Mr. Marciniak had the opportunity to issue this “orange card” option in the game this past Saturday, the implicit weight of the decision would have been relieved, and the call would have been much easier to make. The Swedes would have gotten their penalty kick attempt, likely gotten their goal, and the Germans would have been back to full strength by halftime so the game could run its course properly without the weight of it being decided entirely by the whistle.

Will FIFA ever move to something like this? I would call the chances somewhere between “doubtful” and “impossible.” But I know I would like it.

Especially if I was still refereeing.