Are You Blind, Ref? Yes, in a Sense

At the end of each soccer game, referees add extra time to the match to make up for time spent dealing with injuries, substitutions, and other interruptions to the game.

Fans expect this process to be fairly scientific. But many referees do not track the amount of time that play is stopped, and the rules afford them discretion over the amount of extra time added to the end of the game. So Canice Prendergast, W. Allen Wallis Professor of Economics and Booth Faculty Fellow, and Luis Garicano and Ignacio Palacios-Huerta of the London School of Economics, studied this subjective decision to see if there were any systematic irregularities in the amount of stoppage time added. Before digging into the results, first step into the mind of the referee in three situations.

Situation 1: You are refereeing a game at the Estadio Santiago Bernabéu in Madrid, home to Real Madrid. Madrid is ahead by three goals as the regular 90 minutes of play expire. You and the crowd suspect the game is as good as over. The visiting team must score three goals in a few minutes of stoppage time to draw the game. You have not counted the exact amount of time play has stopped, but it was three minutes, give or take a minute or two. How much stoppage time do you add?

Situation 2: Imagine the same game, but with Real Madrid behind by one goal. More than 80,000 Madrid fans are roaring in the hope of an equalizer, and it’s entirely plausible that they might get one. If the game ended now, the crowd would be dejected or angry: they would lose their game, and it was so close. Just a minute or two more and things may turn out differently. How much stoppage time do you add?

Situation 3: Imagine the same game again, but with Real Madrid ahead by one goal. The crowd is yelling to encourage you to blow the final whistle, since the win is close at hand. Every second that the game continues could present a scoring opportunity for the visitors. How much stoppage time do you add?

On average, referees in these situations add about 2.93 minutes of stoppage time, but the average hides a wide disparity between situations. When the crowd wants the game to continue, the researchers find that referees add 35% more stoppage time than average, for 3.95 minutes of extra time. When the crowd wants the game to be over, referees add 29% less stoppage time, or 2.08 minutes, on average. Stoppage time remains around the average of 2.93 minutes when one team is far ahead.

A change in the game leads to more bias

Beyond the fact that biased decisions tend to cluster around close games, there is another piece of evidence that suggests bias. It is the result of a so-called natural experiment that occurred in the 1994–95 season. During that season, the value of wins increased relative to ties and losses in league competition: wins, losses, and ties changed from being worth two, one, and zero points to being worth three, one, and zero points, respectively. What happened? Bias increased in favor of the home team. The researchers report, “In numerical terms, the 1994–95 season saw a difference of 1 minute and 30 seconds [of stoppage time favoring the home team], which increased to almost 2 minutes by the 1998–99 season.”

When looking at the numbers alone, many initially think that referees are making these decisions intentionally in order to help their home team, but psychologists have a different explanation: the bias is a natural response to social pressure. A whole body of psychological research suggests that people do not “believe it when they see it” so much as “see it when they believe it.” The social pressure exerted by the Bernabéu crowd so deeply influenced the perceptions of the referees that they appeared to believe their decisions reflected objective judgment.

Prendergast and his coauthors find that as crowds contain more home fans, the amount of bias increases. In games with smaller crowds or more visiting fans, stoppage time bias decreases. Both findings suggest that crowd pressure, rather than the officials themselves, are responsible for the bias.

Crowds influence referees

Prendergast’s findings have been replicated across multiple leagues, but two studies in particular provide compelling evidence. A German study finds that in soccer pitches surrounded by running tracks—which insulate the pitch from the crowd—referee bias diminishes markedly.

The second study results from another natural experiment. After two Italian teams’ fans became too unruly and fought with police, the Italian government forced certain clubs to play with empty stadiums. Per Pettersson-Lidbom and Mikael Priks, two Swedish economists, documented 21 games played in empty stadiums. Home-team bias dropped so sharply it became statistically insignificant. As Professor Tobias J. Moskowitz and L. Jon Wertheim summarized in Scorecasting, “the same referee overseeing the same two teams in the same stadium behaved dramatically differently when spectators were present versus when no one was watching.”

If the researchers’ interpretations are correct, little can be done about referees’ home-team bias, so long as fans are allowed in to stadiums. However, given that most sports schedules have similar numbers of home games for each team in a league, this should not necessarily cause alarm. Provided that all teams experience bias approximately equally, the results of biased calls will average out.