Optical Trickery and Offside Calls

This world cup has been marked by beautiful games and people accusing refs of making bad calls. David Hirshey in today's NY Times OpEd section:

Several months before the 1999 Women's World Cup, I accompanied the United States national team to Brazil for a series of exhibition matches. One afternoon, at a training facility outside São Paulo, I was pressed into service to help officiate an intra-squad scrimmage. The team's coach, Tony DiCicco, handed me a red flag and told me to raise it if I detected any infractions.

The field was about 30 yards shorter than the regulation size, which is about 80 yards by 120 yards, and I was to patrol the left sideline. I was confident I could handle the assignment -- I played soccer in college and have reported on the sport for more than two decades -- but I was quickly proven wrong.

Within the first 10 minutes, the feisty American striker Tiffeny Milbrett stormed past me and hissed out of the side of her mouth: "You've already blown two offside calls. What game are you watching?"

She was right. I had missed those calls and who knows how many more. I realized I was watching world-class athletes with world-class speed and, not least, world-class guile. At this level, policing 90 yards of sideline was about 80 yards too many for me.

But is this Hirshey's fault? I will now bring to light an article published in Nature in 2000 (right around the 2000 Euro competition) that demonstrates that linesmen, who patrol the sidelines in soccer matches, can't accurately call offsides. The abstract:

In football (soccer), a player is 'offside' if he or she is closer to the goal than the last defender (excluding the goalkeeper) when the ball is passed to them. We investigated why assistant referees, who have the responsibility of judging offside, regularly make mistakes. We show that this is probably due to the angle of viewing by the assistant referee, who is frequently positioned beyond the last defender -- a viewpoint from which errors are optically inevitable.

In a field experiment, three professional assistant referees (ARs, also known as linesmen) judged 200 potential offside situations played by two élite youth football teams (Fig. 1a). The ARs made 40 errors.

So why are so many mistakes made?

One explanation for these errors is that the AR cannot see passer and receiver simultaneously: this causes the AR to shift his gaze from passer to receiver and so make judgements a split-second after the moment of passing -- long enough for the receiver to have gone past the last defender and to appear offside1. We found, however, that this is an unlikely explanation for these errors, because an AR equipped with a head-mounted camera showed no shift of gaze from passer to receiver.

As is the case with many studies, our initial assumptions are incorrect when the empirical data is analyzed.

In this diagram the defenders are red arrows the attackers are blue circles. Because of the angles, refs who are positioned AHEAD of the last defender often misinterpret angles.

In 179 situations, the assistant referee was positioned beyond the last defender (mean, 1.18 m; s.d.=0.94). In Fig. 1b, the 'outside' attacker is not offside. However, when attacker and defender are projected onto the AR's retina, the image of the attacker is just to the right of that of the defender. This means that the attacker is perceived as being in front of the defender, prompting the AR to wrongly raise his flag to call offside (flag error, FE). By contrast, in Fig. 1c the outside attacker is offside. But the AR will perceive attacker and defender as being in line, and so keep his flag down (no-flag error, NFE).

If these ideas are correct, then, when the attacker goes outside the defender (Fig. 1b), more FEs than NFEs should occur when the players are on the far side of the pitch from the AR, whereas the converse would be expected to occur when they are close to the AR ( Fig. 1). In contrast, when the attacker goes inside, more NFEs than FEs should occur far from the AR, and more FEs than NFEs should occur near the AR. This also holds for judging offside in the middle zone ( Fig. 1c): when the attacker goes right, NFEs are expected, and when left, FEs.

And as with all good studies, they then measured the frequency of flag errors and no-flag errors for plays near and far from the linesman, the data matched their predictions.

So if you are an attacker, it's best to position yourself between the linesman and the defender, thus increasing the number of NFEs and decreasing the number of FEs. If you are a defender the reverse is true. That is, if you want an unfair advantage ...

ref:
Raôul R. D. Oudejans, Raymond Verheijen, Frank C. Bakker, Jeroen C. Gerrits, Marten Steinbrückner, Peter J. Beek
Errors in judging 'offside' in football
Nature (2000) 404:33-33