Media Coverage
Return to Aaron's homepage

Update: After Match 32 the 2010 World Cup tiebreaker rules will all be logically sound.


Introduction

This webpage is dedicated to the tiebreaker rules for the group stage of the 2010 FIFA World Cup as found in Article 39.5 of the official regulations. The primary issue centers around partially-unbroken three-way ties. The FIFA World Cup switched to group play in 1950, and since that time a partially-unbroken three-way tie has never occured. However, this webpage shows that such a situation can arise -- in more than one way -- and illustrates how the official FIFA rules are not entirely clear on how these situations should be handled. In particular, these situations can arise when group play leaves three out of the four teams tied on points, goal difference, and goals scored, and when the next tiebreaker separates only one of these three teams. Depending on how the rules are interpreted, these situations can lead to three different teams having arguments for why they should finish in the top two positions and advance to the next round. FIFA should clarify its position on these situations, before it faces a repeat of the 1958 World Cup where last-minute tiebreaker rules were issued while the tournament was taking place.

Before discussing specific tiebreaker rules, it is mentioned that breaking ties in round-robin tournaments is certainly not a new problem and there are many possible approaches. (For example, the group stage is quite similar in Ultimate Frisbee.) Furthermore, any team that is left behind after a multi-team tie will be disappointed, regardless of the tiebreakers used. For this reason, the primary purpose of this webpage is not to claim that one approach to breaking multi-team ties is better, or even more correct than another. Instead, the primary purpose is to examine whether FIFA's tiebreaker rules will be understood and interpreted in the same way by everyone, thereby ensuring a level playing field for all teams, and avoiding potential controversy.

Rock, Paper, Scissors

To illustrate a partially-unbroken three-way tie, let's consider a simplified example involving Rock, Paper, Scissors. In our round-robin tournament the following rules are used for determining the rankings: In this year's tournament there are three contestants. Each contestant has examined the tiebreaker rules and has decided on a particular strategy: Ron will always use Rock, Peg will always use Paper, and Sam will always use Scissors. The results of their round-robin tournament are as follows:

Tournament
Contestant Wins Rocks Papers
Ron 1 2 0
Peg 1 0 2
Sam 1 0 0

Ron Rock Peg Paper Sam Scissors 
Sam Scissors Ron Rock Peg Paper 

What are the final standings for this tournament? All three contestants won a single match, so all three are tied by rule (a). Since rule (b) is based on the number of Rocks used, then Ron finishes in first-place from using 2 Rocks (above in bold), while Peg and Sam remain tied. However, determining second-place is not as simple. Roughly speaking, we have a partially-unbroken three-way tie, and a discrepancy can arise depending on whether we continue to break the initial three-way tie or instead break the newly formed two-way tie. In the first interpretation, an impartial judge would proceed by applying rule (c). In this case, Peg would finish in second-place based on using 2 Papers (in bold). That is, the final standings would be:
  1. Ron.
  2. Peg.
  3. Sam.
In the second interpretation, an impartial judge may proceed by applying the tiebreaker rules from the beginning, this time using only the remaining two contestants. In other words, an impartial judge may view the current situation as the following:

Two-Way Tie
Contestant Wins Rocks Papers
Peg 0 0 1
Sam 1 0 0

Sam Scissors 
Peg Paper 

In this case Sam has 1 win (in bold), and since there are no other matches between these contestants, then Sam would finish ahead of Peg by rule (a). That is, the final standings would be:
  1. Ron.
  2. Sam.
  3. Peg.
Since there are no additional instructions, the provided tiebreaker rules are ambiguous. A similar situation can arise using the FIFA tiebreaker rules with two important differences. The first difference is that the second-place finisher depends only on whether the remaining situation is viewed as a partially-unbroken three-way tie or as a newly formed two-way tie. In other words, the rules do not need to be applied in a different order to have two different second-place finishers. The second difference is that the wording surrounding the FIFA rules suggests using the former approach (continuing to break a three-way tie). However, the regulations stop short of explicitly mentioning the issue or being completely clear on how it should be handled.

FIFA Rules

The FIFA World Cup begins in eight separate groups. Each group includes four teams, and the teams in each group play a round-robin tournament with the top two finishers advancing to the next round. The tiebreaker rules involve points, goal differential, and goals scored, where three points are awarded for each win and one point is awarded for each draw. The official rules in Article 39.5 are as follows:

"The ranking of each team in each group will be determined as follows: If two or more teams are equal on the basis of the above three criteria, their rankings will be determined as follows:
Notice that the above rules are actually quite simple. The first three rules separate teams based on points, goal difference, and then goals scored. These initial three rules a)-c) are then repeated as rules d)-f) for any teams that remain tied. Finally, the last rule g) resolves ties that cannot be broken by using these three criteria. To test the rules, consider the following scenario for Group C in the 2010 World Cup:

Group C Results
Country Pts W D L GF GA GD
Algeria 6 2 0 1 7 4 +3
USA 6 2 0 1 7 4 +3
England 6 2 0 1 7 4 +3
Slovenia 0 0 0 3 2 11 -9

Algeria2  USA5  England4  Algeria3  USA2  England3 
Slovenia1  Slovenia1  Slovenia0  USA0  England0  Algeria2 

(Pts = points, W = wins, D = draws, L = losses, GF = goals for, GA = goals against, GD = goal differential)

Notice that the scores of each match are all reasonable, so the above scenario could certainly occur. What are the final standings for this group? By applying rule a) it is clear that Slovenia finishes the group in fourth-place since it has 0 points (in bold above). Rules b) and c) do not separate the remaining three teams. Therefore, the remaining three-way tie must be broken starting from rule d), and the teams concerned are Algeria, USA, and England. The results of the group matches played between these three teams appear below:

Three-Way Tie
Country Pts W D L GF GA GD
Algeria 3 1 0 1 5 3 +2
USA 3 1 0 1 2 3 -1
England 3 1 0 1 3 4 -1

Algeria3  USA2  England3 
USA0  England0  Algeria2 

Each team obtained three points within these matches, so the teams remain tied after applying rule d). Since Algeria's +2 goal difference (in bold) is better than USA and England's goal difference of -1, then rule d) implies that Algeria finishes first in the group. However, determining the second-place team is more subtle due to the ambiguity of the teams concerned.

On one hand, the complete rankings of Algeria, USA, and England have not been fully determined, so one could argue that the teams concerned still include these three teams. In this interpretation, we continue to rank all three teams, and so the relevant matches include the three matches given above. Using this interpretation, England beats out USA by rule f) since England scored 3 goals (in bold) to USA's 2 goals. That is, if one continues to break the three-way tie then the final standings are
  1. Algeria.
  2. England.
  3. USA.
  4. Slovenia.
On the other hand, the ranking of Algeria has been determined, so one could also argue that the teams concerned include only USA and England. In this interpretation, we continue by ranking the two teams, and so the only relevant match is between USA and England:

Two-Way Tie
Country Pts W D L GF GA GD
USA 3 1 0 0 2 0 +2
England 0 0 0 1 0 2 -2

USA2 
England0 

Using this interpretation, USA would finish in second-place by rule f) since it scored 2 goals (in bold) while England scored 0. Alternatively, rule d) has higher-precedence than rule f), and since USA beat England then it finishes in second-place based on its 3 points (in bold) among the two teams concerned. That is, if one breaks the two-way tie then the final standings are
  1. Algeria.
  2. USA.
  3. England.
  4. Slovenia.
Which one of these two interpretations is correct? When reached via email, the FIFA Media Department replied that There's a three-way tie to break. You do it as a one operation and not in different stages. The teams concerned are always all the teams involved in the tie-break. In other words, the FIFA Media Department interpreted the teams concerned to be all three teams. However, when Canadian Soccer Association's Director of Referees Joe Guest was presented with this scenario by the Times-Colonist, he interpreted the teams concerned to be USA and England. Thus, the two parites differed on whether USA or England would advance.

Stepping back, the real problem is that rules d)-g) appear to have been written with only two- or three- or four-way ties in mind, and without consideration for partially-unbroken three-way ties. The resulting ambiguity would allow FIFA to logically justify either of the above interpretations, and this could open the door to protests and questions of impartiality. (The analogous scenario given to FIFA and CSA differed from the above scenario only in the specific countries involved. The specific countries involved were upcated to reflect the actual teams appearing in Group C.)

Augmenting the Rules

Currently FIFA has not acknowledged that there is any ambiguity in their rules. However, if they change their mind, then how can the rules be clarified? FIFA could begin by looking at the tiebreaker rules used by the NFL. When determining the two Wild-Card teams in each conference, the official NFL rules include the following clarification: When the first Wild-Card team has been identified, the procedure is repeated to name the second Wild-Card.

With respect to the previous discussion, the NFL changes the teams concerned and restarts its tiebreaker rules from the beginning whenever a tie is partially-unbroken. (This is directly opposite to how FIFA's Media Department interpreted their own tiebreaker rules.) FIFA should learn from the NFL and add a similar clarification to their tiebreaker rules. Whenever a tie is partially-unbroken, FIFA needs to specify: i) the next tiebreaker rule to apply, and ii) the teams concerned when applying this rule.

On the topic of improving the FIFA rules, one can also observe that rules d)-f) cannot be used to break a four-way tie. In particular, given a four-way tie, rules d)-f) are simply repeats of rules a)-c). Furthermore, points, goal difference, and goals scored provide are comparisons in a two-way tie. Therefore, rules d)-f) only need to be applied to three-way ties. This simplification should be used when FIFA is rewriting its rules.

In some situations, points, goal difference, and goals scored cannot be used to break ties. (For example, every match in a group could end in a 1-1 draw.) FIFA should consider adding the first goal of a match into their set of tiebreakers. In this tiebreaker, teams are compared based on the number of times the scored the first goal in a match. This additional tiebreaker would lower the probability of teams having to draw lots. Furthermore, it would reward teams for scoring the first goal of a match, and this could lead to more aggressive and entertaining play during the early portions of a match.

Drawing Lots

While the primary purpose of this webpage has already been accomplished, it is also interesting to point out that the FIFA Media Department's stance also leads to a somewhat unsatisfying ending in another situation that could arise quite easily. Consider the following scenario for Group H in the 2010 World Cup:

Group H Results
Country Pts W D L GF GA GD
Spain 9 3 0 0 4 1 +3
Switzerland 3 1 0 2 2 3 -1
Honduras 3 1 0 2 2 3 -1
Chile 3 1 0 2 2 3 -1

Spain2  Spain1  Spain1  Switzerland2  Chile1  Honduras1 
Chile1  Switzerland0  Honduras0  Honduras1  Switzerland0  Chile0 

Spain finishes first by rule a) (in bold). Since the remaining teams have the same goal difference and the same number of goals scored, then the remaining positions are determined by the matches involving these teams:

Three-Way Tie
Country Pts W D L GF GA GD
Switzerland 3 1 0 1 2 2 0
Honduras 3 1 0 1 2 2 0
Chile 3 1 0 1 1 1 0

Switzerland2  Chile1  Honduras1 
Honduras1  Switzerland0  Chile0 

Since the teams have the same number of points, and the same goal difference, then the teams remained tied after applying rule d) and e). Chile has a lower number of goals scored than the other two teams, so it finishes in fourth-place by rule f) (in bold). Given the FIFA Media Department's earlier response, it seems most likely that they would proceed to rule g) and draw lots. One one hand, it does not seem appropriate to draw lots between all three teams, since the Chile should finish in fourth-place by rule f). On the other hand, it does not seem appropriate to draw lots between Switzerland and Honduras due to Switzerland's victory over Honduras. That is, Switzerland would beat Honduras if the situation was treated as a two-way tie.

Two-Way Tie
Country Pts W D L GF GA GD
Switzerland 3 1 0 0 2 1 +1
Honduras 3 1 0 0 1 2 -1

Switzerland2 
Honduras1 

In other words, it is unsatisfying to draw lots between three teams because the three-way tie was broken, and it is unsatisfying to draw lots between two teams because the two-way tie could also be broken. Again, this problem arises because we have a partially-unbroken three-way tie, and FIFA does not explicitly address these types of situations.

Media Coverage

Details of this story have appeared in print, radio, and television:
Return to Aaron's homepage