Tie breaking in association football championships

Question

I'm pretty sure the algorithm established by FIFA in order to rank teams during 2014 World Cup group stages is ambiguous for the case of three or more teams having equal number of points.

The rule is the following:¹

a) greatest number of points obtained in all group matches;

b) goal difference in all group matches;

c) greatest number of goals scored in all group matches.

If two or more teams are equal on the basis of the above three criteria, their rankings shall be determined as follows:

d) greatest number of points obtained in the group matches between the teams concerned;

e) goal difference resulting from the group matches between the teams concerned;

f) greater number of goals scored in all group matches between the teams concerned;

g) drawing of lots by the FIFA Organizing Committee

Say three teams, call them X,Y and Z, are equal based on criteria a), b), c) and d). Then assume step e) puts Z above the other two who still need breaking apart. In other words, counting in only the games involving X, Y and Z, all three teams have equal number of points but Z has a higher goal difference than X and Y, who are equal from that perspective.

This is where it becomes unclear to me. Imagine that Y beat X the one time they played each other. Then, although step d) does not help in ranking the three teams when considering the games involving them, it does separate X and Y when ignoring Z's games. In simpler words :

Z=Y=X for step d) (i.e. when based on all games featuring any two of them)

Z>Y=X for step e)

Y>X for step d) (i.e. when based only on Y vs X, hence Y is better off when ignoring the outcome of Y vs Z)

Then what happens ?

Options are :

1. Having already applied steps d) and e) to all three teams without obtaining a full determination of their rank, we move forwards to step f)
2. Since step e) reduced the number of teams involved in this process, the algorithm is reinitiated at step d)

If we move to step e), do we still count goal difference for X and Y in games involving all three teams since they initiated the algorithm or only the game involving X and Y.

If you are about to comment that steps d) and e) yield the same result when only taking into account the match between X and Y, then imagine that it's a 2 legged championship and that they both win a game with a nonzero aggregate or else that we have four teams of which only one was moved above the other three by step d) and that we are in a group with 5 or 6 teams (e.g. qualifiers).

I can't find the answer anywhere, but this must have happened once in history surely. This is just 2014 World Cup but I've followed football for a while and the rules have always been similar to these ones.

¹ See Wikipedia or FIFA website (Internet Archive)

Answer 1

Section 50.5 (a) - (c) states that all teams are first ranked by

• points, then
• goal difference, then
• goals scored.

If any teams are level after applying all three criteria in this order, section 50.5 (d) - (f) states that the matches played between the equal teams are then ranked by (once again):

• points, then
• goal difference, then
• goals scored.

The simplest way to do this would be to construct a league table from the matches played between the level teams. As with a full league table used in (a) - (c), this reduced table would be ordered on points, then goal difference, then goals scored.

In your example:

Z=Y=X for step d) (i.e. when based on all games featuring any two of them)

Z>Y=X for step e)

Y>X for step d) (i.e. when based only on Y vs X, hence Y is better off when ignoring the outcome of Y vs Z)

the third step is the error. The procedure states that (d) - (g) are applied to all teams that are

equal on the basis of the above three criteria [(a) - (c)]

It does not state that a level team's matches are excluded with the process restarting if they are ahead on one of the criteria. By restarting the process with just two of the teams at (d), you would not be including all teams level on (a) - (c), and this leads to an erroneous ambiguity.

In this example (if it is even mathematically possible), goals scored in matches between X, Y, and Z would be used to separate X and Y, since X, Y and Z are all level on the basis of (a) - (c).

As an aside, if all criteria are exhausted, in accordance with section 50.5 (g), lots will be drawn to separate the teams.