The Dreaded 6-6-6-0 Round-Robin Group Scenario

In a four-team single round-robin schedule, a team that wins its first two matches is not guaranteed a top-two spot in the group under the rules typically used by FIFA and CONCACAF. There is a scenario where three teams in a group can win two matches each and lose a match each, resulting in the points being 6-6-6-0.

[Notes: (1) This post was inspired by some confusion on my part with regards to whether or not the USA’s U-20 WNT’s two victories in their first stage guaranteed them a spot in the CONCACAF Women’s Under-20 Championship semifinals. (2) The tie-breaker rules used by CONCACAF and FIFA are somewhat ambiguous, so there is room for alternate interpretations. (3) Due to the possible ambiguity and some unclear language, especially in CONCACAF’s rules, this article should be treated as a working draft, which means  that the conclusions and explanations expressed in this article are based on my best understandings of the rules. ]

In the case of the USA’s U-20 WNT, who are currently playing in the CONCACAF Women’s Under-20 Championship, they won their first two matches, and were the first team in their group to reach six points. At the end of the USA’s match second match, which was against Cuba, the two other teams in the group, Guatemala and Panama had not played yet. Panama was sitting on 3 points, as it defeated Cuba 2-1 in its first match, while Guatemala had zero points as it was defeated by the USA 6-0.

At the end of the USA’s match versus Cuba, the group standings were: USA, 6 points; Panama, 3 points, Guatemala, 0 points, and Cuba, 0 points. If in the second match of the night, Guatemala had beaten Panama, then those two teams would level on points with 3 apiece going into the final match day. If the final matches had ended with Guatemala winning over Cuba and Panama winning over the USA, then Guatemala, Panama, and the USA would have been level, with 6 points apiece.

In that three-way tie scenario, it would be mathematically possible for the USA to not be a top-two team under both FIFA’s and CONCACAF’s normal tie-breaking rules, which are not uniform. However, as the USA had a sizeable goal differential cushion going into the final matchday, the possibility of these mathematical scenarios would have been very unlikely.

The second  half of this article goes into more detail about CONCACAF’s and FIFA’s tie-breaking rules, as well as the 6-6-6-0, scenario.

(There are other scenarios which produce three- and four- way ties. I’ll likely post some articles about those and other round-robin points scenarios permutations at a later time.)

* * *

Here are the tie-breaker rules for the current CONCACAF Women’s Under-20 Championship (PDF file, page 20):

5. At the end of group play, if two or more teams are equal on points (including ties among third place teams), the manner in which teams will advance to the next round will be resolved as follows and in the order indicated:

a. Greater number of Points in matches between the tied teams.
b. Greater Goal Difference in matches between the tied teams (if more than two teams finish equal on points).
c. Greater number of goals scored in matches among the tied teams (if more than two teams finish equal on points).
d. Greater Goal difference in all group matches.
e. Greater number of goals scored in all group matches.
f. Drawing of lots.

Note: The CONCACAF rules memo does not directly specify how points are awarded to teams, so I will be assuming that this is the standard 3 points for a win, 1 points for a draw, and zero (no) points for a loss. The only mention of awarding points in the rules memo is in relation to forfeiture scenarios. (Compare the FIFA rules, linked below, which do specify how points are awarded.)

This is significantly different than the typical FIFA group ranking criteria, which only uses how the tied teams directly fared against each other (head-to-head results) as secondary factors. For example, here are the rules for the 2012 Olympics football competition (PDF, page 41), which are also the same for this year’s U-17 and U-20 Women’s World Cups (PDF, page 32):

29.5. The ranking of the teams in each group shall be determined as follows:

a) greatest number of points obtained in all group matches;
b) goal difference in all group matches;
c) greatest number of goals scored in the 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 all group matches between the teams concerned;
e) goal difference resulting from all group matches between the teams concerned;
f) greatest number of goals scored in all group matches between the teams concerned;
g) drawing of lots by the FIFA Organising Committee.

Note: For the purposes of this discussion, I am applying both the FIFA and CONCACAF rules tie-breakers will be applied in a single operation, which seems to be the preferred interpretation at least for the FIFA rules. (see the Victoria Post news article and the related webpage, linked below).

In other words, if three or four teams are tied, one tie-breaker criteria might separate out  the top team, but still leave two or three teams tied. The next tie-breaker criterion in the list will be used to separate those teams, if possible. If that does not separate the two teams, the next criterion will be used.  Another interpretation is that once the tie-breaker criteria separates out a team, the tie-breaker criteria would be reapplied to the teams that remained tied.

For more on the possible ambiguity, see this this Victoria Post (Canada) article about a post-doc graduate student who raised the issue before the 2010 Men’s World Cup, as well as the student’s website which explains the ambiguity in greater detail.

Comparing CONCACAF’s and FIFA’s Rules: Some Examples

CONCACAF’s and FIFA’s tie-breaking rules can lead to different results in the same scenario.

Example A — Two Tied Teams with a Head-to-Head Draw :
CAN: 7 points, +10 goal differential, 10 goals scored
MEX: 7 points, +6 goal differential, 8 goals scored
Head-to-Head Match: CAN 1 – MEX 1.

Under FIFA’s rules, the first tie-breaker for teams tied on points is overall goal differential, so Canada would be ranked ahead of Mexico as Canada has a +10 goal differential versus a +6 goal differential for Mexico. However, under CONCACAF’s rules, the first tie-breaker is “number of Points in matches between the tied teams,” which in the case of two teams is the result of their head-to-head match. In this example, that match was a draw, so Canada and Mexico would be even on head-to-head points earned and head-to-head goals scored. The next criteria is overall goal differential, which would be the decider, in this case, for Canada.

Example B — Two Tied Teams with a Head-to-Head Non-Draw :
CAN: 4 points, +10 goal differential, 10 goals scored
MEX: 4 points, +6 goal differential, 8 goals scored
Head-to-Head Match: CAN 1 – MEX 2.

In this example, Canada would rank higher under FIFA’s rules (due to their higher overall goal differential), but not under CONCACAF’s rules, as Mexico earned 3 points to Canada’s 0 points in their head-to-head result, as Mexico won that match.

A 6-6-6-0 Scenario

Here is a hypothetical scenario, based partially on the current CONCACAF Women’s Under-20 Championship (fictional results are italicized), which I am using (1) to show how earning six points after two matches does not mathematically guarantee a team a top two place in its group, and (2) to show how applying the FIFA rules and CONCACAF rules to the same scenario can result in very different outcomes.

The Scenario (#1):

Match Day 1: USA 6, Guatemala 0. Panama 2, Cuba 1.
Match Day 2: USA 6, Cuba 0. Guatemala 2, Panama 1.*
Match Day 3: USA 0, Panama 6.* Guatemala 13, Cuba 0.*

*The actual results were: GUA 2 -PAN 1; GUA 5 -CUB 2; and the USA-PAN is TBD.

Group standings after the second match day:
USA: 6 points, +12 goal differential, 12 goals scored
PAN: 3 points, +0 goal differential, 3 goals scored
GUA: 3 points, -5 goal differential, 2 goals scored
CUB: 0 points, -7 goal differential, 1 goals scored

Scenario #1 — Final group standings (FIFA rules):
GUA: 6 points, +7 goal differential, 15 goals scored
USA: 6 points, +6 goal differential, 12 goals scored
PAN: 6 points, +6 goal differential, 9 goals scored
CUB: 0 points, -20 goal differential, 1 goal scored

Under FIFA’s criteria, Guatemala would win the group as it has the highest goal differential among the three tied teams. The USA would take the second spot as its goal differential is higher than Panama’s.

However, under CONCACAF’s rules, when teams are tied overall on points, the next tie-breaker is how those teams fared amongst each other. In other words, the tied teams are there own mini round-robin group. In this case, the relevant matches are:

USA 6, Guatemala 0.
Guatemala 2, Panama 1.
USA 0, Panama 6.

And, the mini-group table would be the following:

USA: 3 points, +0 goal differential, 6 goals scored.
PAN: 3 points, -5 goal differential, 7 goals scored.
GUA: 3 points, -5 goal differential, 2 goals scored.

Under CONCACAF’s criteria, the USA would win the group, and Panama would be the second-placed team, with Guatemala (who would have won the group under FIFA’s rules) is out of the tournament.

Scenario #1 — Final group standings (CONCACAF rules):
USA: 6 points, +6 goal differential, 12 goals scored
PAN: 6 points, +6 goal differential, 9 goals scored
GUA: 6 points, +7 goal differential, 15 goals scored
CUB: 0 points, -20 goal differential, 1 goal scored

On the last group match day, if Panama would have beaten the USA by even a larger margin, say 12 goals to nil, then the mini-group table would be as follows:

PAN: 3 points, +1 goal differential, 7 goals scored.
GUA: 3 points, -5 goal differential, 2 goals scored.
USA: 3 points, -6 goal differential, 6 goals scored.

In this scenario, under the CONCACAF rules, the USA would be out of the championship while Guatemala would remain in.

Scenario #2 — Final group standings (CONCACAF rules):
PAN: 6 points, +12 goal differential, 9 goals scored
GUA: 6 points, +7 goal differential, 15 goals scored
USA: 6 points, +0 goal differential, 12 goals scored
CUB: 0 points, -20 goal differential, 1 goal scored

The result would also be the same under FIFA’s rules.