Going into the final six matches of the group stage in the women’s soccer tournament at the Paris 2024 Olympics, only the United States Women’s National Team and Spain have secured a spot in the knock-out phase. Six slots have yet to be determined and none of the other ten teams have been mathematically eliminated.
Please note that the following analysis is contingent on Canada’s 6 point deduction being upheld. FIFA’s decision has been appealed to the Court of Arbitration for Sport and a ruling on the matter is expected on Wednesday, July 31st.
Sections in this Post:
Ranking Criteria
The ranking criteria and tie-breakers are specified in Article 15 of the regulations for the Olympics tournament (PDF).
In the below sections, I have included a few mathematical asides that include simple formulas for calculating rank coefficients for easily comparing teams. Using these rank coefficient greatly simplify comparison formulas in spreadsheets such as Microsoft Excel and Google Sheets.
Intra-Group Rankings
In each group, teams are ranked primarily according to the following criteria: (1) Points; (2) Goal Difference; and (3) Goals Scored.
* * *
Mathematically, a simple rank coefficient can be calculated using the following formula:
RankCoeff = Points + (Goal Difference * 0.001) + (Goals Scored * 0.000001)
Example: For a team that won one match, lost one match, and drew one match, while having a +1 goal difference and scoring five goals, their rank coefficient would be 4.001005.
* * *
If two or more teams are tied, those teams are compared based only on the matches involving those teams. If, after that comparison, any of those teams are still tied, an additional tie-breaker is the Team Conduct Score, which involves applying a points system to the number of yellow and red cards given to each team in all of their group matches.
The criteria for comparing the tied teams is as follows: (1) Points in their respective match(es), (2) Goal Difference in their respective match(es), and (3) Goals Scored in their respective match(es), along with overall Team Conduct Scores.
The Team Conduct Score points are calculated per match and only one of the below deductions “shall be applied to a player or a team official” per match:
- Yellow Card: -1 point
- Indirect Red Card (two yellow cards in a match): -3 points
- Direct Red Card: -4 points
- Yellow Card plus a Direct Red Card: -5 points
* * *
Mathematically, a rank coefficient for comparing the still-tied teams can be calculated using the following formula:
AdjRankCoeff = Adjusted Points + (Adjusted Goal Difference * 0.001) + (Adjusted Goals Scored * 0.000001) + (Team Conduct Score * 0.000000001)
Example: If a team, that was tied with two other teams, lost of one of their respective matches and drew in the other match, while having a -2 goal difference, scoring 3 goals, and had an overall Team Conduct Score of -4, their adjusted rank coefficient would be 0.998002996.
* * *
Regarding what matches are involved in this secondary comparison:
- If two team are tied, then only the respective match between the two teams is used.
- If three teams are tied, the matches involving the fourth team of the group are ignored.
- If four teams are tied, all of the group matches would be used, so the Team Conduct Score is the only tie-breaker.
If any teams are still tied after using the Team Conduct Score criteria, then a “drawing of lots” will be used to determine the rankings of the still-tied teams.
Ranking the Third-Place Teams
To determine the final two spots for the knock-out phase of the tournament, the third-place teams in each group are compared on their overall (1) Points; (2) Goal Difference, (3) Goals Scored, and (4) Team Conduct Score.
* * *
Mathematically, a rank coefficient for comparing the third-place teams can be calculated using the following formula:
ThirdRankCoeff = Points + (Goal Difference * 0.001) + (Goals Scored * 0.000001) + (Team Conduct Score * 0.000000001)
* * *
If any of the teams are tied based on the above, then a drawing of lots will be used to determine the rankings of those teams.
Some General Notes
In normal four-team group tournaments, where only the top two teams in a group advance, finishing with 6 points does not necessarily guarantee that a team will continue on to the next round, as there are scenarios where three of the four teams in the group could end up on six points.
All three groups in this Olympics tournament could each have three teams that finish with 2 wins and 1 loss. Typically, this would mean all nine of those teams would be on 6 points. However, with Canada’s 6 point deduction, Group A could only have 2 two teams at 6 points, France and Colombia, if they both win their respective matches on Wednesday.
Thus, as a result of Canada’s points deduction, the two teams who are currently on 6 points, Spain and USA, are guaranteed to advance.
Regarding the third-place teams, the team that finishes third in Group A is guaranteed to have no more than 3 points, so the third-place teams in Group B and Group C can ensure their advancement if they have at least 4 points.
Of the ten teams that have not yet secured a spot in the quarterfinals, none have been mathematically eliminated. Also, as there have not been any high-scoring blow-out wins so far, none of the potential third-place teams face any extreme goal difference deficits that would all but exclude advancement.
Standings and Scenarios By Group
Group A
| Team | MP | W | D | L | GF | GA | GD | TCS | Pts | Rank |
| COL | 2 | 1 | 0 | 1 | 4 | 3 | +1 | -5 | 3 | 1 |
| FRA | 2 | 1 | 0 | 1 | 4 | 4 | 0 | -1 | 3 | 2 |
| CAN | 2 | 2 | 0 | 0 | 4 | 2 | +2 | -2 | 0 | 3 |
| NZL | 2 | 0 | 0 | 2 | 1 | 4 | -3 | 0 | 0 | 4 |
Final Group A Matches (3:00 pm Eastern kick-off):
- Colombia vs. Canada
- New Zealand vs. France
Advancement Scenarios Matrix:
| Team | Win | Draw | Loss |
| Canada | Yes | No | No |
| Colombia | Yes | Yes | Maybe |
| France | Yes | Yes | Maybe |
| New Zealand | Maybe | No | No |
If the third-place teams in Group B and Group C both finish on 4 points or better, then the third-place team here in Group A would not advance.
Colombia vs. Canada
With its 6 point deduction, Canada has to win to advance. A draw would not be enough as Canada would only be on 1 point, while whoever ends up being the third-place teams in the other two groups are guaranteed to have at least 3 points.
Colombia needs at least a draw to secure advancement as a loss would leave them vulnerable to a third or even fourth place finish, depending on the final scorelines of this match and the other group match.
New Zealand vs. France
Like Colombia, France needs a result to ensure advancement. If France loses to New Zealand, they could still finish as high as second place in the group, depending on the final scores of this match and the other group match.
New Zealand has to win to have a chance at making the quarterfinals.
If the Football Ferns defeat France by 2 or more goals they can finish in second place and lock up a quarterfinal slot if (1) Colombia does not lose to Canada or (2) Canada wins with a favorable scoreline (e.g. 3-nil or 4:1).
The Football Ferns could even top the group, but that would require an epic win and a favorable result in the other match (e.g. NZL wins 6-nil while CAN defeats COL 1-nil).
Group B
| Team | MP | W | D | L | GF | GA | GD | TCS | Pts | Rank |
| USA | 2 | 2 | 0 | 0 | 7 | 1 | +6 | -2 | 6 | 1 |
| GER | 2 | 1 | 0 | 1 | 4 | 4 | 0 | -2 | 3 | 2 |
| AUS | 2 | 1 | 0 | 1 | 6 | 8 | -2 | -2 | 3 | 3 |
| ZAM | 2 | 0 | 0 | 2 | 5 | 9 | -4 | -6 | 0 | 4 |
Final Group B Matches (1:00 pm Eastern kick-off):
- Australia vs. USA
- Zambia vs. Germany
Advancement Scenarios Matrix:
| Team | Win | Draw | Loss |
| Australia | Yes | Yes | Maybe |
| Germany | Yes | Yes | Maybe |
| USA | Yes | Yes | Yes |
| Zambia | Maybe | No | No |
Australia vs. USA
As noted earlier, the USWNT are guaranteed a spot in the quarterfinals, though whether they finish first or as low as third in the group remains to be determined.
The USA can secure first in the group with a win or a draw against Australia. Even with a loss the USWNT could finish first as long as they lose narrowly to the Matildas (e.g. a 1 or 2 goal margin) and Germany does not win their match by more than a few goals.
Australia needs at least a draw to ensure advancement. If the Matildas lose, they could finish in fourth if Zambia upsets Germany and both matches have a margin of victory of 2 goals or more. If both wins are by 1 goal, whether Australia ends up in third or fourth will depend on the specific scorelines.
If this match and the other group match end in draws, Australia is guaranteed to finish in third-place.
Zambia vs. Germany
To guarantee a spot in the knock-out round, Zambia needs to defeat Germany by 2 or more goals along with a USA victory over Australia, as this would give the Copper Queens a second-place finish.
A 1 goal win could be enough for Zambia, as long as Australia loses by 2 or more goals. If Zambia wins and the USA wins by the same margin (e.g., both matches end 2:1), Australia and Zambia will be tied on the first set of criteria. As Australia, thanks to their incredible 6:5 comeback victory on Sunday, has the better head-to-head result, the Matildas would be ranked higher and finish in third.
Like Australia, Germany is ensured advancement as long as they do not lose. A draw will be enough for a third-place finish should the Matildas defeat the USA.
If both group matches end in draws, Germany is guaranteed to have the runner-up slot in the group.
Group C
| Team | MP | W | D | L | GF | GA | GD | TCS | Pts | Rank |
| ESP | 2 | 2 | 0 | 0 | 3 | 1 | +2 | -2 | 6 | 1 |
| JPN | 2 | 1 | 0 | 1 | 3 | 3 | 0 | -1 | 3 | 2 |
| BRA | 2 | 1 | 0 | 1 | 2 | 2 | 0 | -3 | 3 | 3 |
| NGA | 2 | 0 | 0 | 2 | 0 | 2 | -2 | -1 | 0 | 4 |
Final Group C Matches (11:00 am Eastern kick-off):
- Brazil vs. Spain
- Japan vs. Nigeria
Advancement Scenarios Matrix:
| Team | Win | Draw | Loss |
| Brazil | Yes | Yes | Maybe |
| Japan | Yes | Yes | Maybe |
| Nigeria | Maybe | No | No |
| Spain | Yes | Yes | Yes |
Brazil vs. Spain
The reigning Women’s World Cup champions, Spain, with their two wins so far, are more-or-less in the same boat as the USA, as each team are guaranteed to advance and can lock up a first-place group finish by not losing their match.
However, Spain has significantly lower goal difference (+2 versus +6) and goals score (3 versus 7) relative to the USWNT, so they are much more vulnerable to a third-place finish compared to the USA. For example, Spain could easily finish third in the group if Brazil wins by any margin and Japan defeats Nigeria by any margin, except in the next scenario.
The number of yellow and red cards received by each team would be a factor in determining the group standings if the Group C matches finish as follows: Brazil defeats Spain by a 2:1 scoreline and Japan has a 1-nil win over Nigeria. Then, Spain, Brazil, and Japan will be tied on the first set of criteria, as well as the points, goal difference, and goals for criteria of the second set, with only their Team Conduct Scores as potential tie-breakers.
Brazil needs at least a draw to guarantee a slot in the quarterfinals. Even if Brazil loses to Spain, Brazil can still finish no worse than third if Nigeria does not defeat Japan or Nigeria defeats Japan by a larger margin as Spain defeats Brazil (e.g. BRA loses 1:3 and NGA wins 3:0).
If Brazil wins 1-nil over Spain and Nigeria defeats Japan 1-nil, both Spain and Brazil will be tied on the first set of criteria, however with Brazil winning the match, they will have the better head-to-head result, so Brazil will win the group, with Spain finishing in second-place.
If both group matches end in draws, Brazil and Japan will each have 4 points. As both teams have the same goal difference (zero), the next tie-breaker is goals scored, of which Japan has a 1 goal advantage (3 to 2). For Brazil to finish second, the scoreline of their match with Spain will need to be at least 2 goals higher (e.g. 3:3 versus 1:1). A 1 goal difference would mean a tie on the first set of criteria with Japan having the head-to-head advantage.
Japan vs. Nigeria
Like Brazil, Japan must not lose to ensure advancement.
Regardless of the result in the other group match, Japan can finish third or better in the group if they lose by only 1 goal. If Nigeria wins by 2 or more goals, Japan will need Spain to defeat Brazil by at least the same margin or better (e.g., a 1:3 loss to NGA would require a 2:0 win by Spain).
For Nigeria to finish no worse than third, they need to win by 2 or more goals. A 1 goal margin would not be enough unless Spain defeats Brazil by 2 or more goals.
Nigeria, with a 2 goal or better victory could even finish in second place if Brazil falls to Spain by multiple goals. If Brazil and Spain draw, the best Nigeria could do would be third.
Women's Soccer Express 