As the Rugby World Cup reaches the final weekend of pool stage action, seven quarter-finals spots are mathematically still up for grabs and various theories abound as to which teams may upset the apple cart.

POOL A

Remaining fixtures:

October 1 – France v Tonga – 07:00
October 2 – New Zealand v Canada – 04:30

– New Zealand have won the pool and will play the runners-up of Pool B in the quarter-finals.

– France will finish second if they win or draw against Tonga or if they lose but collect a bonus point or if they lose but Tonga fail to collect a bonus point and Canada fail to beat New Zealand.

– Tonga will finish second if they beat France and gain a bonus point and France do not gain a bonus point, assuming Canada fail to beat New Zealand.

– Canada will finish second if they beat New Zealand and gain a bonus point and France lose to Tonga without a bonus point.

– If France, Tonga and Canada all end on 10 points, second place will be decided on points difference, with France likely to take it.

– If in unlikely event that there is a tie regarding points difference, then the second placed team will be decided by the team with the best difference of tries scored and tries scored against them.

POOL B

Remaining fixtures:

October 1 – England v Scotland – 09:30
October 2 – Argentina v Georgia – 02:00

– England will win the group if they beat or draw with Scotland or lose but with two bonus points.

– If England lose and there are no bonus points in the match, either side could qualify but it would depend on Argentina’s result.

– If Scotland win and there are no bonus points leaving England and Scotland both on 14 points and Argentina win with a bonus point, Argentina would win the group with 15 points and Scotland would finish second on their head-to-head result against England.

– If Scotland win and there are no bonus points and Argentina win without a bonus point, all three teams would be on 14 points and positions would be decided on points difference. This would almost certainly eliminate Scotland while the top two positions would be dependent on the margins of victory/defeat in their remaining games.

– If all three teams end up on 14 or 15 points, positions would be decided on overall points difference in the group, which would almost certainly eliminate Scotland. If Scotland lose but gain one or two bonus points, they could finish second, so long as Argentina also lose and gain fewer bonus points.

– If Scotland win with a bonus point and England do not gain two bonus points in defeat they will win the group if Argentina fail to beat Georgia with a bonus point.

– If Argentina win with a bonus point and England lose and do not gain a bonus point, Argentina would top the group.

– If Scotland and Argentina both win with a bonus point and England fail to gain a bonus point, Argentina would top the group ahead of Scotland.

– If Argentina win with or without a bonus point and Scotland fail to win, then Argentina would finish second.

– If both games are draws, England would top the group ahead of Argentina.

Pool C

Remaining fixtures:

October 1 – Australia v Russia – 04:30
October 2 – Ireland v Italy – 09:30

– Ireland will win the group if they beat Italy

– Ireland will qualify if they avoid defeat to Italy

– Australia are guaranteed qualification if they beat Russia with a bonus point.

– Australia will top the group if they beat Russia with a bonus point and Italy beat Ireland (with Ireland failing to secure two bonus points in defeat).

– Italy will win the group if they beat Ireland (and Ireland fail to get two bonus points) and Australia fail to beat Russia.

– Italy will win the group if they beat Ireland with a bonus point and Australia beat Russia but fail to get a bonus point (as long as Ireland fail to secure two bonus points in defeat).

– Italy will finish second if they beat Ireland, with or without a bonus point (assuming Ireland do not gain two bonus points in defeat) if Australia win with a bonus point.

– If Ireland lose to Italy and gain a bonus point, Italy fail to get a bonus point and Australia beat Russia without a bonus point, all three teams would end up on 14 points and positions would be decided on points difference with Italy likely to miss out.

– If Ireland lose to Italy and gain two bonus points, Italy get a bonus point and Australia beat Russia with a bonus point, all three teams would end up on 15 points and positions would be decided on points difference with Italy likely to miss out.

– If Australia lose to Russia and do not gain a bonus point, Ireland would qualify and Italy would qualify if they take at least a bonus point from their match against Ireland.

– If Australia lose to Russia and gain a bonus point, they would still qualify if Italy fail to beat or draw with Ireland or do not gain two bonus points in defeat.

POOL D

Remaining fixtures:

September 30 – South Africa v Samoa – 09:30
October 2 – Wales v Fiji – 07:00

– South Africa will win the group if they beat or draw with Samoa or if they lose and gain two bonus points.

– If Wales win and Samoa lose or draw, Wales will finish second.

– If Samoa win and Wales lose or draw, Samoa will qualify for the quarter-final.

– If Samoa win and there are no bonus points, leaving South Africa and Samoa on 14 points and Wales beat Fiji with a bonus point, Wales would win the group with 15 points and Samoa would finish second on their head to head record against South Africa.

– If Samoa win and there are no bonus points, and Wales beat Fiji without a bonus point, all three teams would be on 14 points and placing would be decided on points difference, with South Africa likely to win the pool.

– If Fiji beat Wales with a bonus point and South Africa beat Samoa (with Samoa failing to secure a single bonus point), then South Africa would win the group and leave three teams tied on 10 points. The second placed team will then be decided via the points difference rule.

In the event of a tie after the pool phase, the basic rules for qualification from the pool phase as stipulated by the IRB are as follows:

“If at the completion of the pool phase two or more teams are level on match points, then the following criteria shall be used in the following order until one of the teams can be determined as the higher ranked:

1. The winner of the match in which the two tied teams have played each other shall be the higher ranked;

2. The team which has the best difference between points scored for and points scored against in all its pool matches shall be the higher ranked.

3. The team which has the best difference between tries scored for and tries scored against in all its pool matches shall be the higher ranked.

4. The team which has scored most points in all its pool matches shall be the higher ranked.

5. The team which has scored most tries in all its pool matches shall be the higher ranked.

6. Should the tie be unresolved at the conclusion of steps 1 through 5, the team that is higher ranked in the updated Official IRB World Rankings on October 3, 2011.