With eight games remaining in the group stages of the Rugby World Cup, there are still six quarter-final spots to be decided.

In some cases, it is a straight shootout to make it through, in others, it may require getting out the calculators.

We have done our best to sum up the different scenarios:

World Cup knockout permutations for Pool A

New Zealand are through to the quarter-finals after a bonus-point win over Uruguay. They top the group on 15 points, while France sit on 13 points, three clear of Italy.

That leaves the meeting between France and Italy as basically a straight knockout. France will qualify with a win or a draw, whereas Italy go through should they win. The only exception would be if Italy win and take four match points from the game (scoring fewer than four tries), while France take two points for getting within seven points and scoring four tries of their own.

Who can qualify from Rugby World Cup Pool B?

Easily the most complex equations come in Pool B, where Scotland, South Africa and Ireland all have a path to topping the pool.

South Africa have played their four games, so it comes down to Ireland’s meeting with Scotland in Paris. If Ireland avoid defeat, they automatically clinch top spot, with the Springboks also qualifying as runners-up.

Where it gets interesting is if Scotland win. A 5-0 return sends Scotland and South Africa through, likewise a 4-0 victory (probably the most plausible outcome if Scotland are to make it). In both of these cases, South Africa would top the group. By contrast, a 4-1 or 4-2 win for Scotland would not be enough for them to go through, with Ireland still topping the group.

The calculators would be needed for a 5-1 Scotland win. If they win by more than 20 points, then it would be Scotland who top the pool and would be joined by Ireland in the quarter-finals. That would be because all three teams would finish on 15 points, with Scotland then topping the pool on points difference. Once the three-way tie is split, the next tiebreaker used is head-to-head result, so Ireland’s win over South Africa would see them through.

If Scotland take a 5-1 win by 5 to 19 points, they would go through as runners-up, with South Africa topping the pool on points difference and Ireland going out. And lastly, if it’s a 5-1 win by four points or fewer, Ireland finish with the best points difference, going through along with South Africa.

Simple, no?

Who can qualify from Rugby World Cup Pool C?

Ok, back to a more straightforward pool. Wales are already qualified and will clinch top spot in the pool should they take a point off Georgia, or Fiji fail to take five points off Portugal.

Second spot is very much in Fiji’s hands. Provided they take at least one point from their meeting with Os Lobos, they will finish as runners-up to Wales. If they cannot get anything out of the Portugal game, then it is Eddie Jones’ Australia who would sneak through.

World Cup knockout permutations for Pool D

Another very easy one. England are already through as group winners, leading Argentina and Japan by five points and having beaten both of them.  

Their opponents, Samoa, are only three points behind second and third so could get to a three-way tie. If Argentina and Japan draw, with neither scoring four tries, then Samoa need to win by 29 points while scoring four tries to sneak through.  

Realistically though, it all comes down to the meeting between Argentina and Japan in Nantes. While they are level on points, Argentina’s superior points difference means that they will go through with a win or a draw. Japan need to win to get through to a second successive quarter-final, although a draw in which they score four tries and Argentina do not, would also do the trick.

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