Rugby World Cup: What Scotland need to qualify against Ireland, the situation South Africa don't want and what is going on in other pools

Nobody said it was going to be easy but the myriad possibilities of qualification from Pool B at the Rugby World Cup would test even our best boffins.

The simple equation is that three into two won’t go and one of Scotland, South Africa and Ireland will be leaving France early and heading home on Sunday. The other two will sail on into the quarter-finals where they will each be paired with a team from Pool A in Paris on the weekend of October 14-15.

South Africa’s bonus-point win over Tonga on Sunday night means they now top Pool B on 15 points having played all their group-stage fixtures. Ireland are on 14 points and Scotland 10 and they meet each other at the Stade de France this Saturday in a match Darcy Graham described as “do or die, a World Cup final almost for both teams”. Only the top two in each group will go through to the quarter-finals and Tonga and Romania have already been ruled out in Pool B, with each yet to win a point. They meet in Lille on Sunday in a dead rubber.

The stakes will be considerably higher in Paris on Saturday night and Ireland’s four-point advantage in the pool standings means the odds are stacked against Scotland, who ideally need to draw level with the Irish on 14 points. Gregor Townsend’s side would claim second place in Pool B in that scenario because competition rules state that if two teams are tied on points at the end of the pool phase then the winner of the match between the two ties teams shall be ranked above the other.

Ireland have won all of their matches so far and led by Johnny Sexton, are one of the favourites for the World Cup.

To draw level with Ireland on 14 points, Scotland would need to beat them and deny them a bonus point. The margin of victory would need to be at least eight points to prevent Ireland taking a losing bonus point which is awarded to teams who are beaten by seven points or fewer. Scotland would also have to ensure Ireland don’t get a try bonus point, awarded when a side scores four or more tries.

Given Scotland have not beaten Ireland since 2017 and have lost all eight matches they have played against them since Gregor Townsend became head coach, it is not hugely surprising that bookmakers are in little doubt about which way this one will go. Scotland are 10/1 against to qualify from Pool B; Ireland are 1/41. South Africa, incidentally, are available at 1/200. Ireland know they can afford to lose and still qualify for the quarter-finals as long as they can pick up a bonus point against the Scots.

Where it gets really complicated is if the three top teams in Pool B end up on 15 points and this is where we are indebted to Kevin Millar, the Glasgow Warriors stats man and the published calculations on his @topofthemoonGW Twitter account. The three-way tie is unlikely but would happen if Scotland were to claim a bonus-point victory over Ireland (beating them and scoring four or more tries in the process) and Ireland were also to take a bonus point (either by finishing within seven points of Scotland or scoring four or more tries).

In the case of a tie between three teams at the end of the pool phase, the side which has the best points difference across all their pool matches shall win the group. Once the highest ranked team has been determined, second and third place would be decided on head to head. As things stand, Pool B leaders South Africa have a points difference of +117 after four games. Second-placed Ireland are on +122 after three games and third-placed Scotland are on +97 after three games.

South Africa concluded all their Pool B fixtures with a bonus-point win over Tonga on Sunday.

Scotland can still win Pool B but it would take an extraordinary result against Ireland. They would need to beat them by 21 points or more, win a bonus point and have Ireland also win a bonus point. That would leave the top three all on 15 match points but Scotland would have the best points differential. Ireland would finish second, having beaten South Africa, meaning the world champions would be going home early.

At the other end of the spectrum, there is also a scenario where Scotland could beat Ireland with a bonus point and still be eliminated if the Irish also claim a bonus point. That would happen if Scotland’s margin of victory is four points or fewer. Ireland would end up winning the group on points difference and South Africa would finish above Scotland by virtue of the fact they beat them earlier in the pool phase.

Where it could get really weird – and this has already been pointed out by some South Africans on social media – is if Ireland are losing to Scotland by 20 points or fewer on Saturday night and both sides have already secured a bonus point. Such a scenario would see the Irish eliminated unless Scotland were to score again and break through the 21-point barrier, meaning it would be in Ireland’s interest to lose by a bigger margin.

Confused? Join the club. At least the other pools at this World Cup are more straightforward. France and New Zealand are in the driving seat in Pool A and it would take the mother of all upsets for Italy to deny the hosts who they play in Lyon on Friday night. As things stand, France are top on 13 points, with New Zealand and France both on 10 points. The All Blacks play their final pool match against Uruguay in Lyon on Thursday and should seal their place in the knockout phase.

Darcy Graham helped Scotland crush Romania last weekend - but a significantly tougher test against Ireland awaits.

In the quarter-finals, the Pool A winners will face the Pool B runners-up, while the Pool A runners-up will take on the Pool B winners, with both ties at the Stade de France. If all goes to form, it will be France v South Africa and New Zealand v Ireland. Much has been made of the lopsided nature of this tournament and nothing bears it out as much as this potential last-eight scenario in the top half of the draw which pitches the top four ranked sides in the world against each other. Scotland, incidentally, are ranked fifth.

Dip into bottom half and there is a distinct drop-off in quality. Wales have already qualified for the quarters are on course to win Pool C. They play their final group match against Georgia in Nantes on Saturday. Fiji need only a point against Portugal in Toulouse on Sunday to also qualify, eliminating Australia in the process. The only hope for Eddie Jones’ side is if Portugal can beat Fiji and deny them a bonus point in the process.

England have already won Pool D and the battle for the runners-up spot is a straight shootout between Japan and Argentina who meet on Sunday lunchtime. Both are tied on nine points so it’s winner takes all in Nantes.

England will meet the Pool C runners-up in the quarters, while the Pool C winners will take on the Pool D runners-up. Both of these ties will be played in Marseille and the likelihood is it will be England v Fiji and Wales v Argentina or Japan.