THERE is one simple way to qualify for the quarter-finals of the Rugby World Cup: win all your pool games. Of the five teams in Pool B, Scotland are the only one who can do that.

Scotland will also qualify if they beat South Africa on Saturday with a bonus point. They will then have 15 points, an unmatchable total. But for the other teams - and for the Scots should they fail to do that - there is a bewildering array of permutations to bear in mind while calculating how they can finish in the top two places that will take them into the knockout stages. Two factors are responsible for the complexity: the awarding of bonus points, and the rules that apply if two or more teams end up on the same number of points.

When Japan beat South Africa in the first match in the pool, the focus, understandably, was on their triumph and the Springboks’ humiliation. But the fact that the South Africans came away with two bonus points - one for scoring four tries, the other for losing by fewer than eight points - could yet prove crucial.

For example, even if South Africa lose to Scotland on Saturday - but get another two bonus points while Scotland fail to pick one up - the former world champions could still finish above Vern Cotter’s team. Admittedly, that is improbable, but many stranger things have happened in sport.

A certain combination of results would then see South Africa, Scotland and Samoa all on 14 points at the end of the pool, with Japan and the United States bringing up the rear. The first way to split teams who are on the same number of points is the head-to-head result, but that will not apply if Scotland beat South Africa, who have already beaten Samoa, who go on to beat Scotland.

The second criterion is points differential in all pool games, then try differential, then most points scored, then most tries scored. If all that fails to separate the teams into first, second and third places, the outcome will be decided according to who is higher in the official world rankings on 12 October. At present South Africa are fifth, Scotland ninth, and Samoa 11th. Japan, incidentally, are 12th, with the USA in 16th place.

The USA’s cause is already all but hopeless - they need to win their remaining two games well, and rely on other results going their way, to have a chance of qualifying. Given the lack of firepower and imagination they showed against Samoa and Scotland, it is all but impossible to see them getting five points against South Africa.

On the other hand, Japan have a decent chance of going through, possibly at Scotland’s expense. They stand on four points at the moment, but if they beat Samoa on Saturday they could then go into the last game in the pool, against the USA, knowing precisely what they have to do to qualify. Provided no two teams have ended up on 15 points or more, a second bonus-point win against the States could take the Japanese through.

There may well be a more straightforward outcome, the most plausible being that South Africa win the group by a couple of points from Scotland. But if they want to spare us all from further befuddlement, Scotland know what they have to do on Saturday.