Number-crunching the final weekend of the tight Top 14

As the Top 14 season enters its final week, the playoff permutations are so complex they would have Pierre de Fermat, of brain-munching theorem fame, reaching for the headache tablets. James Harrington has done the maths, so you don’t have to.

It’s safe to assume that, with one round of the regular Top 14 season remaining, five teams have booked their place in the end-of-season playoffs.

But the competition is so tight that there’s only one dead-rubber match – 12th-placed Toulouse vs already-relegated Bayonne – in the final seven fixtures.

This season’s surprise package, La Rochelle, have a semi-final berth in the bag. Clermont and Montpellier are fighting it out for a bye week in the playoffs, safe in the knowledge that whoever misses out has the luxury of a home quarter-final.

But second-placed Clermont, who have one eye on next weekend’s Champions Cup final, cannot afford a slip-up against the league leaders. Montpellier are chasing hard, and would leapfrog into second – with its quarterfinal bye-week bonus – if Clermont mess up at home this weekend.

Toulon, in fourth, are looking to hold off the challenge of fifth-placed Castres for the still-very-much-at-stake second home quarterfinal.

Technically, the latter’s playoff place is not yet assured, but denying it involves the sort of maths that suggests time travel is possible … and nearest rivals Racing and Stade overturning a 150-plus points difference deficit.

To all intents and purposes, then, there is one available playoff place – which comes with an automatic Champions Cup slot. Six teams could claim it at the death. Here’s how:

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Racing 92 (current position: 6th, 58pts)

Final match: Home vs Bordeaux

Position is nine-tenths of the law – and Racing hold on to that all-important sixth place. They are the only side whose future is entirely in their hands. But it’s close. A bonus-point win over Bordeaux guarantees the defending Top 14 champions are in the playoffs no matter what anyone else does. A win without a try-scoring bonus would be enough if either Stade or Pau fail to pick up bonus-point wins. Even a draw would be fine, if Stade or Pau do not win – and Lyon fail to pick up a bonus-point win at Grenoble.

Stade Francais (current position: 7th, 58pts)

Final match: Away vs Montpellier

Stade need to win. A bonus point would be useful, too. Five points from their final match of the season would mean Racing would have to match Stade’s points tally to hold on to sixth. A four-point win would only be good enough if Racing cannot match the result. But winning could be a problem for Stade. They are at Montpellier, who have compelling reasons of their own to win big.

Pau (current position: 8th, 57pts)

Final match: Away vs Toulon

An admittedly unlikely win at Toulon would be good enough for Pau, if neither Racing or Stade win. If that does happen, the plucky side from southwest France need a bonus point win. And if the two capital sides pick up a five-point win, it’s all over.

Lyon (current position: 9th, 55pts)

Final match: Away vs Grenoble

Okay, now it gets complicated. Lyon will leap up to sixth in the Top 14 if they hammer already-relegated near-rivals Grenoble and pick up a try-scoring bonus, Racing and Pau fail to win, and Stade lose at Montpellier. They could also sneak in if they pick up a no-bonus win at Grenoble, Racing and Stade lose, Pau do no better than draw and Brive beat Castres without a bonus point. Got that?

Brive (current position: 10th, 54pts)

Final match: Home vs Castres Olympique

Brive need to beat Castres – with or without a try-scoring bonus – and hope that Racing 92 and Stade Francais lose by more than five, Pau do not win at Toulon, and Lyon don’t hammer Grenoble away.

Bordeaux (current position: 11th, 53pts)

Final match: Away v Racing 92

First things first: Bordeaux will be out of the reckoning with anything less than a five-pointer at Racing 92. Then, they need to hope that Racing and Stade lose by more than five points; Lyon don’t win; Brive don’t match them with a five-pointer against Castres; and Pau come away from Toulon with no more than a losing bonus point.

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