There are times when a little basic psychology explains the difference between victory and defeat, and Tony Gallopin’s stage win here at the expense of Peter Sagan falls into that category.

The Slovak prodigy is the most consistent finisher in the field and wears the green jersey of points leader with almost twice the total of his nearest challenger. He should carry it to Paris barring accidents, but after coming close to a stage win seven times in the first 11 stages, his is a classic case of desire outrunning performance.

Gallopin is less talented but inhabits the other end of the stress spectrum, all pressure lifted from his shoulders after wearing the maillot jaune for a day – and Bastille Day of all days. While he has lived on a rollercoaster of emotion since winning the jersey in Mulhouse, the instinctive decisions that win and lose a bike race come easier to a man in his position.

“Sunday was one of the most beautiful days of my life, on Monday I suffered like you cannot imagine, on the rest day I had a bit of a cold, and today my legs didn’t feel good early on,” said the 26-year-old, who had made a point of looking over the final kilometres of the 11th stage with his father – the former professional Joël – and his fiancee, the former French road race champion Marion Rousse.

Gallopin made an initial effort over the final climb of the stage – an uncategorised little ascent with 13km remaining which he knew was tougher than the race programme suggested – and on the high-speed descent into Oyonnax, he was joined by three riders: the Australian Michael Rogers, the Pole Michal Kwiatkowski and Sagan.

As the remains of the peloton closed on the quartet at the foot of the descent, Gallopin eased clear of his companions leaving Sagan with the same quandary he had faced in Sheffield when Vincenzo Nibali attacked: quite simply if he failed to chase he would lose the stage, but if he expended his energy bringing the escapee to heel, he stood every chance of losing as well.

As Sagan hesitated, Gallopin pulled away, ending the stage with a few yards lead on the nearest chasers led by the German sprinter John Degenkolb, with the Slovak finishing ninth.

“I want to win a stage, but it’s not easy when everyone is riding against you,” complained Sagan, who had been in a similar quandary on Friday in Nancy when he made a late attack, was caught by the peloton and finished second in the sprint.

“No one wants to work with me, because they know if they come with me I will beat them in the sprint. I can’t chase everyone.”

On Thursday’s stage to Saint-Etienne, Sagan will have another chance over another hilly finale – two long drags in the Monts du Lyonnais after an evocative opening phase through Beaujolais country past Villié-Morgon and Brouilly – but at present, he is a sitting duck on two wheels.

The field was shredded by Cannondale’s efforts to facilitate a win for Sagan by burning off the stronger sprinters - and Marcel Kittel in particular – and then by the battle for the stage win, with Nicolas Roche in the vanguard.

At the end, only 34 riders remained in the lead group, including Vincenzo Nibali and all his closest rivals bar one. The world champion, Rui Costa, dropped 1min 36sec, slipping from ninth to 14th overall.

But for suffering, nothing matched Andrew Talansky’s calvaire. The young American, winner of the Dauphiné Libéré back in June, had been suffering the after-effects of two heavy crashes, the first in the finishing sprint at Nancy last Friday, the second on the descent to Gérardmer on Saturday, and had reportedly been struggling to remove his jersey after stage finishes.

He slipped behind with over 50 miles to the finish as Sagan’s Cannondale team began to chase behind an early breakaway, and was left with no option but to attempt to reach the finish alone.

After 12 miles or so, Talansky pulled into the side of the road – barely able to straighten his back as he got off his bike – and sat down on a crash barrier. After several minutes of discussion with team personnel, the 25-year-old got back on his bike, apparently in tears, clearly determined to get to the finish at whatever cost.

Talansky must have known he had only an outside chance of finishing within the day’s time cut, but he managed it, although he had to be helped up the steps into the team bus afterwards.

If Sagan and Gallopin’s stage finishes merited a little psychoanalysis, there was no call for a shrink in this case.

“The pitbull” is clearly a hard nut of the first order, gifted with determination in spades and no matter how much further Talansky goes in this Tour, he will go far in the future.