When Team Sky changed their jerseys from black to white for this year’s Tour de France, it was a fairly transparent attempt to rebrand themselves as good guys. A line of eight or nine riders in pitch-black uniforms stretching out at the front of the peloton day after day, squeezing the life out of the competition, was never a sympathetic look.

So now, as Chris Froome closes to within one 22.5km time trial around the sights of Marseille and one ceremonial parade into Paris of his fourth Tour win in five years, did it do the job? On an aesthetic level, perhaps it did. The Sky squad still rode on the front, all eight of them en bloc after an accident forced Geraint Thomas to withdraw, but the sight of that crushing might was less oppressive.

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In competitive terms, however, they were even more imposing. Very early in the race we could see how their massive budget had been used to assemble a group of riders of formidable skills to support Froome’s campaign, including some – like Michal Kwiatkowski and Mikel Landa – who might have had legitimate ambitions of their own had they been with other teams. The decision to leave Peter Kennaugh and Ian Stannard at home was made on the basis that for this assault only the very, very best would do.

They began with the unexpected bonus of four days in yellow for Thomas, the winner of the opening time trial. But then day after day Sky’s squadron of domestiques de luxe rode at the front, challenging the teams of Froome’s principal rivals – Romain Bardet’s AG2R-La Mondiale, Fabio Aru’s Astana, Rigoberto Urán’s Cannondale-Drapac – to meet them on their own terms. None could manage it, although Bardet’s men gave it a decent go on Thursday, when they swept to the front of the peloton on the Col de Vars in an attempt to provide their leader with the platform from which to launch a race-winning assault on the Izoard. They crumbled eventually but at least they tried.

As a group, Sky ride to their power meters, and as individuals they are strong and clever enough to execute that carefully plotted strategy with such efficiency that no serious rival can ride away from them. But it has not made them loved, or even admired, by those who value bike racing for its humanity, spontaneity and unpredictability.

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Froome is a likeable man who fought hard to get where he is. His whirring, elbows-out style symbolises his status as something of an outsider. He has spent the past three weeks overcoming a series of minor misfortunes: an off-road excursion, a broken spoke and a sudden loss of power at the top of Peyragudes. Yet he continues to bear the brunt of the team’s unpopularity. On the way to victory in 2015 a cup of urine was thrown in his face. This year a New York Times reporter wrote of seeing fans on the Mont du Chat painting a syringe on the road, bearing Froome’s name, until a race official persuaded them to erase it. Last Sunday he was booed by local fans as he chased after Bardet on the road towards Le Puy-en-Velay.

As Barry Hoban said on ITV, the French have always tended to boo foreigners who take over the race and threaten their favourites. The great Eddy Merckx, he recalled, was mercilessly abused. Sometimes they even boo their own: “In the days of the rivalry between Jacques Anquetil and Raymond Poulidor, Anquetil got booed because they liked Poulidor.” In a way it is a compliment: Merckx and Anquetil were both as close to unbeatable as it gets.

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In fact Froome is probably getting an easier time from the French than from the British. Many fans in his adopted country find it difficult to warm to a man born in Kenya and educated in South Africa who joined Sky to take advantage of a setup based on British Cycling’s Olympic programme.

He has never lived in Britain or shown much of an interest in racing in the country whose flag he flies, except when it came to the 2012 Games. Even if he goes on to win five or more Tours de France, it is hard to imagine him carrying off the BBC sports personality of the year award.

There is also the issue of the doubts surrounding his team’s ability to live up to their original proclamations of rising above cycling’s tainted past. Since the Fancy Bears hackers broke the news of Bradley Wiggins’s previously unpublicised use of therapeutic use exemptions, Sky’s leaders have provided an object lesson in how not to deal with a crisis.

Dave Brailsford, having begun his campaign of denial at the start of the year by borrowing from his friend Alastair Campbell’s playbook, has suddenly switched to the mode of public relations employed by Sean Spicer (until Friday’s resignation). A policy of restricting press briefings to selected broadcasters and denying access to print journalists was bad enough. To tell a couple of journalists from the Cycling News website this week he would not talk to them because they had “been writing shit about me” was to go the full Donald Trump.

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It was also unwise, not least because neutrals could see the piece to which Brailsford referred, published last month, was reasonable in its criticisms of the way he has handled the recent crisis. It was Brailsford’s failure to make a convincing case for his team’s innocence – or, failing that, to admit to errors – that got him into this unhappy position, where formerly sympathetic journalists are now calling for his resignation.

“We make history – you just write about it.” Those were the scornful words spoken by Ron Dennis, the former mechanic who built the McLaren grand prix team into a technology company worth billions, to a reporter. It’s true, of course. All journalists know that but Dennis was stupid to say it. All his claim did was reveal the arrogance that brought about his downfall when he was finally forced out of the company a few weeks ago (if, that is, accepting £250m for his shareholding can be described as a downfall).

It’s something for Brailsford to bear in mind when he leaves the celebrations of Froome’s success in Paris on Sunday night. By accepting the responsibility of a public position and by making claims for the probity of his organisation, he invited constant scrutiny. The best way to handle that is to remain calmer than your critics, to recognise truth is stronger than PR, and to accept your own vulnerability.