We live in a volatile age, our judgments blown this way and that by the slightest scrap of evidence. A cracking victory for Chelsea at home against Liverpool on Saturday would bring a swift halt to weeks of speculation about the causes of the apparent meltdown at Stamford Bridge. Suddenly there would be much calculating of the results needed to carry José Mourinho’s team back into the top four by the end of the season.

Lying 15th in the Premier League, with 11 points from 10 matches, Chelsea require an average of 2.1 points from each of their remaining 28 fixtures in order to match the 70 points that secured the final Champions League slot for Manchester United last May. In Mourinho’s three title-winning seasons at the Bridge, the averages were 2.5, 2.4 and 2.3. So if he can persuade his players that their season starts here and now, the target should be within reach.

Chelsea’s José Mourinho admits he ‘cannot promise’ top-four finish Read more

Despite an improved performance in defeat against Stoke City in midweek, however, it is hard to imagine Chelsea losing their persistent misfire overnight and going from a stuttering second gear to peak revs in sixth without a pause. The collective collapse of form suggests a malaise with deeper roots.

Eden Hazard’s decisive failure from the penalty spot at the Britannia Stadium on Tuesday seemed every bit as significant as the improved performances from several of his team-mates in the preceding 120 minutes. It is hard to believe that had the reigning player of the year been taking that kick this time last season, the ball would not have found its way past Jack Butland.

Even before his team lost to Arsenal in the Community Shield on 2 August, Mourinho appeared to have entered the new season in a darker mood, as if the recaptured title had to be defended with a spikier combativity off the pitch as well as on it. The man who returned to England two years earlier proclaiming his new mellowness and maturity was back in his familiar toxic mode, spraying poison at an increasingly random series of targets.

Six days after the defeat at Wembley came the row with Eva Carneiro and Jon Fearn. The two senior members of Chelsea’s medical staff were disciplined by Mourinho for obeying the instincts of their profession – as well as the referee’s instruction – rather than the dictates of gamesmanship by entering the pitch to treat the injured Hazard in the closing minutes of the first league match of the season against Swansea City, with Chelsea already down to 10 men and on the brink of dropping points. Carneiro has become a cause célèbre, like the Reading ambulancemen so irresponsibly and inaccurately criticised by Mourinho after Petr Cech suffered a serious head injury during a match at the Madejski Stadium in 2006.

Another target, however, is not random at all. For Mourinho, Arsène Wenger is a rival who must not only be brought down but held down. He must be poked and prodded constantly, his weaknesses held up to insult and ridicule.

Mourinho uses the Frenchman like a scratching post, as something on which to sharpen his claws. Amusing to some, this one-sided feud provides a regular supply of back-page headlines. But what kind of achievement is it to provoke a man like Wenger, whose 19 years in north London have brought great benefits to the English game as a whole, into losing his composure and his dignity?

Wenger can look after himself, of course. Whatever the justice of the complaints made against his recruitment policy by Arsenal’s fans in the seasons since their last Premier League title was won, he has presided over a period of consistent achievement and progress for his club on and off the pitch.

The same could never be said for Mourinho, whose priorities are different and more selfish. His failure to supervise any sort of successful pathway from the club’s well-endowed academy to its first-team squad is a significant blemish on his record. Despite recent promises, there is no sign that he can do anything to rectify it.

In terms of trophies, the only currency in which he deals, Mourinho ranks among the great coaches of football history, his achievements in Portugal, Italy and Spain perhaps even outshining his successes in England. Eight league titles in 13 seasons in four different countries cannot be denied and his treble-winning season with Internazionale was genuinely historic. But apart from at Porto, which was only ever a stepping stone to the highest level, it never ends well. The cloud of sulphur in which he envelops his adversaries eventually escapes his control and chokes him, too. When he departs, there is a sense of relief among his employers.

Perhaps this time will be the exception and a faltering project can be revived. Faced with the challenge of Liverpool, who are now led by a manager hoping to emulate the sort of impression Mourinho made first time around, Chelsea’s players may rediscover the qualities that took them to the title, while their manager sets aside the feuds that waste emotional energy and rededicates himself to the task of drawing the maximum from his squad. But through a catalogue of recent errors – the rejection of Kevin De Bruyne and André Schürrle, the failure to sign John Stones, the willingness to let Cech go, the reliance on defensive midfielders such as Mikel John Obi and Nemanja Matic who are not fit to lace Claude Makélélé’s boots – he has made the process harder.

There was always something not quite right about his second coming at Stamford Bridge. Whatever his protestations, he would have regarded it as his manifest destiny to be the man to succeed Sir Alex Ferguson at Old Trafford. That door was locked then and is likely to remain so, whatever the future holds for Louis van Gaal. Mourinho’s departure from west London, when it comes, is most likely to be followed by an offer to succeed Laurent Blanc at Paris Saint-Germain, where the salaries are paid by Qatar Sports Investments.

We know Mourinho has a soft spot for the legend of Brian Clough. But would he ever be ready for the sort of challenge that Clough accepted in 1975, taking on a team lying 13th in the second tier of English football and leading them to the very summit of the European game? Imagine him accepting Kuwaiti money to replace the apparently imperilled Dougie Freedman at the City Ground, with Forest currently lying 17th in the Championship. That would be a real test of his talents, even greater than the one he faces now.

• This article was amended on 2 November 2015. It mistakenly stated that Paris Saint-Germain salaries are paid by the Qatar Investment Fund. The club is owned by Qatar Sports Investments, an arm of the Qatar Investment Authority. This has been corrected.