Most of the Premier League attention will be on Anfield and the north-west derby this weekend, even if Liverpool’s stuttering start to the season means Jürgen Klopp’s side already have seven points to make up on Manchester United. For different reasons that will probably suit Crystal Palace and Chelsea, who meet at Selhurst Park in one of the lesser London derbies.

Roy Hodgson said his struggling Palace side were like a boxer on the ropes after their last outing at Old Trafford, trying to fight in a class above their weight and taking too many blows to the chin. Just what you need in those circumstances is a visit from the defending champions, though the only sliver of good news for Hodgson and his stricken side – apart from Wilfried Zaha nearing a return – is that Saturday’s game is the last of a daunting run of fixtures. Palace take on Chelsea after two successive trips to Manchester, where City and then United hit them with a total of nine goals to no reply.

Normality resumes a week after Chelsea, in the form of a trip to Newcastle. Not exactly a doddle, but that’s the Premier League for you. After three Champions League sides in a row, Palace just have to be grateful for opponents more familiar with the Championship.

Hodgson is right in saying his side will not have to face top-four teams every week, though the awkward truth is that they have not been doing so. Admittedly mostly before he arrived, Palace were also beaten and held scoreless by such Premier League powerhouses as Southampton, Burnley, Swansea and Huddersfield. As Burnley are now sixth as a result of picking up points against some of the stronger sides around, it seems the Palace chairman, Steve Parish, blundered in not recruiting Sean Dyche in summer when he appeared to have the chance.

It remains to be seen whether Hodgson can turn Palace around in time to secure survival but no one is kidding themselves that the season will not be one long relegation battle after the most unpromising of starts. Should Hodgson succeed from here he will deserve even more credit than Tony Pulis and Sam Allardyce for Palace’s latest astounding feat of escapology.

With each side having played seven games, this is the stage of the season when most of the zeros have disappeared from the Premier League table. Most of the way down there are only two that remain – no defeats yet for either Manchester City or Manchester United – but then you reach the bottom line and Palace have four of their own. No wins, no draws, no goals and no points. Hodgson’s side have twice as many zeros to their name as the rest of the division put together and, depending on what mood Chelsea are in, the situation may not have significantly altered by Saturday night.

Chelsea’s mood will not be improved by defeat in their last match against Manchester City, or by the hamstring injury Álvaro Morato picked up that is likely keep him on the sidelines for another week, though on the other hand the news from Belgium appears to be that Eden Hazard is fully recovered.

Chelsea never seem to kick on from winning the title; not since José Mourinho’s first couple of years in England has one successful season been followed by another. They managed to sack both Carlo Ancelotti and Mourinho the season after their next two titles and it was hardly a surprise to hear Antonio Conte yearning for a return to his native Italy so soon after delivering the latest.

Álvaro Morata was injured against Manchester City and is likely to be out for another week. Photograph: Martin Dalton/Rex/Shutterstock

Given Chelsea’s record no one could blame him for fearing the worst, although that wily old fox Claudio Ranieri probably read the situation most accurately when suggesting Conte was simply disappointed with the club’s summer transfer business and apprehensive about what was turning into an uneven financial contest with the two Manchester clubs. Romelu Lukaku, in other words. Or perhaps, come January, Lukaku and Alexis Sánchez.

Yet before writing Chelsea off as also-rans it might be as well to remember that this time last year they were not doing particularly well either. They had just been thumped 3-0 by Arsenal and Conte was so dismayed he decided to change his system. They came back after the international break with three at the back and wing-backs, handed out a 3-0 thumping of their own to the defending champions, Leicester City, and never looked back.

It is already clear that Chelsea miss Diego Costa’s aggressive input up front, although Morata when fit has shown plenty of promise, though it is equally evident that Lukaku is working for United in a way that Conte must have hoped he would at Stamford Bridge. Especially bearing in mind that Conte probably thought Lukaku was coming as a replacement when ill-advisedly alienating Costa.

Again, it may be best not to form too hasty a judgment. While Lukaku at present leads the Premier League goalscorers’ table, United have not had the most demanding of starts to the league season. On Saturday at Liverpool they will be facing a side from the top half of the table for the first time. Chelsea, in contrast, have already come up against Arsenal, City and Spurs. Among the criticisms levelled at Lukaku after his move for an initial £75m from Everton, in addition to the legitimate concerns that his first touch is unreliable and his proportion of missed chances high, was that he does not always perform against top opposition. The cricketing expression would be flat-track bully, for Lukaku’s record suggests he picks up a lot of his goals against lesser teams and does not show up so well in games against title contenders.

The same could be said of Everton, of course, who did not always provide Lukaku with a platform to score against leading sides, so now he is at United he should have a better chance to answer his critics. Beginning this month, for in addition to Liverpool on Saturday United will meet Tottenham before the end of October. Spurs themselves face Liverpool and United in their next three games, meaning Liverpool have United and Spurs in the same period.

If Lukaku can keep up his scoring sequence through October he will go a long way to proving his worth. Conte will probably end up even more disappointed should that happen, though on paper there is no reason why Chelsea too should not have another productive October. While teams above and around them are playing each other, Chelsea’s next three games involve Palace, Watford and Bournemouth.

While it is a truth universally acknowledged that there are no easy games in the Premier League, it perhaps might be admitted that some runs of fixtures are slightly gentler than others, and Palace, Watford and Bournemouth certainly sounds a gentler October than the month facing United, Spurs and Liverpool. As ever, Champions League exertions can easily upset domestic calculations, though at least Chelsea’s game against Roma is at home, as is their Carabao Cup tie against Everton.

October, in short, could put the smile back on Conte’s face. Chelsea will know it is time to worry if he is still dropping hints about returning home come the end of the month.