Five things we learned from the Premier League weekend

1. Liverpool show there is life after Coutinho.

A dismal day for Arsenal had a solitary benefit for them: Manchester City’s 4-3 defeat at Anfield means they will retain their status as the Premier League’s only Invincibles for at least one more year. What could have been a damaging day for Liverpool, deprived of the sold Philippe Coutinho and the injured Virgil van Dijk, turned into a wonderful one. Brilliant as the Brazilian can be, they proved again they can be devastating without him.

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They scored four goals against Arsenal in August when a back injury – officially, anyway – sidelined their classiest performer. They added four more against unbeaten league leaders in City, who had only conceded five on the road in the league, with a supreme display of speed and skill. Roberto Firmino, Sadio Mane and Mohamed Salah, the three remaining members of the Fab Four, all scored and all in memorable fashion. Alex Oxlade-Chamberlain probably would have begun on the bench had Coutinho still been at Anfield. He got the opener and was terrific. Perhaps, somewhere in Catalonia, Coutinho watched on enviously.

2. Arsenal show why Sanchez wants to leave.

Alexis Sanchez’s mind has long seemed made up; a player Arsene Wenger described as “half in, half out” wanted to go. If he needed any persuasion, however, Arsenal probably supplied it, inadvertently and rather incompetently. Defeat to Bournemouth provided more reasons to suggest his future is better served elsewhere. It leaves Arsenal eight points behind the top four with a considerably inferior goal difference; their chances of Champions League football rest more and more on the Europa League.

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It was their fifth successive game in all competitions without a win and it showed some familiar failings: another poor away result, signs of the increasing frailty of Petr Cech, who was at fault for Callum Wilson’s equaliser, and the defence, which are compounded by the absence of a high-class defensive midfielder. Sanchez was absent, distracted by the prospect of a move to Manchester, and without him and the injured Mesut Ozil, Arsenal lacked stardust. Alexandre Lacazette went a ninth consecutive game without scoring and Arsenal relied on a right-back, Hector Bellerin, to get their goal. If this was a glimpse of life after Sanchez, it looks a depressing prospect.

3. Cautious Chelsea make the wrong sort of history.

March will mark Chelsea’s 113th birthday. In that time, they had never drawn 0-0 in three successive matches. Until 10-man Leicester emerged from Stamford Bridge after securing a stalemate. Perhaps that could be deemed an irrelevant statistic: those three games came in three different competitions and the side held by Norwich in the FA Cup was very much of the weakened variety. Yet it is notable that Chelsea also failed to score twice in December, away at West Ham and Everton, and it is a fact that Alvaro Morata has only struck five times in 22 games.

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The reliance on the out-of-sorts Spaniard is exacerbated by Antonio Conte’s tactics. The Italian has developed a fondness for a 3-5-1-1 formation. It has brought the best from Eden Hazard at times. Yet it also means that when opponents keep Hazard and Morata quiet, there are too few other players in the final third and too few potential scorers. Conte was entitled to cite fatigue after Chelsea’s seventh game in 21 days, but it was pertinent that he said: “We are not creating chances.”

There are reasons for that. In home games where Chelsea are hot favourites, that highlights his caution. Starting with two defensive midfielders and beginning by benching both Pedro and Willian felt unnecessarily negative.

4. New striker Tosun discovers the difficulties of playing for shot-shy Everton.

It was a tale of two strikers at Wembley, one bringing the new and the other the familiar. Cenk Tosun made his Everton debut. Harry Kane scored a distinctly predictable brace, overhauling Teddy Sheringham to become Tottenham’s record Premier League scorer by taking his tally to 98. It was also a story of two attacks: Christian Eriksen scored a lovely goal and Son Heung-Min was perhaps better than either the Dane or Kane. Everton’s, in contrast, gave Tosun inadequate support: the £27 million newcomer showed some fine hold-up play and offered indications he may be an excellent signing.

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But he was isolated. His team-mates created too few chances for him. The problems predate his arrival. The damning reality is that Everton have failed to record a shot on target in three of their last five league games. They have only drawn three saves in those five matches and scored a solitary goal. One of the major concerns about appointing Sam Allardyce was that his style of football is too defensive for a club with Everton’s aspirations. One with their players, albeit after last summer’s strange recruitment, ought to be capable of better. This is not just about a new striker. It is about a style of play.

5. Palace and West Ham revivals show how much they underachieved at the start.

They are the top of the bottom half. West Ham are 11th and Crystal Palace 12th after beating Huddersfield and Burnley respectively. They testify to the improvements made under new managers. David Moyes has only lost one of his last eight league games, Roy Hodgson one in 12. Both clubs have been rewarded for wielding the axe. But both have also proved that awful starts – no points in seven games for Palace, just 10 in 15 for West Ham – need not be fatal for clubs with high-calibre players. Two of the Hammers’ match-winners, Marko Arnautovic and Manuel Lanzini, ran riot in a 4-1 triumph at Huddersfield. Two of Palace’s best, Wilfried Zaha and Christian Benteke, were involved in the move that led to Bakary Sako’s winner against Burnley.

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They are players of the quality and, in some cases, cost that clubs of Huddersfield’s ilk can only envy. They do not have the margin for error that the London clubs displayed in their underachieving starts and subsequent revivals. It is why it remains a far greater feat for the promoted clubs to stay up. Moyes and Hodgson deserve plenty of credit, but there was so much scope to improve in their squads.