Five things we learned from the Premier League weekend as Arsenal's problems resurface and Man United's charge continues

1. Dreadful defending shows Arsenal’s problems at the back remain

It is strange to think that, an hour before kick-off at Anfield, the issue was the composition of the Arsenal attack. It remains odd that Arsene Wenger demoted his record signing Alexandre Lacazette for a match of the magnitude of a trip to Liverpool, especially when the Frenchman had one actual goal and one controversially disallowed strike in his first two games. But by the end of a 4-0 thrashing, Arsenal had fare greater problems. It was hard to argue a centre-forward, even one who is a much better finisher than Danny Welbeck, would have made a decisive difference.

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Arsenal were hammered. They were humiliated. They were shambolic, lacking both organisation and spirit. It reflected badly on Wenger’s back three that all of Liverpool’s front three scored. It was a sign his tactics failed that he swapped to a back four for the second half.

Yet problems abounded elsewhere. The midfield did not shield them. Liverpool overran Arsenal in predictable fashion. And while issues relate to both personnel and structure, it feels weird that the substitute Skhodran Mustafi may be permitted to leave at a time when Arsenal need quality defenders. They conceded 44 league goals last season, the most of the top six. They have already let in eight in the current campaign. Both numbers are far too high and the spring switch to a 3-4-2-1 formation has not certainly not solved their problems.

2. Chelsea expose Everton’s weaknesses again

Ronald Koeman has gone from one extreme to another. On Monday, he extended his unbeaten record against Pep Guardiola. Six days later, the aggregate score in his meetings with Chelsea as Everton manager extended to 10-0, and not in the Merseysiders’ favour. If Chelsea’s 2-0 victory could have been more emphatic, it represented a second successive win against high-quality opposition, providing a fine response to the champions’ opening defeat to Burnley.

Antonio Conte’s Blues produced their first dominant display of the season in a win over Everton at Stamford Bridge

Yet while the scorelines have been one-sided, Everton may feel themselves unfortunate and not just because they were in Europa League action in Croatia three days earlier. When they lost 5-0 at Stamford Bridge last season, they were without the suspended Idrissa Gueye. When they were beaten 3-0 at Goodison Park in April, they missed the injured Morgan Schneiderlin. And for Sunday’s rematch, the Frenchman was banned. Since his January arrival, Everton have possessed one of the best pairs of defensive midfielders in the division. But they have been unable to field both against Chelsea. And those games have illustrated their importance.

3. United stage another late, great show

Manchester United have an indelible association with late goals, and not just because of the 1999 Champions League final. They have been evidence of attacking intent, signs of their relentlessness, proof they have had substitutes desperate to make a late impact. Not in recent years, however. United only scored 12 league goals in the final quarter of an hour of league matches last season, whereas Everton got 22 and Arsenal 23. Go back to Louis van Gaal’s final season in charge and United scored nine goals in the last 15 minutes. To put it another way, that was five fewer than Sunderland.

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But three games into the current campaign, United already have six goals scored in or after the 80th minute. They already have four goals from substitutes, including Marcus Rashford and Marouane Fellaini’s decisive strikes against Leicester on Saturday. Once again, United have strength in depth. That clinical touch is giving them a fine goal difference. It will produce extra points, too.

4. Sullen Guardiola needs to accept there is no conspiracy against City

Three games is a small sample size but Manchester City have not been on the right end of many decisions so far this season. Kyle Walker was sent off against Everton when his second yellow card came for backing into Dominic Calvert-Lewin. Raheem Sterling was dismissed at Bournemouth for celebrating a late winner.

The Cherries’ Nathan Ake ought to have seen red for a first-half foul on Gabriel Jesus when he was the last man, but was only booked. Equally, manager Pep Guardiola, by referencing Walker’s expulsion in answering questions about Sterling, appears to be developing a persecution complex. Continually mentioning how much possession his side have, as he did last season, as if it should spare them red cards is a poor argument.

All bar one of last season’s sendings-off were justified. This year’s are a different case but, from referee Bobby Madley’s angle, it looked as if Walker had elbowed Calvert-Lewin, though an assistant referee or the fourth official should have advised him otherwise.

It is a moot point how much Sterling went into the crowd and how much they encroached on to the pitch to come to him, but referee Mike Dean thought he was applying the law, albeit a law few agree with. Punishment exceeds crime, with Sterling suspended for September’s game with Liverpool, but Guardiola’s sulky overreaction hardly helps City.

5. Bilic and De Boer lead sack race

There are different ways of flying out of the blocks. Manchester United have done so in the title race, Slaven Bilic and Frank de Boer in the sack race. West Ham and Crystal Palace are both pointless, even if their problems are rather different. Palace are toothless, one of only two teams without a goal. The Hammers are shambolic, with much the most goals (10) conceded. They can at least argue in mitigation that they have had to play their first three games away from home whereas Palace have contrived to lose home games to less talented teams, in Huddersfield and Swansea.

But Bilic spent heavily on proven Premier League players whereas De Boer has been trying to use Sam Allardyce’s charges, but with a radical shift in style of football. It is an understatement that it isn’t working. If neither capital club picks up by the next international break, the Premier League may have its first managerial casualty of the season.