Another wild weekend in the Premier League is done and dusted. We get you caught up on the action with the Weekend Review.

JUMP TO: Are Arsenal going to get any better? | Statistic of the weekend | Man United's unnecessary fightback | Relentless Liverpool | Man City's costly three points | Leicester couldn't ... could they? | Improved perception of Spurs | Pellegrini's dangerous decisions | Silva won't last to Christmas | The start of something for Norwich

Do Arsenal really think this is going to get better?

It's gotten to the point now that you wonder whether the decision-makers at Arsenal are actually watching the games. The trick to assessing whether a manager should stay is not to react when things are going badly, but the ability to spot when things are not going to improve.

What evidence do they have that good times are ahead under Unai Emery? That they didn't lose to Southampton? Well, big whoop. Emery set up, at home, against a team who have very recently lost 9-0, with five defenders and two holding midfielders. But it was more the intent that was galling and excessively negative, and indicated that after 18 months at the club, he has yet to instill any sort of method or style of play -- or at least any sort of style that anyone wants to watch. Or that wins games.

Arsenal haven't done that at all in their past six, and only twice in the league since August, and neither of those were especially convincing.

The team isn't winning, they're playing bad football, the crowd have turned and there are a selection of potential replacements out there. Keeping Emery has turned from admirable but misplaced patience to negligence.

Statistic of the weekend

To borrow a statistic from the BBC's Simon Stone, Liverpool now have more points than Manchester United and Arsenal combined.

United might not have needed their fightback

If you were being generous, you could say there was some logic in Ole Gunnar Solskjaer matching up his Manchester United side's system with Sheffield United's. Fight fire with fire and all that. But it was more like watching a man rubbing two sticks together fight another with a flamethrower.

Or, perhaps more accurately, one man who had been using the flamethrower for a few years against another who had just picked it up. Eight of the outfield players who started on Sunday were with Sheffield United last season, when they played 3-5-2 or variants thereof every week. United have used it once in the Premier League this term, against Liverpool's 4-3-3, and that time for a very specific purpose: to shut down their rivals' full-backs.

What did Solskjaer think was going to happen? They, of course, deserve credit for the extraordinary seven minutes in which they pulled back the two-goal deficit and went ahead, but had they not tried to compete with a system that is second nature to their opponents, the comeback might not have been required in the first place.

Liverpool plough on relentlessly

Of course, plenty has been said about Liverpool's mentality, and Jurgen Klopp never tires of talking about it, but their reaction to in-game adversity really is extraordinary. Wilfried Zaha's equalising goal -- a fabulous, flowing, team effort that deserved better than to be ultimately meaningless -- might have put most teams on their backsides. But parity with Crystal Palace lasted two minutes before Roberto Firmino scuffed home the winner, their ninth goal after the 75th minute in all competitions this season, and they've collected eight points with goals after the 85th.

They're relentless, haven't lost a domestic game since the FA Cup defeat to Wolves in January, and if they avoid defeat against Brighton next weekend, then they will equal their record league unbeaten run of 31 games.

They didn't play especially well against Palace, but they keep winning with these sort of performances. So often that it's impossible to think it's a coincidence.

A victory for City, but at what cost?

Manchester City needed the win against Chelsea: a nine point-gap is already looking pretty tough to close, but 12 would have been edging toward the impossible.

But at what cost did the win come? David Silva's injury isn't ideal, but they have adequate cover. Sergio Aguero's could be longer term, but they have Gabriel Jesus. Oddly, Rodri's could be the most costly, if it keeps him out for an extended period.

Pep Guardiola seems determined to stick with Fernandinho as a central defender, which means they need someone else to be the reliable screen in front of the back four. Rodri has been performing that role, but if he's missing, then they will have to rely on Ilkay Gundogan in a position that is not his best.

For a team so expensively assembled, suddenly squad depth is looking like a problem.

They couldn't ... could they?

Leicester's win over Brighton took them to 29 points from 13 games. It's worth pointing out that at the same stage of their title-winning season in 2015-16, they had 28 points.

Could perception of winning help Spurs?

Harry Kane's words after Jose Mourinho's first game in charge of Tottenham were interesting: "He wants to win, he's a proven winner," said Kane of his new manager. "I've made it clear that I'm at the stage of my career where I want to win trophies.

"I've made it clear I want to win them here, and it's a big year for this. Realistically, we look at the Champions League and the FA Cup to try to do that. We will see how that goes, and, from my point of view, I will keep doing what I'm doing and keep fighting for this club on the pitch."

While there are obvious and valid philosophical concerns about Mourinho's appointment, it could pay off in the short term at least, simply because of the perception that he's a manager who wins things. Mauricio Pochettino, for all his strengths, has never won a thing, and it would be interesting to discover whether that harmed his standing in the dressing room after five excellent but trophyless years.

Even the idea of Mourinho as a manager who will bring medals to these players could help: that could make them more likely to commit to his ideas, which could not only lead to success in cup competitions, but also carry over into their league form. In the short term, at least, Mourinho's reputation could be his biggest asset.

Pellegrini won't last if he keeps picking Roberto

West Ham apparently do not know when Lukasz Fabianski will return to action, which must be profoundly troubling for Manuel Pellegrini, one of a few Premier League managers in danger of losing their jobs at the moment.

Never mind mustering only two draws from their past seven games, you could make a case that Pellegrini deserves to go if he picks Roberto in goal again. If a goalkeeper had saved Son Heung-Min's opener for Tottenham, then he probably wouldn't have deserved much praise, it being a moderately well-hit effort at the fabled "good height" for a keeper to stop. But Roberto let it pass his hands like it was a flaming cannonball, leading one to wonder if he is actually a professional keeper or if we've all been taken in by an elaborate prank.

David Martin was on the bench on Saturday. Under normal circumstances, it would be a big call to throw him in against Chelsea next weekend, but now it seems like the only responsible thing Pellegrini can do. If he's still in charge then, of course.

Silva won't last until Christmas

The good news for Marco Silva is that, even after the defeat to Norwich that completed the sought-after treble of losing to all three promoted sides before the end of November, the sense is Everton are reluctant to sack another manager after getting through Roberto Martinez, Ronald Koeman and Sam Allardyce in the past three years.

The bad news is that their next three games are against Leicester, Liverpool and Chelsea. Don't bet on Silva still being in place by the second week of December.

This must be the start of something for Norwich

The trick for Norwich is to now put some sort of run together. Their previous wins this season, over Newcastle and Manchester City, were followed by two defeats and one point from seven games, respectively.

The victory over Everton lifted them off the bottom of the table, but they will need plenty more where that came from, and their next two games are winnable: at home to beleaguered Arsenal, and away at Southampton. These games could be crucial, not just for the points they might gain, but the confidence for the rest of the season they could bring.