Anthony Martial needed, but not as a No 9, Kevin De Bruyne the 'Invincible' and Swansea crying out for firepower

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It’s been non-stop during this festive period, with fixtures flying at us thick and fast from every direction.

After a jam-packed weekend of Premier League action, the New Year ushered in yet more football.

The likes of Manchester City and Manchester United returned to winning ways while Crystal Palace continued their resurgence under Roy Hodgson.

Elsewhere, Leicester got back on track and Liverpool left it late to claim all three points from their trip to Turf Moor.

Here are seven things we learned from the Premier League at the turn of the new year:

With Romelu Lukaku unavailable due to injury, Jose Mourinho handed Anthony Martial the chance to shine against Everton as he stepped in to fill the Belgian’s shoes. With six goals and three assists to his name so far this season, Martial has enjoyed a relatively fruitful campaign but has ultimately failed to nail down a starting spot under Mourinho. This, then, was Martial’s big chance to shine and stake a claim in the side’s starting XI.

But until he hit the opener, the Frenchman looked somewhat uncomfortable in the forward position. There was a confidence and authority lacking to his play, as highlighted by his clash with Ashley Williams in the 37th minute when he was brushed aside by the defender. Prior to that, his touch let him down as he attempted to meet an Ander Herrera through ball early on and was generally unconvincing in tight areas. Given his pace and direct running, he seems far more suited for the wings.

However, his ability shone through with his sublime goal, picking up possession on the edge of Everton’s box before stroking the ball into the top-right corner with the inside of his foot. It was a genuinely top-class goal that showed just what’s he capable of. When offset against his general all-round play on Monday night, here was further confirmation that United need Martial in their starting XI but not as an out-and-out forward.

Andy Carroll finally has his scoring boots (and head) on again after clinching a match-winning brace against West Brom. Carroll celebrated his first goal since April, and his first at the London Stadium since January last year. West Ham attempted to play to the striker’s physical strengths, forcing the ball down both wings with the intention of whipping the ball into the Geordie giant.

The tactic paid off just before the hour, when he equalised with a header, and again with his feet in the 94th minute. Carroll’s season, as ever, has been marred with injury problems, so this will naturally be a huge boost. The 28-year-old had last been given a start back in November. It definitely gave the home fans a lift, taking the Hammers out of the relegation zone. But there’s still just a point separating them and Stoke in 18th.

Just 48 hours after leaving the Selhurst Pitch on a stretcher, Kevin De Bruyne was back in action for Manchester City last night after convincing manager Pep Guardiola of his readiness. More than this, the Belgian went on to pick up the man-of-the-match award as City returned to winning ways with a 3-1 win. It was a typically polished performance from De Bruyne, who was praised by Guardiola after the win for his “great character”. It’s this sort of desire and passion which has to be commended and goes some way to explaining why the 26-year-old will be named Player of the Year for this season.

After the highs of their trip to Vicarage Road, last night's showdown with Tottenham was always going to serve an unwanted dose of reality for the Swans. And so it proved. In the near-torrential conditions of South Wales, Swansea toiled against their London visitors but to no avail.

Among a string of other issues, the lack of firepower up front was perhaps the most glaring issue for the hosts. Indeed, the home side failed to record a single first-half shot on target against Tottenham – the 12th time this has happened this season. And when the Swans did get their chances, they failed to capitalise. Jordan Ayew was a prime example of this, slaloming his way into the visitors’ box, shifting it past Hugo Lloris, only to fluff his lines. Mike van der Hoorn came close moments later, hitting the crossbar from a corner. But there was to be no salvation.

If Swansea are to stand any chance of avoiding relegation this season, they must invest wisely during this transfer window in a proven goal-scorer. Tuesday’s 2-0 defeat was another stark reminder of this. If they fail to recruit, they’re destined for the drop.

It was a consistent theme across all four games on a wet, windy Tuesday night where the appetite for 90 minutes of football was diminished, particularly among the men who have been flogged by fixtures for the past ten days or so.

West Ham, who have played just two games over the festive period, had the staying power that West Bromwich Albion, a team that have complained about fixtures overload, couldn’t muster. That late winner from Andy Carroll could be crucial come the end of the season.

Elsewhere, Southampton threw away a lead because they couldn’t keep up with Bakary Sako’s fresh legs from the bench.

The Premier League has no plans to introduce a winter break at this point but there has to be some way they can avoid this ludicrous glut of fixtures over Christmas and New Year.

The only reason they might actually change their minds and act on the issue is that the quality of the play, as evidenced by this slate of games, indisputably suffers.

Until Crystal Palace have mathematically escaped relegation, there will be the lingering fear that hiring Frank de Boer was not only a mistake, but one that ultimately cost the club their longest-ever stint in the top flight.

The Dutchman was sacked by the club after four games but the club went seven without a goal to start the season, seven defeats and a feeling that they were probably already relegated by the autumn.

But Roy Hodgson has performed one of the most impressive resurrections of his career and increasingly Palace are looking like a team that could pull clear of the relegation battle altogether.

It is important not to get carried away after a few results but when the bottom half of the table is as muddled (and poor) as this, a few results can propel you up the league.

And had Palace not fluffed last-minute penalties against Bournemouth and Manchester City they would already have leapt from stone dead under De Boer to the top half under Hodgson.

He may have tired in the second-half against Burnley – allowances have to be made after five months out with injury – but Adam Lallana impressed on his first start for the club this season. Alongside Alex Oxlade-Chamberlain, he was one of Liverpool’s better players and he will surely play a significant role in the second half of the season, as the Reds chase a spot in the top-four and look to prolong their run in the Champions League.

Crucially, Lallana also showed little fear of aggravating the thigh injury which ruled him out for so long. Against Bournemouth he was booked just moments after coming on and here his defensive contributions particularly caught the eye. He has lost none of his bite and continues to be an invaluable player at both ends of the pitch for Liverpool.