So far at Man United, Alexis Sanchez has failed to improve on his Arsenal form

A skip, a feint, a surge into the penalty area and a bending finish from an inside-left position that reminded of Ruud van Nistelrooy: there was no better way for Anthony Martial to announce himself as a Manchester United player.

And best of all, that September 2015 goal came in a 3-1 defeat of Liverpool.

The equation is simple: score against those bitter rivals and become an instant United hero. It can buy vital leeway for a player finding his way at English football’s most expectant club.

And even among the oldest, most experienced stagers, Liverpool is the opponent that all the players want to score against. “Gary Neville’s just told me that is his dream and I’ve just gone and done it,” said John O’Shea in the aftermath of scoring his famous March 2007 winner at Anfield.

For Alexis Sanchez, Saturday’s lunchtime North West summit supplies a golden opportunity to quieten growing murmurs that he has been a misfit in Manchester. Since arriving on that “free” January transfer from Arsenal that made him his new club’s best paid player, he has supplied just two assists in his eight starts so far and is still yet to get on the scoresheet beyond tapping in the rebound of his own missed penalty against Huddersfield.

His struggles so far have led many United fans to call for Martial to be restored to the left side of United’s attack and Sanchez to be relocated elsewhere in the team. At Manchester United, even this current incarnation, one looking on as City sweep the Premier League before them, there is always another player waiting to step in, no matter your reputation elsewhere.

Thus far, Sanchez’s most telling impact has been as an unwitting catalyst for the United culture war taking place between Paul Pogba and Jose Mourinho. It has quietened down for now, but no armistice has yet been declared. With Sanchez playing as a left-side attacker, and Pogba inside him in midfield during Monday’s first half at Crystal Palace, Mourinho’s reluctance to combine that pair on that side of his team gained compelling evidence in its favour.

It took the arrival of Marcus Rashford for Scott McTominay to shift United from helpless to hopeful of mounting the comeback they eventually pulled off to win 3-2 via Nemanja Matic’s thudding winner. Sanchez, though, was little but a bystander as Palace’s injury-wrecked, exhausted team fell at the finish.

There have been only a few signs of the petulance that filled his last year or so at Arsenal, but Sanchez, a player who utterly thrives at being in the centre of the action – – see his World Cup and Copa America performances for Chile for the best examples of that – –  does not look to be enjoying his football.

Instead, he is suffering the doubts that so many have endured after arriving at United in the post-Ferguson years. The club’s desperation to live up to a still-recent glorious past has made it careless with the players it continues to spend hundreds of millions on. Radamel Falcao, Bastian Schweinsteiger, Henrikh Mkhirtaryan and Angel di Maria are previous United signings of standing and elite-level ability who were chewed up and spat out by the club’s transfer churn.

Making the grade at United requires patience and perseverance, from both manager and player. Instrumental in United’s surge at Selhurst Park on Monday was Juan Mata, a January 2014 signing who took time to settle at Old Trafford, and did not start producing anything like his Chelsea form until well into the next season.

Mata well knows the soothing effect of scoring against United’s greatest rivals. “When you play for United and score at Anfield and win the game, it stays in peoples’ minds,” he said last year of the March 2015 bicycle kick that was the deciding goal of a 2-1 win.

Similarly to the market opportunism that brought in Sanchez, Mata was signed in January 2014 from Chelsea as a desperate United attempt to turn back the tide of David Moyes’ doomed regime. He was signed without a proper, planned portfolio or purpose, for not much more reason than his being a good player who was gettable, unwanted by a peer now ready to offload him.

Once Arsenal decided that getting rid of Sanchez was preferable to having him linger at the club until the summer, and Manchester City decided that they did not want to reprise their interest of the last transfer window, then United stole in for a coup that had the club’s worldwide fans celebrating the arrival of a world-class talent.

But without serious improvement in United’s remaining nine Premier League matches and whatever remains of their Champions League and FA Cup campaigns, Sanchez is in danger of becoming the latest avatar of the club that throws good money after bad.