Arsenal Football Club, the well-oiled, functional and almost self sufficient business that it is, rarely ever pay over the odds for a player. £35m is a vast sum of money, but was never really going to prove to be a poorly judged piece of business for the signature of Alexis Sánchez. However, few would have expected him to become quite so essential to their chances of success so quickly.  Sánchez now leads the Premier League for combined total of goals and assists, having directly contributed to 19 goals in 20 appearances since signing from Barcelona in the summer. When Arsène Wenger bought the Chilean there was understandable excitement among the fans that this could be the player to take the last decade’s Premier League nearly men to the next level. Their squad suddenly looked like title challengers. On paper, at least, they surely were.  Even the pessimistic fans would not have foreseen the problems their team have suffered this campaign. Yes, everyone predicted defensive problems when Wenger opted against recruiting further reinforcements at the back, but with such vast, widespread and varied attacking talent in their squad, few fans would have expected Sánchez to have played as integral a role as he has.  Back in the 2011-12 season Robin van Persie carried the team, scoring 30 and setting up 10 of their 74 goals, thus accounting for 54.1% of their Premier League goals. Third place was the best they could manage that season, and with Alexis having been directly involved in a similar proportion (51.4%) of Arsenal’s goals this season, alarm bells should be ringing.  What is most stark about Arsenal’s reliance is the specific nature of his contribution: he is not just scoring goals, but doing a great deal to make chances possible. He put in an inch-perfect cross for Laurent Koscielny to break the deadlock on Sunday, and then scored two goals that owed very little to his team-mates. Tomas Rosicky’s layoff for his first goal was deft enough, but Sánchez still had an awful lot to do; his second was from a free-kick. He scored a perfect 10 in our WhoScored rating system, with Santi Cazorla closest behind (8.37) and no other midfielder or attacker breaking the 8.00 mark.  Arsenal have been plagued by injuries but their squad should be giving more. Sánchez has been directly involved in 12 more goals than any other team-mate; a bigger gap than any other team in the Premier League, with the likes of £16m Danny Welbeck in particular failing to live up to expectations. Discount Sánchez’s input and Arsenal would be 16 points worse off. Given how much he has played over such a concentrated Christmas period, he will probably need a rest soon, but Arsenal cannot afford to leave him out.  Charlie Austin’s importance to QPR is arguably even greater. Austin has scored or set up 10 more goals than any of his team-mates. He has been responsible for 15 of their 23 goals – a Premier League high of 65.2%.  Austin leads the line tirelessly, running the channels and linking play. However, he remains a relatively limited player, primarily concerned with finishing off moves. Joey Barton’s assertion on Match of the Day that the statistics somewhat exaggerate the reality has an element of accuracy. Austin’s chances are generally not of his own making. In fact, nine of his 13 goals have come from chances deemed “clear cut”, including three penalties, so QPR’s creative midfielders are due some credit. Only Diego Costa (12) has scored more clear-cut chances in the Premier League this season. It would be wrong to say that Chelsea are too reliant on him; plenty of his goals are the result of the craftwork of Cesc Fabregas and Eden Hazard.  In the case of Manchester City, for whom Sergio Agüero has contributed to 17 goals, there has been a distinct sharing of the workload. Agüero missed the games around Christmas through injury and yet City are now in a better position – two points off top spot – than they were before the festive period. Other players have stepped up to perform when most needed and their strength in depth, in the face of playing with no fit senior striker, has shone through.  Reports that Saido Berahino could be the subject of a whopping £23m bid from Liverpool will have West Brom fans worried about losing the most exciting prospect they have had in years. The youngster is the Premier League’s fifth highest scorer with nine goals so far, accounting for 45% of their goals, though his status as a finisher is even more pronounced than Austin’s. Berahino has yet to provide a single assist this season, with seven of his goals (77.7%) scored from “clear-cut” chances, three of which were penalties and one of which was an indirect free-kick from eight yards. Berahino’s finishing prowess should not be doubted, but he is not as integral to his team as Sánchez is to Arsenal.  In his first season without a winter break, Sánchez is showing an almost superhuman lack of fatigue as he continues to carry Arsenal towards a top-four finish. An over-reliance on any one player has rarely ever been the platform for significant success for any team, and if Arsenal’s great many other talented players do not raise their game soon, it could well be another mere top-four finish for a team that should be – but once again are not – title challengers.  All statistics courtesy of WhoScored.com, where you can find yet more stats, including live in-game data and unique player and team ratings.  • Follow WhoScored on Twitter and Facebook• Follow Guardian Football on Facebook
Best XIs from the Premier League, La Liga, Serie A and Ligue 1, plus analysis of Alexis Sánchez, Charlie Austin, Sergio Agüero and Saido Berahino