Four years after promotion from the Championship, West Ham United, who take on Arsenal in the early kick-off on Saturday, are challenging for Champions League qualification under an exciting manager and on Wednesday face Manchester United for a place in the FA Cup semi‑finals. As West Ham prepare to move to the Olympic Stadium, people are asking whether this season is a flash in the pan or if they are capable of establishing themselves as title contenders. What are the key factors determining current success and future prospects?

1 The manager

It always was a marriage of convenience between West Ham and Sam Allardyce and no one was getting anything out of it in the end. Supporters pined for a manager with a more expansive approach, someone who got their desire for attractive football and Slaven Bilic ticked that box. As a former player, he understood the West Ham way.

At the same time, the club knew that replacing the pragmatic Allardyce with someone who had not managed in the Premier League was a risk, despite Bilic’s experiences with Croatia, Besiktas and Lokomotiv Moscow, and a shambolic 4-3 defeat at home to Bournemouth in August generated a sense of foreboding around Upton Park.

Those fears quickly proved unfounded, though, as Bilic demonstrated he is a quick learner, reacting to the Bournemouth game by masterminding a 3-0 victory at Anfield, West Ham’s first win there since 1963. The holder of a law degree, he is a highly intelligent man and those close to him speak of a manager whose charisma, charm and passion allow him to command the respect and admiration of his squad.

The players have embraced his methods. They are free to express themselves on the pitch and those who have been around for a long time cannot remember training being this intense. A day off early in the week is followed by sharp sessions as match day approaches and Bilic is a prominent figure on the training ground, allowing his assistants, Nikola Jurcevic and the popular Edin Terzic, to run the sessions while occasionally stepping in to offer a quiet word of advice here and there.

West Ham are not flawless. They have struggled to assert themselves in several games, often starting slowly against lesser sides, and have ridden their luck at times. It makes their overall level hard to assess. Which is the real West Ham? The one that took 30 minutes to string two passes together against Norwich in September? Or the one that outplayed Tottenham Hotspur last month? Either way, they know how to stay in games. Take the 2-1 victory over Southampton on 28 December, when they were fortunate to be only 1-0 down at half-time, before Bilic’s substitutions changed the game. He can make tactical tweaks on the go and he is not afraid to ditch Plan A, which is why West Ham have recovered 12 points from losing positions this season.

Bilic is capable of surprising his rivals, with the win over Spurs notable for his use of a 5-3-2 formation after months of veering between 4-3-3 and 4-2-3-1, and his calm demeanour behind the scenes has helped the team maintain their composure when they are behind. Survival was the main objective at the start of the season but it was not long before West Ham were setting their targets higher.

Slaven Bilic has breathed new life into West Ham’s attacking play. Photograph: Paul Childs/Reuters

2 The board

As one board member puts it, 20 minutes in Bilic’s company is all it takes for people to warm to him and David Sullivan and David Gold, the club’s co-owners, knew that they had their man at the end of the interview with the Croat. There is chemistry, trust, a sense that the owners and the manager are pulling in the same direction.

Sullivan and Gold have not got everything right since buying the club just over six years ago. Hiring Avram Grant in 2011 was a huge mistake. West Ham went down and needed Allardyce to piece them back together. Yet Sullivan and Gold are experienced and the good has outweighed the bad. Reeling under Icelandic ownership in 2010, West Ham were on the brink of financial oblivion. The squad was a mess and Mark Noble has admitted that the club was run like a circus. Now they are challenging for the Champions League qualification and will move into the Olympic Stadium this summer.

The challenge is to keep growing. West Ham have had successful seasons in the past but the problem has been backing it up consistently. Previous regimes have stood still, leaving supporters cold with faceless PR. Sullivan and Gold are not everyone’s cup of tea but they have engaged with fans via traditional and social media and while West Ham cannot compete with the financial muscle of the traditional big clubs they are starting to challenge.

Survival was the objective at the start of the season but it was not long before West Ham set their targets higher

3 Recruitment

Without spending eye-watering sums, West Ham have been astute in the transfer market in the past two years. Sullivan is heavily involved in identifying and securing targets, while Tony Henry, who worked with David Moyes at Everton, has performed excellently since being put in charge of the recruitment department.

Diafra Sakho, signed for £3.75m, was playing in the French second division. Cheikhou Kouyaté joined from the Belgian champions, Anderlecht, for £5.63m. Angelo Ogbonna arrived for £8.25m from Juventus, the £4.5m midfielder Pedro Obiang has impressed since joining from Sampdoria and even Dimitri Payet, signed for £11.25m from Marseille, was overlooked by other clubs.

It has reached the point where even the groundsmen cannot tear their eyes away when Payet practises his free-kicks in training and sighs of disappointment can be heard around Chadwell Heath when the ball flies off target. West Ham believe that the 29-year-old is worth every penny of his £125,000-a-week, five-year deal.

That was a sign of West Ham’s intent and perhaps they will look to make one marquee signing this summer; they have targeted two expensive forwards, for instance, Lyon’s Alexandre Lacazette and Marseille’s Michy Batshuayi.

Yet they have not been afraid to sign players from the Championship. Aaron Cresswell cost £3.5m from Ipswich Town, Sam Byram cost £3.7m from Leeds United and Michail Antonio cost £7m from Nottingham Forest. Antonio, 26, has scored seven goals despite breaking into the team only in December.

Loan deals have also given West Ham time to think. While they signed Manuel Lanzini on a permanent basis last month, waiting before spending £9m on a 22-year-old Argentinian who had been playing in the Middle East, Emmanuel Emenike, Victor Moses and Alex Song will probably be sent back to their parent clubs.

Michail Antonio has scored seven goals since breaking into the team in December. Photograph: Arfa Griffiths/West Ham United via Getty Images

4 Squad depth

Bilic has selection headaches now that he has a fully fit squad and, although West Ham’s FA Cup quarter-final replay against United is a few days away, he will play his strongest side when Arsenal visit Upton Park on Saturday afternoon.

But for the injury crisis that decimated West Ham’s attack in the winter months, they might have challenged for the title. Yet Bilic looks back on that period positively. The squad players stepped up and West Ham had to graft during a nine-game unbeaten run.

Bilic did not hide his frustration about the spate of muscle injuries that threatened to derail his side, prompting the former West Ham winger Matthew Etherington to criticise the quality of the pitches at Chadwell Heath. There is respect for the experienced fitness coach, Miljenko Rak, and West Ham hope that moving to their new site in Rush Green will solve the problem.

5 The stadium

Arsenal are generating more match‑day revenue than any club in the world, making over £100m from the Emirates Stadium last year. Manchester United made £87.96m from Old Trafford, Chelsea made £71.84m from Stamford Bridge. Liverpool made £57.85m from Anfield and Tottenham made £41.83m from White Hart Lane. West Ham made £19.9m from Upton Park, which holds 35,000.

Although the majority of income for Premier League clubs comes from the broadcast money, moving to a bigger, commercially attractive stadium will strengthen West Ham’s position. Far from struggling to fill the Olympic Stadium, West Ham are expanding the capacity from 54,000 to 60,000 and could eventually increase it to 66,000. The attraction is clear. Upton Park can be difficult to reach and even harder to get away from after full time. Getting to Stratford is simple. The team are playing well. There are whispers of a visit from Barcelona in pre-season. Champions League football is a possibility.

What West Ham can hope to make from the stadium remains unclear, with critics of the move pushing the London Legacy Development Committee to release the full terms of a deal that has led to disputes over the use of public funds and the cost to taxpayers, but it has boosted their commercial potential. Last year they agreed a record shirt sponsorship deal with the online bookmakers Betway, who agreed to pay £20m over three and a half years.

“When the deal was signed with West Ham United we were in the right place at the right time, but there was certainly a long term view towards the Olympic Stadium and the growth of the club because of that move,” a spokesman for Betway told the Guardian.

The challenge for West Ham is to keep their identity after the move. Upton Park remains one of the most atmospheric grounds in the country and, while the club are pulling out all the stops to make the Olympic Stadium feel like home, the adjustment will not be straightforward. Ambition must not come at the cost of the club’s soul.