It may take a while for a proper sense of perspective to set in but, once the spreadsheet was filled and the columns totalled up, only Manchester City had spent more money than Chelsea in the Premier League this summer. The champions’ outlay stretched beyond the £180m mark, albeit with a hefty chunk recouped through sales and with Diego Costa potentially still to be jettisoned to Atlético Madrid. Antonio Conte had wanted a wave of reinforcement across his squad, a policy that was always going to require heavy expenditure. He made that clear even before the title was claimed in the spring. So, in theory, the Italian should be approaching the next phase of the campaign with a sense of satisfaction.

Except, of course, the numbers do not tell the whole story. There was a chaotic scramble on deadline night with Davide Zappacosta, a player schooled in 3-4-3 and well known to the head coach, plucked from Torino and Danny Drinkwater secured in the small hours of Friday morning while Leicester City frantically sought to complete the purchase of Adrien Silva as a replacement from Sporting Lisbon. Both additions were welcome. And yet, when Conte first aired his thoughts over the necessity to deepen his pool of players earlier in the year, he probably envisaged seeing more than five outfield personnel and a reserve goalkeeper added to the ranks down at Cobham, particularly with so many members of last season’s first-team group having been offloaded in the interim.

Comparing team and squad strength with last May remains tricky but it is not outlandish to suggest gains may have been only marginal where Conte had expected them to be considerable. To have Tiémoué Bakayoko and Drinkwater as midfield options is an upgrade, at present, on Nemanja Matic and Nathaniel Chalobah. Zappacosta – this year’s Marcos Alonso, perhaps – will compete with Victor Moses at right wing-back, and Antonio Rüdiger is an international defender who, with Andreas Christensen, will provide proper competition across the backline. But out have gone the two central midfielders, the defenders John Terry and Nathan Aké, and Kurt Zouma and Ruben Loftus-Cheek among the customary squad of departing loanees. Some of those who left were adamant the time had come to move on, most notably Matic and Chalobah, but was it really wise to let them all go before replacements had been tied down? Options on the bench still feel flimsy, and the onus being placed on Álvaro Morata to maintain his excellent start and fill the void left by Diego Costa already feels oppressive. If he struggles, Chelsea may too.

More pertinently, how many of those secured at considerable expense were first-choice targets? Arguably, only Bakayoko of the club’s or Conte’s preferred list was signed, with Romelu Lukaku opting to join Manchester United from Everton, Virgil van Dijk now contemplating a bridge-building exercise at Southampton and Alex Sandro still very much ensconced at Juventus. The other rejections will have stung just as much. Conte had done all he could to persuade a board happier recruiting younger talent that Fernando Llorente should be prised from Swansea as his forward line’s Plan B. And yet a player who had worked under the Italian at Juventus ended up joining Spurs, a club who cannot compete under their current wage structure with the salaries on offer at Stamford Bridge.

Then there was Alex Oxlade-Chamberlain, the man Conte eventually came to consider his right wing-back in waiting but a player who has apparently grown tired of time on the flank and, ultimately, preferred the role on offer at Liverpoolunder Jürgen Klopp. The less said about Ross Barkley’s U-turn on deadline night the better but, while the England midfielder would not have been available for the Champions League group stage because of injury and was still some way off a medical when he chose to return to Merseyside, the sense of anticlimax his change of heart promoted did rather fit the mood of the summer.

All of which leaves the Premier League title winners utterly reliant upon their coach’s tactical brilliance to see the team challenge on four fronts. Conte started 16 different outfield players in the league last season before the penultimate match, by which time the crown had been won. That success seemed miraculous given the tight nature of the group used, a squad that benefited from no major injuries or untimely suspensions. This year he is in effect being asked to repeat the trick while also competing in the Champions League, a competition he would ideally have targeted, with a first-team set-up only slightly stronger in terms of numbers despite the £180m-plus outlay.

It is safe to assume that, privately at least, he will be agitated. Conte, after all, is hardly calm at the best of times. His message had been consistent to date. After the opening day defeat to Burnley he had shrugged: “The club is trying to do the best. I am ready to fight with these players.” After the win at Spurs there was a repeat offering: “We know the club is trying to do its best in the market to improve the team and squad.” In the wake of the win over Everton on Sunday the record was still stuck: “The club is working very hard to try to improve our squad.”

Yet he had followed that latest nudge towards Michael Emenalo and Marina Granovskaia by revealing the crux of his concerns. he said: “Don’t forget, in September we have to play seven games. I need to rotate my players because it’s very difficult to play seven games in a month with the same players. The club know very well our situation.” The coach knows it all too well now, and will recognise numbers are still slightly thin on the ground. But his frustration will be born as much of the vagaries of the market as any disillusion with club policy on recruitment. Chelsea considered the talent pool of players available relatively shallow, with a lot of clubs, boasting similar funds and pulling power, competing for the same players. Some have been secured. Others have slipped through the net.

Conte will work with what he has, and Chelsea’s first team still looks balanced and the stuff of champions, but the month ahead will demonstrate what their objectives for the season should truly be. September sets the tone for the campaign: trips to Leicester City and Stoke; home league games with Arsenal and Manchester City; Champions League ties with FK Qarabag and at Atlético Madrid; with the under-23s presumably eyeing up a Carabao Cup home tie with Nottingham Forest. That is a logjam of games that will truly test squad depth. Come October, the world will know better how astute Chelsea’s business has been.