Now the dealing is done, who will profit the most in the coming months in the Premier League?

The maths ...

Bookmakers have framed the betting market in line with net spend, so Manchester City are a best-price 7-5 to win the title after investing 130.9 million ($236.3m), Manchester United are next (9-4 after parting with 127 million), with Chelsea third at 11-2 with 74.5 million. But there is no dramatic change in the odds there, and the spending obsession can now cease.

Problems solved

City now sport an abundance of attacking full-backs - Pep Guardiola's dream - and two international midfields. A new goalkeeper (Ederson) puts paid to the doomed Claudio Bravo experiment. Chelsea have added strength at centre-back and replaced Nemanja Matic with two good central midfielders, Tiemoue Bakayoko and Danny Drinkwater. United worked chiefly on their spine, with Matic, Victor Lindelof and Romelu Lukaku. Liverpool gained at left-back (Andrew Robertson), midfield (Alex Oxlade-Chamberlain). Mohamed Salah, who could make himself an Anfield idol. Spurs found a dependable striker to support Harry Kane with Fernando Llorente's late signing. With Kyle Walker sold, they also now have two fine right-backs: Serge Aurier and Kieran Trippier. Even Arsenal made one significant addition, in attack. Alexandre Lacazette is no slouch.

Problems not solved

Liverpool's central defence is no stronger. The same could be said of City. Arsenal are no steelier nor more coherent and face a diplomatic challenge to bring Alexis Sanchez back onside. Alvaro Morata is probably a title-winning class striker but will have to fill the gap left by Diego Costa. Antonio Conte has no grounds for complaining about the thinness of his squad.

Advertisement

Painful losses

Almost none. On the contrary, the culling was impressive, Guardiola dispensing with a swarm of players who had passed their peak: Gael Clichy, Nolito, Pablo Zabaleta, Jesus Navas, Samir Nasri, Bacary Sagna, Joe Hart, Wilfried Bony, Alexsandr Kolarov and Fernando. Similarly, Wayne Rooney's time was up at United while Tottenham recruited well to replace Walker. Oxlade-Chamberlain and Gabriel would have been worth keeping for Arsenal.

Fan unrest ...

Only Arsenal supporters are within their rights to howl at the moon, after the failure to correct long-standing flaws and the farce of the Alexis Sanchez-Thomas Lemar deadline-day duet. Can any of the other top-six tribes really complain about their club's comings and goings? Chelsea's fans might feel aggrieved that Lukaku and Llorente were among those who went elsewhere, but they will hardly mind that Ross Barkley backed out of the stalls on a move from Everton.

Entertainment ...

Even more intensity has been added to the title race, but more excitement, too, especially at City, with their marvellous midfield orchestra, United back on the good foot and Salah running free at Liverpool. If August was a provisional month in the Premier League, with transfer uncertainty everywhere, business now falls away, leaving no place to hide.