Luis Suárez is the best player in England, so paying him £10 million a season to stay for 4½ more years is the best piece of business open to the Liverpool board as they aim to secure top spot in the Premier League against chaotic Cardiff City.

For a club who blew £35 million on Andy Carroll — and made £50 million from the sale of Fernando Torres — lifting Suárez’s salary into the top tier of Europe’s superstars was a calculation a child could have made. In a market where Marouane Fellaini cost £27 million, and Spurs spent £26 million on Roberto Soldado, a £10 million annual outlay to keep Suárez counts as a bargain, assuming you accept the insane economics of modern football in the first place.

Anyone who has watched Suárez in recent weeks knows that here is a prolific, elusive striker who has become unplayable for most centre-halves. The misery he inflicted on Tottenham’s Michael Dawson and Étienne Caboue in Liverpool’s 5-0 win at White Hart Lane on Sunday was almost painful to witness.

In a newly energised and confident Liverpool side, Suárez has found a support cast capable of allowing his talent to fully flourish. Where once the sight of Jordan Henderson on the team sheet might have caused his spirits to sag, Suárez can now expect maximum assistance from the young midfielder, and several others. Everywhere he looks, he sees dynamic team-mates working to provide him with chances.

This is nirvana for a world-class striker. Liverpool are improving fast and were inspired by the 5-0 win at Spurs to think they will return to Champions League action. Football being an uber-pragmatic industry, the 17 goals scored by Suárez this term, and his brilliant all-round play, have shifted the focus from his diving, biting and use of racist language against Manchester United’s Patrice Evra.

Some of his performances since he returned to the side on Sept 25 could be described as symphonic. Darting runs, feints and drifting moves across the forward line have been adorned by stunning finishes: particularly in the 5-1 victory over Norwich, in which he scored four.

The better he looks, the more obvious the disparity between regular Premier League games and the big stage where a player of his talent belongs. Equally, the Champions League is missing Suárez. These days, personal ambition is inseparable from pay packet. Yet we can be sure he craves trips to Milan and Madrid as much as Liverpool fans want to see him there in a red shirt.

Against that background, this new 4½-year deal will look fragile if Liverpool fall away into the Europa League places or even lower.

In September, Steven Gerrard, the captain, said: “If we don’t qualify for the Champions League this season, he can go to Real Madrid, Barcelona or Bayern Munich – and he can go with his head held high.”

When Gerrard said that, Liverpool had no realistic hope of being top of the league four days before Christmas, as they will be if they beat Cardiff. Everything has shifted up a level. But we can still assume Suárez would want to leave next summer if Liverpool again miss out on a Champions League place. Even then, the club would be protected by this new deal. As Suárez scribbled his name on that sheet, Real Madrid and others must have let out a sigh. The cost of buying him has just doubled: to £80 million or so.

Enough, though, of maths and business. For £10 million a year, Liverpool have tightened their hold on one of the few players worthy of mention in the same paragraph as Kenny Dalglish. This is a strictly footballing assessment, aside from the moral baggage. With a simple act of logic, Liverpool have asserted their pedigree, with pen and paper, as well as the ball at their feet.