Barcelona are expected to test Liverpool’s resolve with one final bid for Philippe Coutinho in the next few days before looking around to see if there are any credible alternatives. For the sake of Jürgen Klopp’s peace of mind it is to be hoped they do not settle on his other Brazilian, Roberto Firmino, because in the absence of the little magician this season the former Hoffenheim player has not only stepped up to the plate but also stepped up his game.

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There is a tendency to see Firmino as simply a top-quality finisher, and he certainly is that, though there are other aspects of his game too, and when Liverpool raced into a three-goal lead before the mid-point of the first half their mobile No9 was pulling the strings just as effectively as the object of Barcelona’s attentions does.

Liverpool could quite easily have been four goals to the good by that stage, for Firmino’s first act of note had been to play Sadio Mané clean through with an inspired diagonal ball. The winger only had Oliver Baumann to beat but had far too much time to think about how to do it and ended up tamely waiting too long. No matter, Firmino played exactly the same pass five minutes later and once again Hoffenheim were sliced open. This time Mané was not quite on his own, and as the cover moved in to block his path he produced a backheel for Emre Can to open the scoring.

Firmino was involved in the second goal as well, cutting in from the left to provide the cross from which Georginio Wijnaldum struck a post for Mohamed Salah to tuck away the rebound, then when set free down the left by Mané’s pass the Brazilian produced a perfect first-time cross to present Can with his second goal of the evening.

The cross was just the end result really, for Firmino had begun the move in his own half with a lay-off to Wijnaldum, before setting off on a 50-yard run into free space on the left flank.

All Firmino needed to do to complete a virtuoso evening was score, and he almost did that when Trent Alexander-Arnold’s cute pass allowed Salah to cross from the right. Firmino was quickly on to it but Baumann came out to deny him on the six-yard line.

One of the most impressive things about Firmino is that, though blessed with vision and a range of skills, he resists the temptation to overcomplicate. If a short or simple pass is the best pass, that is the one he will play, as at the end of the first half when he almost put Mané away again with a pass of no more than a few feet. He also covers the ground well, coming deep in search of the ball then materialising almost unnoticed in the opposition danger area as soon as an attack has been put in motion.

With such a whirlwind start the tie looked as good as over when the third goal went in, though that is not quite the modern Liverpool way and Alberto Moreno allowing Mark Uth to get outside him on the half-hour put a brake on any premature celebrations.

Klopp himself had been somewhat guilty of that, perhaps not assuming victory was in the bag when the third goal went in but certainly celebrating wildly with the fans behind him. To be fair to him he might just have been overjoyed in recognition of a hallmark Liverpool goal.

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Quick passing and movement, crisp first touches and a man spare at the end of the move to apply a slick finish, it was all there. The crowd liked what it saw as well. “Bobby Firmino” was the chant from the Kop at the start of the second half, and Firmino was also the player Kevin Vogt barged over in frustration a few minutes later, a challenge that earned the German captain a booking.

Vogt was also the player Jordan Henderson caught in possession just after the hour to unselfishly set up Firmino for a richly deserved goal. One could readily understand Hoffenheim’s frustration, however.

It cannot be much fun chasing a three- or four-goal deficit when your opponents have Firmino, Mané and Salah ready to hurtle into any space you might leave behind your back-line. Whatever happens on the Coutinho front, Liverpool look well-equipped to give a good account of themselves in the Champions League group stage.