Ever since he first arrived at Chelsea, bursting on to the scene like a labrador puppy at a family gathering unsure of whose face to lick, whose leg to gnaw, which plate of sausage rolls to attack first, David Luiz has had a reputation in England for going walkabout.

David Luiz makes the wrong move. David Luiz is in the wrong place. David Luiz appears to be fundamentally confused, head out, chest puffed, galloping off towards the wrong part of the world entirely. In this context it seems inevitable, a matter of destiny, that David Luiz should have found his way to the centre of the Arsenal defence.

This is of course a cheap joke; a cheap joke that is, like all the best cheap jokes, unfunny because it’s also untrue but there are plenty of confusing and divisive things about David Luiz’s move from Chelsea to Arsenal on transfer deadline day. Getting David Luiz wrong: English football has been doing this for a while now.

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For now the most notable part of David Luiz’s move across London is the familiar wave of scepticism, the snarky chuckles, the idea floated around that Arsenal’s mop-haired defensive stroller has been overpriced and overvalued throughout his career; that he lacks good sense, spatial awareness, steel in the trenches and all the rest of it.

There is an obvious point of confusion here. On the one hand we have an acknowledged flake, chancer and gadabout. On the other a defender who has strengthened every team that signed him; who was a kind of clown-shoed Virgil van Dijk for Antonio Conte’s title-winning Chelsea two years ago; and who has in terms of style and impact been one of the most influential overseas defenders in the Premier League.

Someone is getting football wrong here. It might not be the bloke with league title medals in three countries and a world-record combined career transfer fee for a defender.

Last season 93 defenders were dispossessed more often than the league’s top-ranked goofball. Only two made more passes.

One thing is clear. David Luiz is a wonderful signing for Arsenal, even aged 32 and with almost 600 games on the clock. This shouldn’t need saying but in a way Gary Neville did him a favour with those famous comments about resembling a PlayStation player controlled by a child. Neville was referring to a specific performance in a specific game but it was a funny line and it stuck, planting the idea of a player who could be consistently underrated, mocked for his foibles and for his progressive intent.

We mock David Luiz because his failures are so often spectacularly cinematic. Against Spurs at Wembley last year he didn’t just fail to tackle Son Heung-min, he dematerialised completely and winked back into existence doing something different on the other side of the pitch, breakdancing, cooking an omelette, rewiring a plug.

We mock David Luiz because when he makes these mistakes he looks so sad and noble in the TV close-up reaction shots, like a plucky orphan child in a Disney adventure whose best friend is a streetwise duck. Meanwhile beyond all this the real David Luiz has made two errors leading directly to a goal in his entire Premier League career. Last season 93 defenders were dispossessed more often than the league’s top-ranked goofball. Only two made more passes.

Three years ago he shifted his game to become the deep playmaker in a three-man defence who drove Chelsea’s last league title win. Last year it was his brilliant drilled crossfield V2 bomb pass at Stamford Bridge that set Manchester City en route to a defeat that might have derailed that brilliant team.

Facebook Twitter Pinterest David Luiz celebrates his goal for Chelsea against Manchester City last season, a seizing of the moment that underlined his enduring worth. Photograph: Tom Jenkins/The Guardian

Risk and reward. Adaptability. Unconventional lines and angles. In many ways David Luiz is a kind of litmus test for insularity, for the idea that leaders can’t have floppy hair and romp about like a triumphant pedigree pantomime horse; or that there is only one kind of sporting bravery and it doesn’t involve taking imaginative risks or sucking up your own errors and continuing to play it the same way.

The emergence of any young English defender with the ability to pass the ball tends to generate a whisper of solemn excitement. Meanwhile David Luiz is already out there: a clown, a joke, a human error message, and a leader in a more basic sense.

His penalty in the 2012 Champions League final remains an outstanding moment in Chelsea’s modern history, the ball thumped with such furious will into the top corner you felt the game, the day, rearranging itself around him. In the aftermath of a horrendous showing in that 7-1 meltdown against Germany at the 2014 World Cup it was easy to forget David Luiz had led that blubbing, weeping Brazil team to the semi-finals by the hairs on its neck.

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At which point the prospect of Arsenal and a reunion with Unai Emery starts to make quite a lot of sense. There is no doubt Arsenal’s ball-romping defensive shield has it in him to produce some terrible moments over the next few weeks. He is also an instant spirit injection, a player who remains brilliantly fun and brilliantly funny but also uplifting for those around him.

Four years ago Arsène Wenger was at pains to reassure Arsenal’s fans his new signing Gabriel Paulista was “nothing like David Luiz”. Since then David Luiz and successive groups of teammates have won the Premier League, FA Cup, Europa League, French League (twice) and French Cup (twice), while David Luiz has been voted into the PFA team of the year in France and England.

It seems fair to say had Arsenal signed the world’s most amusingly watchable defensive shield back then and maybe taken a punt on Diego Costa too they’d have won at least one league title since. For now we have this, a late-breaking injection of something entirely unexpected. The results might be predictable but they won’t be dull.