On Wednesday night, as his Manchester City team limply surrendered their undefeated home record this season, the previously imperturbable Mancini was seen by 45,000 people suddenly losing it, attacking his opposite number without provocation. He claimed afterwards he was merely trying to retrieve the ball and return it to the field of play, to speed up the action.
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While Mancini flapped and blinked, Moyes kept his icy blue gaze unwaveringly focused on the City manager's chin, a slight smile playing on his lips as he considered momentarily whether it would be worth the lengthy touchline ban that would ensue from administering a warning slap.
Though he didn't raise a finger throughout the fracas, Moyes had the air of someone who would not be remotely averse to the concept of the league being decided by the managers going mano-a-mano.
But if the Everton man would clearly be in contention in such a table, who else would fill the Champions League places? Twenty years ago Moyes's fellow Glaswegian, Sir Alex Ferguson, would have been a shoo-in. But that string-puppet St Vitus' dance he does on the touchline every time United score suggests his co-ordination is not what it was.
Arsène Wenger simply does not look scary enough, and although his gnomic hand movements imply he might have a background in karate, Rafael Benítez is no longer in the sort of shape to be engaging in roughhouse.
Still, even without Roy Keane, a man with whom only those bent on suicide would pick a fight, there are plenty of potential Premier League pugilists. Sam Allardyce, Tony Pulis and Mick McCarthy would clearly know how to handle themselves, while, behind those studious glasses, Martin O'Neill looks a tad unpredictable, the kind of bloke whose neighbours, interviewed in the aftermath of an incident, would say he always kept himself to himself and was the last person you would expect to have done such a thing.
Meanwhile Iain Dowie and Avram Grant don't have much to worry about preserving, facially, if the fists start to fly. Nor does Steve Bruce, a man who appears to have seen considerable service down his local boxing club. As a punchbag.
My money, though, would be on Harry Redknapp seizing one of the European slots. Twitchy and hangdog these days, he might not seem a particularly worrying opponent. But he has back-up. Particularly in the shape of Joe Jordan, who is in possession of such a fearsomely bone-crushing handshake everyone he greets ends up in accident and emergency.
There is, however, no doubt who would finish bottom of a table decided by managerial scrapping. Never mind sizing them up for a touch of fisticuffs, uniquely among his Premier League peers, before every game his team plays, West Ham's Gianfranco Zola insists on engaging in a man hug with his opposite number. It doesn't matter if it's icy Arsene or suspicious Sam, Franco is in there, embracing them like a long-lost relative. And they always reciprocate; confronted by someone nice for a change, they invariably respond in a friendly manner.
Of course a cynic might suggest there is a reason for this: Zola's team are as open and generous as their manager, always willing to surrender three points to those in need. It would be a cold-hearted visitor not to appreciate the Sardinian's kind hospitality. Indeed, if Mancini's idea ever caught on, it would prove merely another managerial competition in which Zola is way too nice to succeed.