Alastair Cook has fronted up again and will leave with Australia's respect, writes Gideon Haigh

The tone was soft, the eyes downcast, the smile shy. The speaker scratched behind his ear, stroked his mandible. The sentiments were honest but not maudlin, mainly of relief, seasoned with some regret.

The Melbourne Test involved more than one vintage Alastair Cook performance. Not only was Cook on the field for the entirety of the game, but he put in extra duty at the press conferences, as double-centurion and man of the match.

Walking off at the end of day three, he first dealt politely with Mark Taylor on the boundary line - he looked astoundingly fresh, as though he could immediately have gone around again. Then he was presented before the written press, many of whom had recently doubted his ability to come back after five Tests without a fifty. Cook had news: so had he.

Media conferences are a routine of the tour, a bugbear for players but seldom onerous, because they are usually appearing in the context of success. There's the opportunity for some schadenfreude, maybe a bit of braggadocio, of which several Australians have taken advantage this summer. Cook started instead by reflecting on his failures coming into the game. "All tour I've been struggling with rhythm," he confessed. "I've actually been embarrassed about my performances."

Had he felt his place in question? "They would have been entitled to drop me, just because I literally hadn't scored a run since Edgbaston."

Had he doubted himself? "One hundred per cent. I've doubted myself for 12 years. I'll probably continue to doubt myself. The longer it goes, the harder it becomes. That's why I'm quite proud, going to the well again and delivering a performance. It's just a shame it's four weeks too late [to help retain the Ashes]. I'll have to live with that for a long time."

Funnily enough, psychologising Cook has been a popular hobby of this tour. Old rivals such as Ricky Ponting and Mitchell Johnson have doubted whether he retained the 'fire in his belly' to continue. Old teammates Kevin Pietersen and Graeme Swann have wondered 'how hungry he is to carry on'.

Interestingly, Cook excluded this from his self-analysis: he ascribed his lack of form mainly to the faltering sync in his trigger movements. But perhaps it was audible in that homelier metaphor of 'the well', with its hint of a finite supply - an acknowledgement that he might return one day and find it empty.

Certainly it was the antithesis of a press conference another opening batsman held three weeks ago. Asked after the Bangladesh Premier League final whether his 146 not out off 69 balls entitled him to be considered the Bradman of T20, Chris Gayle responded: "No, I am actually the greatest batsman of all time." It was classic hashtag bait, fodder for a five-minute Twitter furore.

Cook neither plays T20 nor is on Twitter, and in his presence you could sort of see why, that it's a matter of attitude as well as aptitude. "Most of my runs are pretty ugly runs," he conceded. "It's quite hard work." Asked about surpassing Brian Lara's runpile, he shrugged his shoulders: "I can't really explain that. I just feel sorry for Brian Lara." This was not the feigned modesty of 'I'm-just-happy-to-contribute-it's-all-about-the-team', but an entirely genuine humility.

There must, of course, be a part of Cook that savours the battle, the sense of genuine measure, however cruel and unsparing. Short-form cricket not only accents the exhilarating and explosive, it relieves obvious responsibility.

The batsman never need feel truly defeated: it was the game that made you do it. The bowler can cop it sweet: the reality is that sometimes you will go the journey. With Test cricket, as is often observed, the name is on the tin. And tests get failed, chasteningly, sometimes depressingly. I cannot tell whether a humbling game has made Cook a humble man, or whether as a humble man he suits a humbling game, but they do seem strangely bound together.

It may be Cook's limitation that he is confessedly susceptible to doubt, cannot simply shrug it off, feels the burden of failure, can only allow himself to feel 'quite proud' in success - some would identify it as a clear case of the English talent for morbid self-deprecation. But it also has an authenticity that's disarmingly relatable.

When Cook reached his double century, every Australian clapped - and I mean seriously clapped. A few stopped after a while, others went on. Mitchell Marsh at cover kept applauding as the bowler walked all the way back. His face wore a broad smile. He has lately bounced back from a long period of enfeebling doubt, and anxiety about letting his teammates down, to taste his first real Test success. There was assuredly something in Cook's innings for every cricketer who has known how harsh the game can be and wondered if they could put themselves through it again.

At the close, Australian players came from every corner of the ground to shake Cook's hand, which was a fine tribute, for Cook does not play cricket in that rather self-praising, prolier-than-thou 'Australian way', of always 'moving the game on', of 'there is a line you can't cross'. But Australians also put store in fronting up, in stoicism and resilience, in toil and faith.

It was a double century against Australians, for Essex at Chelmsford in 2005, that first presented Cook's credentials as a potential Test cricketer. And here he was more than a dozen years later still shaping up against them. In eyes here, that sort of endurance wins a lot of credit.

Cook has won the Ashes and defended them, been beaten and come back for more. The fifth Test this week, his 152nd, may be his last in these parts. More than a few locals will wish him well.