I can think of some players who would have got bored batting against a West Indies attack which is far from being the most challenging to have lined up in a Test match.

Not Alastair Cook, who once again showed himself to be a master of concentration.

The 243 he made over the best part of 10 hours was typical Cook, guiding England to their 514-8 declared on the second day of the day-night Test at Edgbaston.

Characters like Cook, or my Test Match Special sparring partner Geoffrey Boycott, simply love grinding bowlers down.

They don't couch big scores with an asterisk that denotes the strength or weakness of the bowling. They put Test runs in the bank - that is their currency.

When Cook opted to give up the captaincy at the beginning of the year, we wondered how his batting might be affected.

Because of his solid character, the feeling was that he would slot back into the ranks without any problems - but it still had to be seen to be absolutely sure.

'Root and Cook critical to England's Ashes hopes'

Cook took a lot of flak as skipper.

Over the course of his four-year reign there were probably as many downs as there were ups, but I honestly believe that he really enjoyed the job. He was certainly very proud to do it.

He is definitely much more relaxed without the burden of the captaincy - he looks like a young man again - but he may have needed to convince himself that he could still stir himself to play Test cricket without the responsibility of leadership.

Innings like this, his fourth double century, will be further reminder of the joy of scoring big runs for England, and a reinforcement of his importance to the team.

Cook played well in the series against South Africa, but failed to make the big score we associate him with. That was partly down to the touring bowlers and the tricky surfaces.

It was also indicative of a longer-term trend that has seen the left-hander struggle to convert fifties into hundreds. Before this knock, only five of his previous 31 half-centuries became tons.

Cook would have been aware of and annoyed by that. He is a man who talks about making hundreds - big hundreds - probably because he has had Graham Gooch in his ear for so long.

Therefore, Cook making such a big score here stands him and England in good stead for the Ashes, especially when you think that their triumph of 2010-11 was built on three of his big centuries.

Alastair Cook faced 407 balls and hit 33 fours

Along with Joe Root, Cook is absolutely critical to England's hopes of defending the urn down under.

The Essex man has now played 143 consecutive Tests, so new captain Root will have everything crossed that nothing afflicts him either before or during that gruelling tour.

Put simply, it's hard to imagine England having much chance against the Aussies without both Cook and Root having good series.

That is because they have got themselves into a mess with the rest of the top order, to the extent that they have almost no further options if the current incumbents do not establish themselves.

'Malan owns the space he occupies'

Dawid Malan fell for 65 - his maiden Test fifty - on the stroke of lunch

Mark Stoneman has played only one innings, but England will be dearly hoping that he does well in the rest of this three-match series because they have tried pretty much every other decent county opener - he is the 12th in five years, after all.

Tom Westley made a half-century against South Africa, but he looks so keen to score through the leg side and Australia simply won't allow him to do that.

At least Dawid Malan, who made 65 at Edgbaston, looks to have presence. It's difficult to define exactly what I mean by that, except to say he seems to own the space he occupies.

He seems solid and resilient. I can imagine him batting at the first Test at the Gabba, dealing with all the pressure and noise that comes with the beginning of an Ashes series in Brisbane.

This was a chance for him to make a century, a score that would have probably punched his ticket to Australia. By falling 35 runs short, Malan may well need another score against what has so far been a disappointing West Indies attack.

Jonathan Agnew was speaking to BBC Sport's Stephan Shemilt.