It's been a funny old week for cricket in Scotland and their national coach Grant Bradburn.

Last Saturday, they beat England, the world's No1-ranked ODI side, in Edinburgh for the first time.

Spectators whooped and hollered around the Grange Cricket Club as the boom was lowered on, historically, their oldest rivals at, well, anything.

"If we beat them at Scrabble, there's big celebrations," quipped Scotland Cricket chief executive Malcolm Cannon.

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The victory was overseen by former New Zealand allrounder and Northern Districts coach Bradburn.

He has been running the Scottish team since mid-2014.

His reputation over there is strong, partly for the work ethic instilled in the players, but also a growing measure of professionalism he has overseen.

They have beaten four full member nations and are crying out for more chances to show how close they are to warranting a full member place, especially after the promotions of Ireland and Afghanistan last year.

As it happens, Scotland are playing a T20 series against the Irish and Dutch in the Netherlands over the next few days.

With New Zealand now about to look for a replacement for outgoing coach Mike Hesson, the timing seemed to fit ideally for Bradburn on a couple of fronts.

However, within three days, Scotland had been well beaten by Pakistan in a couple of T20 internationals.

There was just a hint of air going out of the tyres, although Scottish minds may have drifted a touch off the job in the wake of toppling England.

Pakistan are a strong T20 side, ranked No 1, and whether or not the Scots had won, that might not have materially affected Bradburn's chances of getting the New Zealand job he has made no secret of fancying.

Cannon, an unabashed admirer of the work done by Bradburn - whose son is in the Scottish under-17 team - has said Scotland wouldn't stand in his way if the coach wanted to return home. But he suspects New Zealand is the only country Bradburn would want to give up the Scots job for.

"Grant has professionalised the whole approach Scotland has to the men's game," Cannon said.

"Professional cricket has only existed nine years in Scotland.

"What he has done is put other parts of professionalism into the team in terms of approach, training, diet, strength and conditioning.

"But more than that, he's brought a different attitude. He's taught the players to take responsibility."

That is impressive but is a different set of requirements to what the New Zealand team need.

Cannon is confident Bradburn would have no problems adapting his work philosophy to New Zealand's demands.

Bradburn, who has encouraged his players to play with "their teeth", ie a smile on the face, and has adopted the Kaizen philosophy, a Japanese word made popular for a time on Brian McClennan's watch as Kiwis coach - essentially pursue continuous improvement in small, incremental steps - deserves credit for his work there.

However, there will be a solid list of candidates chasing the New Zealand job, including quality overseas options who have had top drawer international experience.

At 52, the time is probably right for him to have a crack. But the competition may prove too stiff.

"Grant, if he's not being talked about for [the New Zealand job], he should be," Cannon said.

That said, Scotland don't want to lose Bradburn.

They feel they are on a slow but steady upward curve, and would love to speed the process with more full member opportunities. They certainly deserve them.

If they get there, and it's under Bradburn's guidance, that would undoubtedly rate as a significant achievement.