Statistics rained down from a blue sky as Joe Root continued his run-drunk start to the season with the second double century of his young career, and Jonny Bairstow ensured that he too will resume battle with New Zealand next week in much better touch than when he suffered a double failure against them during the Auckland Test in March.

Root's 236 off 336 balls was a career best and the highest score by a Yorkshire batsman at Headingley since Darren Lehmann's famous 339 against Durham in 2006. After his match-winning century against Durham at the weekend in his only previous appearance this spring, the 22-year-old Root has now scored 467 runs from three innings and is averaging 156. "It's nice to get some runs early doors," he said with considerable understatement. "You go out there and try to be as greedy as you can because you don't know when the next drought is coming."

But the most resonant fact of all came with the discovery that he had passed 2,000 runs in the County Championship in exactly the same number of innings – 52 – as two of the greatest, Herbert Sutcliffe and Geoffrey Boycott.

His career will now take a very different path to those of Yorkshire stalwarts of the past: whereas Sutcliffe amassed 38,588 runs in 602 first-class appearances for the county, and Boycott 32,570 in 414, Root seems highly unlikely to add to his modest tally of 31 Championship matches for the rest of this season, as he heads off to lead England Lions next week, and then for the international summer proper having established himself as a likely selection in all three forms of the game.

He is beginning to justify some of the excited chatter that compared him to Michael Vaughan, a product of the same Sheffield Collegiate club, before he had even made his debut. Having left Yorkshire at the end of last season as a player of promise, and an England contender, Root has returned with the authority of an international regular – on this pitch, and against a Derbyshire attack missing the injured Tony Palladino, there was a feeling of inevitability he would dip his bread from the moment he took strike on Tuesday evening.

That was not the case for Bairstow, who scratched around unconvincingly in taking two singles off his first 29 balls before lunch – having come to the crease when Phil Jaques was run out after a mix-up with Root for the second consecutive match, showing that even the man of the moment is not flawless. Bairstow was under some pressure having failed to pass 29 in five first-class innings this spring, after a difficult winter in which he scored 18 runs in three Test innings – in matches four months apart.

Perhaps that explained the enthusiasm with which he celebrated reaching three figures for the first time since an England Lions game against Australia A last August. He had started to play with freedom, and occasional audacity, and by the time he was dismissed for 186 he was savaging the Derbyshire spinners, and had lifted his scoring rate to almost a run a ball.

"It seems like he's been under a bit of pressure, but that was a hell of a knock," added Root, having swapped congratulations with Bairstow as they passed their various milestones during a stand of 231 in 51 overs. "I'm chuffed to bits for him."

• This article was amended on 6 May 2013. The original said Root had scored 527 runs from three innings, averaging 176. He scored 467 runs from three innings, averaging 156.