Root is already the second highest run-scorer in Test history and Stokes is a double World Cup winner responsible for some of the most remarkable individual performances the country has seen.
But neither has tasted victory Down Under, with Root winless in 15 matches and his skipper having nothing to show from 10 attempts. With both men now 34, the next few weeks could be their final chance to fill a notable gap on otherwise glittering CVs.
A two-day defeat in Perth was a huge anti-climax to a tour that has enjoyed a huge build-up and Botham, who won eight Tests and two Ashes series on Australian soil in his time as a swashbuckling allrounder, is desperate to see the pair respond in Brisbane next week.
"To be one of the very best you need to win in Australia, 100 per cent," he told the PA news agency.
"People remember you for what you've done over here. In Joe and Ben we've got two world-class players - Joe's got 39 hundreds for goodness sake - but they are desperate to make an impression here. You can only do that by winning. They need to get the monkey off their back.
"They are the two who will want this the most because a lot of the others will get another bite at the cherry. I can tell you from experience, winning over here feels really, really good and it means absolute respect.
"I don't have a favourite time because every time you beat Australia is a great day. That alone should be driving England."
Botham celebrated his 70th birthday on Monday and should have marked the occasion by commentating on day four at Perth Stadium. The early finish bought him a bigger window to celebrate with former teammates and rivals, including David Gower, Dennis Lillee and Rodney Hogg, but the manner of England's loss left a bitter taste.
In a typically uncompromising assessment, he had some tough words for the tourists.
"It was horrendous, there's no other word for it," he said.
"England need to fire up and fire up quickly. I'm fed up of hearing, 'this is the way we play'. If I hear it once more, I think I'll throw something at the television.
"If that's the way you play, you might as well go home now because it's going to be 5-0. They probably won't like me saying that but they need to get their heads around it. I want more pride when I see people pulling that sweater on."
Botham is remembered most fondly for his stunning attacking cricket in the 1981 Ashes, when he conjured up his own miracle of Headingley 38 years before Stokes produced another, but worries the current side go for top gear too soon.
"Maybe we need to rethink our tactics. You're not going to smash these Australian bowlers around all the time," he said.
"Be selective, be sensible. Pull your horns in a little bit. When I did it I got myself in first. They've got four more Tests to get it right and let's hope they do because if they go down again, it's gone."
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