The best batsman in the world is an Englishman. Just think about that, let it marinate, because it doesn't happen very often. A few will argue about the validity of the ICC rankings, but they are as good an indicator as any. And ever since the first Ashes Test, in Cardiff, when Joe Root made one of the great tone-setting hundreds and it became clear why the England bowling attack were still Steve Smith deniers, it felt like a matter of when rather than if Root would top those rankings. That he did so as England won the Ashes made for a perfect day.

Since 1980, only six England players have been top of the Test batting or bowling rankings: Ian Botham (as a bowler) in 1980, David Gower at different points between 1984 and 1986, Graham Gooch for the majority of a three-year period between 1991 and 1994, Michael Vaughan after his Ashes mirabilis of 2002-03, and Steve Harmison in 2004. Other countries have had plenty of players at No. 1 in that time. For reasons that are not really apparent, England no longer produces all-time-great cricketers in the quantities it once did.

A look at the averages supports this. They are not a perfect barometer, and for different reasons cannot do justice to the undeniable greatness of Botham and Alan Knott in particular, but they still tell a pretty persuasive story. Since 1968, when Ken Barrington (batting average: 58.67) and Ken Higgs (bowling average: 20.74) played their last Test matches, 43 players around the world have finished their career with a batting average in excess of 50 or a bowling average below 25*. The lists are like a who's who of modern cricket. But none of the players on them are English.

It's true that such numbers aren't a watertight indicator of greatness - the average of Higgs, a fine and underused bowler, but not a great one, confirms that - but when the evidence is this strong, it has to indicate something. And until 1968, England had 32 players whose averages were above 50 or under 25. Root's current average is 56.58.

Definitions of greatness, and whether there is a distinction between a great and an all-time great, are sufficiently personal that it is not really worth arguing the merits of, among others, Geoff Boycott, Graham Gooch, James Anderson, Kevin Pietersen, David Gower and Andrew Flintoff. What we can say is that Root has the chance to leave the kind of historical stamp that was beyond even those players. "In Joe Root, we are looking at a batsman who I think will go down as our greatest player if he continues in this manner," said Vaughan in the Telegraph at the weekend.

"He accentuated the positive by freeing his mind and expanding his game. In Australia, Root was batting time; now he bats runs"

He will have another bad patch, like all players, but his most emphatic response to the adversity of 2013-14 suggests he will be fine. There are only two real concerns: the captaincy, which has doctored many an English batting average in the last 20 years, and his ongoing back problem. It would be unwise to assume anything - we have been burned far too often by post-Ashes giddiness in recent times - yet at the moment there is a sense that Root's potential is infinite.

It's quite a change from the misery of January 2014. When Root was dropped for the final Test of the last Ashes series, plenty felt he had been found out. His Test average was 36.73; he was 38th in the batting rankings. Those ahead of him included three Bangladeshis, a Zimbabwean and Shane Watson. Just another Pom who had been talked up and who couldn't hack the hottest kitchen. That tour, he said, was "a feeling I don't want to ever go through again".

Rarely has failure been so efficiently turned into fuel. Since then Root has played 16 Tests, scoring 1761 runs at an average of 80.04. With the exception of a more decisive transfer of weight onto the front foot, he has focussed on harnessing his strengths rather than working on his weaknesses. He accentuated the positive in another way too, by freeing his mind and expanding his game. In Australia, Root was batting time; now he bats runs. In this series he has not batted significantly longer than in 2013-14 - he is averaging 103 balls per dismissal as against 83 in the previous series. But his average runs per innings has leapt from 27 to 74. To put it another way, his strike rate has more than doubled, from 33.27 in the 2013-14 series to 71.79 in 2015.

His performances in the last 18 months reinforce a truism of sport and life: that positivity is rewarded more often than negativity. The story of Root's career can be told not only in averages but also in strike rates. Through the years he has gone through the gears: 33 runs per 100 balls in 2012 (albeit from one Test), 41 in 2013, 58 in 2014, and now 70 in 2015.

There was a sense before the series that this would determine whether Root was to be merely a very good player or a great. The absence of Ryan Harris, who Root struggled against in 2013 and 2013-14, is a shame in that regard, but Root has answered every other question. It is not an abuse of hindsight to say that his first innings in Cardiff always had the capacity to shape the entire series, and his 134 is thus one the great tone-setting performances in Ashes history. England were 43 for 3, the entire country was sighing wearily, Root had almost largely negative previous against the Australians, and their pace attack had been talked up like the three horsemen of the apocalypse.

Had Root been caught by Brad Haddin on nought that day, England could easily be 4-0 down now. Root would surely have come again but whether England would, in this series, is debatable. It was not just that somebody had to debunk the spook stories about the Aussie attack but that Root, the golden boy of the team, had to succeed for symbolic reasons. As the official vice-captain and the unofficial leader of the new generation, he had to show the way to all the other inexperienced players in the side - even though he was the second-youngest player in the team, after Ben Stokes. It was not just that he made 134; it was that he made them from only 166 balls. The mini-session before lunch, when he ignored the fact he had been dropped and smashed 33 off his first 24 balls, including nine statement runs off the first three deliveries he faced from Mitchell Johnson, was a glorious example of seizing the initiative under extreme pressure.

That England went on to win the game was no surprise. Root scores feel-good, resounding runs. In Tests he averages 81.89 when England win and 21.64 when they lose; it's rare to see such a dichotomy. England have never lost a match in which he has made a hundred. He is acutely aware of the importance of first impressions and averages 76 in the first Test of a series. Since 2013-14, the second phase of his Test career, he averages 127 in the first Test and 223 in the first innings of a series.

His performance in Cardiff brought to mind a quote used by Steve Waugh to describe the impact that Vaughan's batting in 2002-03 had on the England side he later captained. "It's amazing how once one player excels, his team-mates find the leap from good to excellent to be not so difficult," Waugh said. "It suddenly becomes real rather than a dream."

Root brings Waugh to mind in other ways too: those momentum-reversing counterattacks at the start of an innings, the mercilessness once he gets in (both have specialised in huge and often unbeaten hundreds), the use of early Ashes misery as a positive. But whereas Waugh was cold and inscrutable, Root loafs around the ground with the most infectious smile in sport. At the moment, in more ways than one, he is scoring runs for fun. Watching him bat is one of the great pleasures of modern life - a reminder that "sport" used to have a much broader definition. He's the perfect summer song in human form. With Root, you know there's gonna be good times. He's an instant cure for a bad mood, oozes charisma, and could make a supercentenarian feel young.

Yet he is also extremely tough. We should not underestimate how difficult it is to combine these qualities. You don't see many wise-cracking hardasses. This, apart from his talent, is Root's greatest quality. You often have to sacrifice or at least compromise one quality to have another, but Root manages to make the contradictory compatible: toughness and niceness, youth and maturity, seriousness and mischief. It is a rare skill. He's like an expert tightrope-walker. Even his Bob Willis impersonation on Saturday managed to be very funny and perceptively satirical without veering towards the cruel. All of us who have gone for the cheap laugh know how easy it is to be guilty of that.

Root's generosity of spirit was evident again over the weekend when he highlighted the importance of Gary Ballance's forgotten innings in Cardiff. Root's salute from the balcony to Ben Stokes when he made his hundred against New Zealand at Lord's was brilliantly funny, but it also told something else: Root's face was swollen with pride at what his mate had just achieved. The joy of Joe is not just one thing, it's everything. Including the fact he is now the best batsman in the world.

* This is with a qualification of 20 innings with the bat or 2000 balls bowled, to weed out statistical freaks like Albie Morkel (with the bat) and Alastair Cook (with the ball). It also excludes Shivnarine Chanderpaul and Mohammad Asif, who could theoretically play another Test.