An outstanding fielder with the highest catch rate in Tests, Simpson was a top-level right-handed batsman and semi-regular leg spin bowler.

Some of the team's greatest achievements in his time as coach were winning the 1987 World Cup, regaining The Ashes in England in 1989, and overcoming the previously dominant West Indies on their home grounds in 1995.

In a match in 1956, Simpson appealed for lbw against John Shaw after he had been hit in the head by a low bouncer from Pat Crawford, whereas his teammates were busy coming to the aid of the injured batsman.

He switched to leg spin at the age of thirteen, and a week after turning 15 he was playing for Petersham's First XI in Sydney Grade Cricket after hitting string of centuries in the under-16 competition.

Coming on as 12th man, Keith Miller casually pointed him to the slips,[6] which in that era was against convention, as substitutes were expected to not field in close catching positions.

[6] He was still 11 days shy of his seventeenth birthday when he was selected to make his Sheffield Shield debut as a middle order batsman for New South Wales against Victoria in the 1952–53 season.

Nevertheless, umpire Hugh McKinnon turned down the appeal, and after Victorian captain Sam Loxton reacted angrily, the arbiter said "it's the last ball of the game and his first match".

[11] New South Wales were the strongest state at the time with many Test players and won the first of nine consecutive Sheffield Shield titles,[12] and Simpson found it difficult to break into the team at full strength.

[9] The following season in 1954–55, Simpson had more chances in the New South Wales middle order as the Test players were often playing for Australia against the touring English cricket team.

[9] In the second innings, Simpson reached 98, when light drizzle began to fall and English captain Len Hutton decided to engage in mind games by ordering his men to leave the ground even though the umpires had not adjourned the match.

When the visitors returned to the field, Simpson feared another rain delay would stop him reaching his century, so he charged English spinner Johnny Wardle and was stumped.

[14] After his unconvincing performances with the bat in the South African Tests, Simpson needed runs at the start of the 1958–59 season to retain his position in the national team for the Ashes series against England.

[9] In the Southern Hemisphere winter in 1959, Simpson played a season in the Lancashire League in England as Accrington's professional player, receiving a 950-pound contract.

[9] During this period, Simpson transformed into a less flamboyant and more solid player who eschewed the hook shot and swayed backwards to avoid short balls.

[9] Nevertheless, as a result of his strong domestic form, Simpson was recalled to the Test team for the 1960–61 home series against the West Indies, as an opener partnering Colin McDonald.

[23] Simpson's captain Richie Benaud instructed him to immediately attack West Indian spearhead Wes Hall at the start of run chase.

Against the Marylebone Cricket Club, which fielded several Test players, he struck an unbeaten 92 in an unbroken 186-run opening stand with Lawry in the second innings to set up a match-winning declaration, and took a total of 4/105 with his leg spin.

[18][23] In the Second Test at Lord's in the absence of Benaud, Simpson took 1/32 from 19 overs in the second innings,[9] removed Ray Illingworth caught at leg slip from a googly immediately after stand-in captain Harvey moved himself to the position.

[9][10] After the triumph at Old Trafford, Simpson had a run of heavy-scoring in the county matches before the final Test, scoring 116, 132 and 6, and 160, ending unbeaten in all but the last innings, against Glamorgan, Warwickshire and Yorkshire.

His bowling was less successful, with 11 wickets at 46.63[9] Simpson started the 1962–63 season looking to rectify the disparity between his prolific run-scoring at first-class level and his modest returns in the international arena.

[9] Simpson started solidly in the international matches, scoring twin half centuries in the drawn First Test in Brisbane, although he was punished with the ball, registering 1/100 from 25 overs.

On a dry surface where almost the entire square was devoid of grass, Simpson took his Test best innings haul of 5/57, removing specialist batsmen Colin Cowdrey and Geoff Pullar after they had been set, and then cleaning up the tail to restrict England to 279.

[34] Later in December 2016, an Indian cricketer Karun Nair, joined this elite club when he scored 303 not out, as his maiden century against England at the M. A. Chidambaram Stadium in Chennai.

[7] In 1964–65, Simpson led Australia on a tour of the Caribbean, which was marred by controversies over umpiring standards and the legality of West Indian Charlie Griffith's bowling action.

[47] A considerable turnover of players due to constant failure in the past eighteen months had seen the likes of Steve Waugh, David Boon, Dean Jones, Craig McDermott and Geoff Marsh all make their debuts under captain Allan Border.

[51] The 1991–92 Australian season saw a heavy 4–0 win in a five Test series over India,[52] but was marred by Australia's ignominious 1992 Cricket World Cup campaign on home soil.

The Waugh brothers, along with Taylor, Slater and Boon were to be the core of Australia's batting lineup which was to re-establish the nation at the top of international cricket in the following years.

Despite having the ascendancy for most of the First Test, they lost by one wicket, and after two high scoring draws in which they held the initiative, Australia suffered a 1–0 series loss, still unable to win a match in Pakistan since 1959.

[citation needed] The core group of players cultivated by Simpson went on to strengthen Australia into the overwhelmingly dominant cricketing nation in the decade after his retirement.

With the retirement in 2007 of Warne and McGrath, the driving force behind Australia's domination of the era with more than 1,200 Test wickets between them, the generation of players established under Simpson's watch came to an end.