WHEN Irish amateur Paul Dunne shared the lead going into the final round of The Open, we permitted ourselves the magically romantic thought of his name being engraved on the Claret Jug, and the sobering one of his being denied a penny of the £1,150,000 first prize.

In the end, even burnishing the silver medal proved beyond Dunne. Three amateur rivals overtook him on the final day and he finished in a 10-way tie for 30th. The other nine pocketed £40,519 each.

Changed days. The tournament was five years old when old Tom Morris won for the third time at Prestwick, collecting the first Open prize money – £6. That was the equivalent of 11 weeks' wages for an Ayrshire farm labourer. In last place on Monday, Thomas Aiken collected £14,047.

Sport for the game's sake is what ordinary mortals still do for fun, yet the word "amateur" has become one almost of contempt. Unjustifiably. But Dunne's prodigy provokes us to evaluate rewards and the impact of money on sport.

The Open is effectively a unique arena in major sport: where an amateur can play against the world's best in an individual event. An unranked wild-card player facing Novak Djokovic in the opening round at Wimbledon seems the only comparison.

Dunne is in no hurry to become a professional. The Walker Cup beckons, but when he does turn pro, Irish companies will be queuing to have him endorse goods and services. He will become a millionaire overnight.

Players can turn pro too soon. Justin Rose was 17 when he holed his approach to the final hole at the 1998 Open to finish leading amateur at Birkdale. However, when he turned pro soon after, he missed the cut in his first 21 tournaments. Yet he won the US Open in 2013, was second in this year's Masters, and was in a four-way tie for sixth at St Andrews. He now boasts career earnings of more than $44m.

Edinburgh's Lloyd Saltman won The Open silver medal in 2005, two years before Rory McIlroy, then turned pro in 2007. But he has struggled to maintain his European tour card, with career earnings of under $400,000.

Sporting success can make one's fortune, but many sportsmen make more money on retirement, sometimes from activities little related to their earlier careers.

According to the current Sunday Times rich list, Monaco tax-exile Lewis Hamilton is Britain's wealthiest active sportsman, worth £88m. He is £16m ahead of Manchester United captain Wayne Rooney, with Jensen Button on £71m. Fourth is Andy Murray with earnings valued at £48m, then Rio Ferdinand at £44m.

Shaping up to join them is Raheem Sterling, on a five-year, £180,000 per week contract with Manchester City following his £49m transfer from Liverpool.

Yet far ahead of them all is brand Beckham. The former England captain and his wife are at No.410 on the UK rich list with £240m. Not far behind is Roger Jenkins with £217m. The brother of Scotland's former European 400m champion and confessed steroid-abuser David Jenkins, Roger won the Scottish 400m title in 1974 and 1976 and was a member of the 1978 Commonwealth Games team. The brothers were in the 4 x 400m quartet that finished sixth.

Roger made his money as a banker – once reputedly the highest paid in the City of London. His place on the rich list would be much higher but for the £150m divorce settlement he made to his Bosnian-born wife. He was soon consoling himself with Australian model Elle McPherson.

Sporting icons such as Jessica Ennis-Hill, Mo Farah, Sir Bradley Wiggins, and Sir Chris Hoy rank nowhere among Britain's highest sports earners. Football dominates, with 16 of the top 30 on the rich list. There are nine golfers (including Colin Montgomerie, with £35m), two from basketball, and two from F1, plus tennis's Murray.

Yet all the competitors on the list are surpassed by others elsewhere in sport. Even Ross Brawn, former F1 engineer and team principal (No. 968) is worth £100m; a lap ahead at 287 is one-time mechanic and McLaren founder Ron Dennis (£350m); while Bernie Ecclestone, erstwhile minor motor-sport driver and Brabham team owner, is now the wealthiest and most powerful man in Formula One (No.33, worth £2940m).

The politics of envy are ubiquitous, but those who recall the £100 minimum football wage, and Test cricketers forced to find menial winter jobs, must feel the world has gone mad. We deplore that era of player exploitation, when proprietors raked in millions while paying a pittance, and well-heeled defenders of the Corinthian ethic looked down on artisan sportsmen, shunning and excluding them.

But salaries boosted by TV rights fees have become obscene – morally indefensible and an insult to many in society like carers and life-savers in the medical profession.

Aggressive tax policies and salary caps are needed to restore the balance.