Had he given up Castro's Cuba, the amateur Stevenson could have gone on to become a great professional.
Best Olympic athletes: Boxer Teofilo Stevenson would not be swayed to turn pro
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Teofilo Stevenson, then, is one of the bigger mysteries in boxing history. The greatest fighter in Olympic annals, that seems clear. But one of the greatest boxers ever? Perhaps the big Cuban could have been. But the answer remains: we will never know. Stevenson arrived on the Olympic stage with the subtlety of a hammer banging on an anvil.
A chiselled, 20-year-old heavyweight, he knocked out his first opponent at the 1972 Summer Games in Munich.
In his second fight he trailed the much fancied Duane Bobick after two rounds, and the American appeared to be three minutes from another step towards that preferred US boxing diploma, Olympic gold, which already had launched the professional careers of Floyd Patterson, Muhammad Ali (then Cassius Clay), Joe Frazier and George Foreman.
The boxing world was to discover that Stevenson's destiny was not as a way station for the career of Bobick.
In the third round the Cuban turned on a display of power punching as ferocious as it was clinical. Bobick was knocked down three times, counted out, and an Olympic legend was born.
Stevenson also won the heavyweight division at Montreal in 1976 and at Moscow in 1980, becoming the first boxer to win three golds in the same Olympic weight class. That he remained an amateur long enough to win three golds cuts to the heart of the enigma that is Teofilo Stevenson.
His Cuban passport meant he could not turn professional without abandoning Fidel Castro's doctrinaire communist regime.
Stevenson never took the capitalist plunge, although he was often tempted by American boxing promoters who saw him as the next Ali, even while the original Ali was still fighting.
But this also was an era when sports figures in the communist world were hailed as selfless heroes of the working class, even as they received special treatment back home.
Befitting his propaganda value, Stevenson lived in a two-storey house in Havana before his career ended, and had two Soviet-made cars. The only real escape from the socialist embrace was to defect, and if Stevenson ever considered it, he certainly never admitted to it.
"No, I will not leave my country for one million dollars or for much more than that," he told Sports Illustrated in 1974. "What is one million dollars against eight millions Cubans who love me?"
At times, the figures were closer to US$2 million (Dh7.34m) than $1m, prompting the unrepentant capitalist Ali to remark: "If he's offered two million and he don't take it, he's a damn fool."
Some were confident Stevenson would hold his own against all comers. Bob Surkein, a veteran referee who had seen every Olympic heavyweight bout from 1948 to 1972, told Sports Illustrated: "Stevenson is the best. Better than Foreman or Frazier and as good as Ali but Ali fought as a light-heavy in the Olympics. Stevenson has quick hands and he already moves almost as well as Ali, and he's bigger. He is a classic boxer, like all the Cubans. He has a strong jab and a punishing one. He turns his hand over as he punches so he makes contact with his palm down, with all four knuckles at once. He has a tremendous straight right."
Stevenson, who stood 1.91m, had the reach and punching power of a big man but retained the quickness of a smaller fighter.
Some suggested that his left hand was nearly useless, but that did not keep promoters from spinning schemes for matching him with the greats of the 1970s. "He would be phenomenal as a pro. In a class with Ali and Frazier," Don King said.
Stevenson burnished his reputation at Montreal in 1976, when he knocked out all four of his opponents, including a first-round KO of the well-regarded American John Tate.
Four years later, Stevenson reached the target he had set for himself back in 1972, three Olympic golds, when he won at Moscow. By 1980, however, he was showing signs of decline, or perhaps boredom at the lack of quality amateur opponents.
He won his first two bouts by knockouts, but his final two fights were dreary decisions, the only non-knockouts of his Olympic career.
He did not get a chance to fight for a fourth gold; Cuba followed the lead of their Soviet patrons and boycotted the 1984 Olympics in Los Angeles.
In 1982, Stevenson lost to the Italian Francesco Damiani in the world championships, his first defeat in 11 years, and in 1983, he could not win a place on Cuba's Pan-American Games team.
However, before the 1984 Olympics, Stevenson twice defeated the American Tyrell Biggs, who was to win the super-heavyweight gold in Los Angeles. Had he made the Cuban team, had Cuba gone to Los Angeles, a fourth boxing gold could have been his.
He retired in 1986 with a record 302 victories and 22 defeats and was named as the coach of Cuba's national boxing programme.
His unwillingness to abandon his country certainly kept fans of the fight games from seeing him matched against the other greats of his era, but Stevenson later made telling points about the wisdom of boxing for money.
"So there are world champions who earn a lot of money," he told the Washington Post a year after his retirement, "but they don't know how to sign their names. They are not useful to their society. They are in the same condition they began, without a penny. And they are even worse because they have burnt all their youth."
Given the toll that 12-round prize fights take even on the greats, and how quickly huge purses can evaporate, maybe Stevenson had the right idea. Not that he had a choice that did not pivot on his being portrayed as a traitor in his homeland.
The top 10 Olympic boxers1. Teofilo Stevenson, Cuba, 1972, 1976, 1980 - The first boxer to win three gold medals in the same weight class (heavyweight). All but two of his 11 Olympic victories were by knockouts.
2. Cassius Clay, US, 1960 - Soon to be known as Muhammad Ali, the 18-year-old Clay seemed to go through the Rome Olympics without a glove touching his (self-described) pretty face.
3. "Sugar" Ray Leonard, US, 1976 - Won all six of his bouts by 5-0 scores, avenging a previous defeat in the semi-finals and nearly knocking out the future 1980 gold-medallist in the final.
4. Felix Savon, Cuba, 1992, 1996, 2000 - His career closely paralleled that of his predecessor and compatriot Stevenson, with three consecutive heavyweight golds, but against lesser foes.
5. Laszlo Papp, Hungary, 1948, 1952, 1956 - The first man to win three boxing golds, one in the middleweight division and two in light-middleweight.
6. Lennox Lewis, Canada, 1984, 1988 - After losing in the quarter-finals at Los Angeles, he trained four more years and won super-heavyweight gold at Seoul by knocking out Riddick Bowe.
7. Oleg Saitov, Russia, 1996, 2000, 2004 - The gold medallist at Atlanta and Sydney in the welterweight division, a bronze-medallist at Athens. Studied journalism at university.
8. Mario Kindelan, Cuba, 2000, 2004 - Won consecutive lightweight golds, defeating future professional Amir Khan of Britain in the 2004 final. Dominated amateur boxing from 1999/2004.
9. Henry Mallin, Britain, 1920, 1924 - A two-time gold medallist in the middleweight division, winning at Antwerp and Paris. Never lost an amateur bout and never turned professional.
10. Guillermo Rigondeaux, Cuba, 2000, 2004 - Won consecutive gold medals in the bantamweight division before defecting to the US and entering professional boxing.
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