Which is not to say Spitz, or others such as Thorpe’s sometime mentor, sports psychologist Diedre Anderson, who said that without the burden of his secret Thorpe would have been able to extend his career for longer, are wrong. They may be right. Who knows? But the bigger issue is sport is supposed to reveal character – this, for many, is the main reason for watching it – and it’s an intriguing speculation that sporting performance may in some way reflect what Anderson called the effort and anguish of "keeping a balloon underwater"; that sports are a public version of an Alcoholics Anonymous meeting, where you are only as sick as your secrets.

No sport is so public a laboratory test of human frailty as golf. So is Adam Scott’s sometime propensity for missing putts on Sunday afternoons a reflection of some secret dirty laundry? Perhaps Scott has secretly worn a shirt again without washing it? Was Greg Norman’s major curse a result of a strained conscience – did those putts in the 1993 PGA Championship lip out not because the secret was in an unnoticed rogue break in the green, but because Norman’s heart of hearts was telling him he did not deserve to win? Did Larry Mize hole out at Augusta in 1987 because he was a good Christian with no secrets before God, and the magnetism of this moral imbalance steered the ball into the hole? The potential for cod psychology, not to mention God psychology, is mind-blowing. Jean Van De Velde, what were you hiding from us?

When it comes to keeping secrets, though, surely Thorpe’s was minor compared to others’. His dear dad, Ken, said he had no idea Ian was "that way inclined". A parent’s love, like any love, is blind. To most of the world, Thorpe’s sexual orientation wasn’t a secret, but rather something a kid who’d had to grow up in the spotlight clearly needed to deal with in his own way and his own time. He did lie about it, but that is hardly unusual, and it was nothing compared with the double life maintained by Tiger Woods for all those years.

And what happened to Tiger? While he was keeping the balloon underwater, he won 14 majors. After Tiger’s secrets became public knowledge, he lost the psychological stranglehold he once had on his opponents. So what do we make of that? That until 2008 Tiger might have believed he was not only a better player than his rivals but was able to fool them as well? That, as Spitz said of Thorpe, it ‘may have been the reason he was so good, the pain he suffered [or whatever, in Tiger’s case] was channelled into becoming one of the best athletes in the world’? Hang on, wasn’t Spitz saying the exact opposite before he said that?

There are numberless other closeted gay and lesbian sportspeople out there. Are they burdened on the field by their secret – or are they secretly advantaged by its hidden dynamo? And what about all the other secret keepers: not just the drug cheats but the tax cheats, the larcenists and arsonists, the adulterers, the forgers, the onanists and catamites, the insider traders and sheep-rustlers, the problem gamblers and problem eaters, the closet epileptics, the compulsive liars, the unconfessed Bee Gees lovers, the men and women with Dark Pasts? Is the whole world of sports distorted by the secrets they keep? If so, should rugby league players’ (and coaches’) secrets be accounted for under the salary cap?

The truth, as Spitz well knows, is there may not be any psychological explanation for anything. A psychological factor can as easily be used to explain one result as its opposite. Lance Armstrong held the biggest, darkest secret in all sport. Was he debilitated, or powered, by that burden? Was the impact of the drugs he took reduced by the weight of the secret he had to keep, but he’d worked out it was still a net gain? Or did the lies and the drugs have a synergistic effect, combining to anaesthetise Armstrong from all pain and all conscience?

A year ago, Phil Mickelson won the Open at Muirfield with one of the great closing rounds. His nerve held as he nailed one perfect shot after another. We have since learned that he was being investigated by the FBI and the Securities and Exchange Commission for insider trading – which Mickelson denies. His previous trouble over gambling debts was well known. Is Mickelson’s genius on the golf course a "channelling" of inner turmoil, or are his numerous near-misses in majors another case of a man betrayed by his secrets?

Or none of the above? In his 1996 classic golf book A Good Walk Spoiled, American journalist John Feinstein was told by pro golfers there’s really no such thing as a choker. Why? Because everyone chokes. Or, in the golfers’ words, everyone "throws up". As Davis Love III told Feinstein, "I was one shot off the lead with four holes left and then I threw up all over myself." A player who says he does not feel pressure is just another secret-keeper.

Come Sunday, everyone on the leaderboard at Hoylake will be throwing up all over himself. One will win the tournament, but it won’t be because he is the one who doesn’t choke. He will have choked as well as all the others. And it won’t be because he has no secrets weighing on his conscience. Nor will it be because he has bigger secrets. It mightn’t really have anything to do with the balloon he’s keeping underwater. It might just be because he plays better shots and has the greater share of luck on the day. The biggest, darkest and most unacceptable secret may be that there is no secret.