There are truths, blessed truths and statistics. Sometimes a body of quantitative evidence is so powerful that it leaves only one credible interpretation: a batting average of 99.94, a bowling average of 99.94, and Australia's propensity for being involved in cricket's most dramatic matches. In the history of Test cricket, and particularly in the last 25 years, they have a monopoly on spandex-tight contests, those that are won by one or two wickets or a handful of runs. They have also been involved in both tied Tests.

To some extent that is not especially surprising: their generally consistent excellence means that their spread of results is likely to be different to other countries'. What is startling is the number of those matches that Australia have lost. It is something we might expect of England, who are traditionally perceived as being vulnerable during squeaky-Pom time, or South Africa, who are stalked by the ch-word. But Australia? It's as incongruous as finding out that Ian Chappell and Dennis Lillee drink alcopops.

Until recently Australia lost most of these matches while chasing a small target; that became the theme on which most focused. But Edgbaston 2005 (target: 282) and Trent Bridge 2013 (target: 311) have changed that and pointed to a different theme: the inability to win close games.

England's win in the first Test was the 17th match in Test history with a victory margin of 15 runs or fewer. Australia have lost 11 of those, seven since 1993. Their three victories in those 17 games all occurred over a century ago. The margin of Australia's Test defeats by runs reads like a particularly bewildering mathematical pattern: 1, 2, 3, 5, 7, 10, 12, 12, 13, 13, 14. By way of comparison, England's list of tightest defeats by runs is: 3, 6, 11, 17, 19, 22, 24, 28, 28, 28. It is the same with one-wicket wins: there have been 12 overall, five against Australia, three since 1994. Australia have won once by a single wicket.

In the last 25 years, the statistics are even more pronounced. There have been six one-wicket defeats, three by Australia; five defeats by fewer than 10 runs, four to Australia; and 11 by 20 runs or fewer, with eight to Australia, two to Sri Lanka, and one India.

Australia have won a few tight games themselves - particularly in World Cups - but their record in Tests is too pronounced to dismiss as a statistical freak. What is unusual is their pattern of defeats in the last 25 years: they have lost eight Tests by between 1 and 20 runs, but only four by between 21 and 150 runs. The tighter the game, the likelier Australia are to lose. This is an uncomfortable and unfathomable paradox given everything we know about Australian cricket.

Some may see this as delicious evidence that Australia are the real chokers. An alternative and more persuasive explanation is that only they would be in a position to lose such games. It is a subject discussed by Steve Waugh in his autobiography, in reference to Damien Martyn's notorious dismissal against South Africa in Sydney in 1993-94. Martyn, the ninth man out, drove Allan Donald to cover; Australia lost by five runs and Martyn did not play Test cricket again for over six years.

"Damien paid the price for doing the hard work early then tripping up with the finish line in sight," wrote Waugh. "As the last visible top-order player, he became the scapegoat. Greg Norman was a notable sufferer of this curse of being almost too good. Many golfers never got themselves into a position where their moment of weakness was noteworthy. In effect, they weren't good enough to be found out, because their race had already been run and no one took any notice. To succeed, you must be willing to face failure and its consequences. Not to know the depths of despair is to live in a bubble of safety and never test yourself."

Norman won two golf majors and finished runner-up eight times. Jack Nicklaus won 18 majors and was runner-up 19 times. Did he fail on 19 occasions or was he in the top two on 37? The pattern of Australia's defeats, particularly in modern times, suggests that they have not so much underachieved by losing as overachieved by getting so close to victory.

They are baggy green cockroaches. Almost all of their failed run-chases involve lower-order partnerships that capture the essence of defiance, such as the one between Brad Haddin and James Pattinson on Sunday. At 231 for 9, with 80 still needed, most sides would have closed their eyes and gone to sleep, but Australia always rage, rage against the dying of the Test.

At Edgbaston in 2005, when they lost by two runs, they were 175 for 8 chasing 282. Against South Africa in 1994 (a five-run defeat) they were 75 for 8 chasing 117. In the heartbreaking one-run defeat to West Indies in 1993 they had been 104 for 8 chasing 184. When they lost to New Zealand by seven runs in Hobart in 2011, they had been 199 for 9 chasing 241. When they lost by 13 runs in Mumbai in 2004, they had been 58 for 7, needing 107 on a vile track. The pattern goes back further, most notably to Melbourne in 1982-83. The last man, Jeff Thomson, joined Allan Border with 74 needed. They got to within four.

In Adelaide, Edgbaston, Sydney and Mumbai, Australia's highest or second-highest scorer was the No. 9 or No. 10: Tim May, Brett Lee, Craig McDermott and Nathan Hauritz. For every tight Australia defeat there is usually a hero: Haddin on Sunday, David Warner against New Zealand in 2011, Shane Warne in Karachi in 1994-95, the young Justin Langer and May in Adelaide in 1992-93.

This is not to say there hasn't been a failure of nerve or ability in some of Australia's defeats. The lower-order heroism has often come after a top-order collapse, while Ian Healy's uncharacteristic imperfections led to one-wicket defeats against Pakistan in 1994-95 and West Indies in 1998-99. But the nature of the fourth-innings chases, and our understanding of Australian cricket, suggests there is strength as well as weakness.

Australia are a side who refuse to accept the logic of defeat. The bastards won't let themselves be ground down. They sculpt classic Tests out of cussedness; and if they lose the majority, at least they got so close. In short, the opposition have to beat Australia twice. The game is apparently over, then Australia stir like a horror-movie baddie before finally taking a decisive one between the eyes.

A similar phenomenon is evident in football. Germany have lost more World Cup and European Championship finals than any other country - not because they have failed on the big occasion but because they have excelled in getting there. Long after the 1986 World Cup, Franz Beckenbauer, the West Germany coach, was discussing his side's campaign in that tournament when he started laughing. "Well," he said, "can you believe we reached the final of the World Cup with these players?"

Having inferior players is rarely a problem for Australia. Yet theirs is a similar tale: of mental strength and how the habit of victory ensures defeats become more memorable, because of their scarcity and especially their nature. It seems like a contradiction that Australia are both the perennial winners and heroic failures of Test cricket. It is anything but. Their culture of victory is so powerful that it has almost turned defeat into a virtue.

21.18 GMT, July 18: The article was amended to correct Australia's record of one-wicket victories

Rob Smyth is the author of The Spirit of Cricket - What Makes Cricket the Greatest Game on Earth