That is exactly what happened in South Africa's case. Even casual observers of the series may have noticed how calm the South African players looked when the "big" moments arrived at various points during the three Test matches.
There had been several big moments for them in the Swiss Alps seven weeks earlier, such as ascending the face of a 1 000m glacier. There was no safety net. A slip or a loss of concentration and the result would have been a little more serious than a wicket or a dropped catch.
For the Proteas, it was a pre-series training camp and team-building exercise with a difference, led by South African-born Swiss adventurer Mike Horn. Learning to breathe steadily and hold your nerve when something rather more important than a sports result is on the line can do wonders for your ability to stay calm under sporting pressure, such as that applied by England's lower batting order at Lord's on Monday when they briefly threatened to win an "unwinnable" game.
Horn's personal achievements are mind-boggling – but that is all they would remain were it not for his ability to tell a good story and to give his feats relevance in other people's comparatively dull and normal lives.
When JP Duminy tweeted in the aftermath of the Lord's victory: "Getting to the top of the mountain is just the start of the work", he was referring to one of Horn's stories.
Unlike the travel bore who always has a tale to tell about the day he was almost trampled by an elephant in Borneo, Horn really has done it. When he talks, people listen.
As children, most of us climbed a tree or scrambled up a rock face, only to discover that the reverse journey was infinitely harder. Horn found the same to be true, having completed the hardest climb on Earth, up the "dark" side of K2, the world's second-highest peak. Only when he finally reached the summit did he realise how much work he still had left to do.
The analogy only partly works for the Proteas, of course, because they have no intention or desire to climb back down from the number one Test ranking, but they are aware that staying there will be harder than getting there. Horn and his companions never looked behind them (or down, for that matter) on their way to the top of K2. It was only after they had got there that they took stock of their situation.
Graeme Smith used some colourful phrases after the match, too – "Hornisms", if you like. "We need to make sure that, when the wind blows, it doesn't blow us over."
Walking unaided to the South Pole for six weeks in the never-ending blackness of winter in temperatures hovering somewhere between -40°C and -50°C would be enough of a challenge without having to worry about wind speeds of up to 170km/h. And worse: if the wind blows you over, you could end up in a ravine. And that's that.
One can only imagine the images in Smith's mind when talking about strengthening the bowling reserves for the months ahead.
A good show
The immediate challenge for the Proteas now is a little more manageable – a five-match one-day series against England, followed by three T20s and the T20 World Cup in Sri Lanka. As we are quickly realising, coach Gary Kirsten is sensitive to the players' emotional space. Only two members of the Test team (Hashim Amla and Imran Tahir) played in Wednesday's warm-up match against Gloucestershire in Bristol, while the others continued their "recovery" from the dizzying heights of victory at Lord's.
And the newcomers put on a good show, too, beating a motivated county side by three wickets with an over to spare while chasing 262.
Kirsten instinctively "knows" how players are feeling – he sees through eyes that have seen it all already and he creates the environment in which they can be honest.
The morning before the Lord's Test dawned grey and drizzly. One of the many established routines that had upset Kirsten's equilibrium as a player was going to prescribed training in the knowledge that hitting balls in the artificial confines of an indoor net centre was the best he could hope for. He knew it did more harm than good. Yet everyone did it.
Not any more.
Besides, the majority of the players' wives and partners had arrived two days earlier, so why not have a relaxed breakfast? Training was optional. Amla and Morné Morkel went, but only to "visualise" and gain a sense of what lay ahead.
Andy Flower, the England coach, was flabbergasted: "They must be very confident," he mused.
Yes, they were. But, crucially, not overconfident.