“I believe in miracles”
“I got incredibly lucky”
“I don’t deserve this one, but I’m standing here and obviously very happy.”
“I wanted to make him win it”
I always believe till it’s actually over, never before.”

The way Roger Federer described his great escape in the fifth set – his second in less than a week this Australian Open – it was almost as if even he couldn’t explain how he managed to win.

The 38-year-old saved seven match points – three at 4-5 in the fourth set and four more in the tie-breaker – to beat Tennys Sandgren 6-3, 2-6, 2-6, 7-6 (10/8), 6-3 and reach the semi-finals.

It was a match that he had no business winning. Sandgren had better numbers and definitely the stronger legs. The normally calm veteran lost momentum, argued with the match officials over a code warning and needed a lengthy medical timeout.

Considering the odds it was a remarkable win, yes. But was it a miracle?

At the highest level of competitive sport, what is “miracle” and “luck” even? The intangible concepts that Federer was describing was actually just another word for mentality and spirit. The winning mentality of champions, the fighting spirit of warriors.

And while circumstances may have played some part in the victory – Sandgren is an unseeded floater who could have been overawed by the occasion after all – fortune tends to favour the brave. And brave Federer was, battling from a hopeless position to claim an ugly but memorable win.

At 38, with 20 Grand Slam titles, Federer does not lack experience at the big stage. He certainly had more than Sandgren, the world No 100 who has been in a Grand Slam quarter-final just once before.

Federer also knows what it is to have “luck” not go your way, most recently and excruciatingly at the Wimbledon final when he had two championship points but lost to Novak Djokovic, his next opponent in Melbourne. But having been where Sandgren was in the past, he also knows how to dig himself out of holes, all while waiting for an opportunity to strike back.

Sandgren had the numbers, Federer the fight

In the quarter-final on Tuesday, the numbers will tell you the match was not on Federer’s racquet.

Sandgren won more points than Federer, though there was a difference of only one – 161 to 160. But the American had 73 winners to 53 unforced errors while the Swiss had only 43 winners to 56 errors. He also 27 aces to Federer’s mere 5 – as good an indication as any of his faltering physicality in the match – and converted just two breaks (of 14 chances) while got broken four times off 14 break points.

But it is not on the racquet or the court that Federer won, instead he won by not giving up; he won because of his unyielding will.

After taking the first set with a single break, Federer was all but pummeled in the next two as he committed a total of 30 errors and was broken four times. To make matters worse, he was unable to get a start in any return game and early in the third set received a warning for an audible obscenity, which infuriated him further, as he walked up to the line judge and chair umpire – mid-game – to show his displeasure.

If this display was to unsettle his opponent, it didn’t work because he squandered a 0-40 lead on Sandgren’s serve and was 0-3 down. That is when, still arguing with the chair that he had not used wrong language, he asked for an off-court medical treatment.

That seemed like the end of the match as he struggled to move cleanly after that. He later confirmed that he felt stiffness in the groin and the leg. And while his movement was restricted, Sandgren muscled his way into a commanding lead, breaking to win the two sets and serve first in the next set.

Now, Federer is the kind of player who commands a legion of fans worldwide and a sizeable contingent was out in full force at the Rod Laver Arena egging their man on from the brink. And he usually doesn’t like to let them down.

It may be that or just the gritty resistance from the 38-year-old – who held his serve for the first five games – but when he had his first match points, he lost them on errors despite rallying against a physically hampered Federer. In the tiebreak as well, he had a chance to close out the match, but more errors and the fact that Federer finally found some rhythm meant he couldn’t take it. And when the Swiss got his second set point at 9-8, he committed a pivotal error to lose the plot.

To win that set and force a decider when his lateral movement was severely restricted was a lease of life that emboldened Federer, who rediscovered the touch on groundstrokes and then sealed the deal with a single break.

The 38-year-old celebrated by showing exhaustion instead of elation as he hunched in relief. It was another close escape. It was another great escape. But it was not founded on fortune as he later stated. Rather, it was built on his absolute refusal to give up.

When his touch deserted him, when the opponent was serving out games with ease and when his own legs weren’t moving, Federer found the steely resolve and used it to win. He was careful with his physical movement as he didn’t want to aggravate his injury, but his mental calculation was simple – you will have to win this match, I won’t lose it.

And just as we saw in his fifth-set match tiebreak win against John Millman, with the match on the line, Federer refused to blink even once and that obstinate stare put his opponent off.