Emma Raducanu’s run to the third round of the Australian Open is a reminder of why she remains such a fascinating player to watch and follow.

Not only does she strike a stylish ball, but she also beats good players like Thursday’s victim: the former French Open semi-finalist Amanda Anisimova.

This is why a rival ranking system – the Elo ranking, which takes into account the quality of your opponents rather than simply stacking up wins like the Tour system – places her at an eye-catching No 13 in the world.

As she heads into a challenging meeting with world No 2 Iga Swiatek, Raducanu has already proved herself a big-match specialist. Even without playing May’s French Open, she has still won five slam matches over the past year, more than any other British woman.

The conclusion is obvious. Despite Katie Boulter’s superior performances on the WTA Tour, when the big events come around it is Raducanu who is the true British No 1.

A threat to the bigger names

The Elo ranking system (named after Hungarian physics professor Arpad Elo rather than 1970s prog-rock band ELO) was originally used in chess. The idea is that you get more points for beating better players – and particularly for scoring upsets against opponents you are not expected to beat.

Raducanu’s low volume of tennis means that she stands at No 61 in the WTA rankings, but her ability to upset good opponents – including Jessica Pegula, Maria Sakkari and Sloane Stephens over the past year – pushes her up to No 13 on the Elo system.

The only other woman to deliver such a big differential is Belinda Bencic, the former US Open semi-finalist who is ranked a misleading 294 by the WTA because of the year she recently spent on maternity leave, but stands at 22 on the Elo table.

Boulter’s results, by contrast, point in the opposite direction. She plays a lot of events – 26 last year to Raducanu’s 15 – and grinds out wins week after week. Her readiness to stack up the air miles, from Fukuoka to Ningbo, shows admirable dedication.

But two of Boulter’s three WTA titles have come at Nottingham, a relatively soft spot on the Tour, where she has won 10 straight matches without playing a top-50 opponent. This explains why her Elo ranking of 30 sits five places behind her WTA figure.

Keen bettors should note that Elo rankings (which are compiled by Jeff Sackmann, the brains behind the world’s biggest online results database Tennis Abstract) consistently outperform their Tour counterparts when it comes to predicting future results.

Growing into her career and body

The Raducanu we have seen in Melbourne this week is a very different woman to the anxious figure who initially struggled to build on her US Open breakthrough.

She has been full of good humour, extolling her love of the Australian sun, and her superstitious insistence on carb-loading with salmon and rice before each match. We have also heard about her eagerness to clear the air with Andy Murray after last summer’s Wimbledon fiasco, and her sense of relief that they are exchanging friendly greetings again.

This all fits with the encouraging signs from Raducanu’s off-season. During a get-together with reporters in London last month, she explained that the foot injury she sustained in Seoul in October had given her time to think: “OK, next year, what do I want for myself?”

The answer, she concluded, was to avoid the constant niggles that have restricted her court time since she first exploded on to the scene. Hence the hiring of her first full-time fitness trainer, the experienced Yutaka Nakamura. The move did not stop her from suffering a back issue in mid-December, but then we should not expect a radical transformation overnight.

One insider told Telegraph Sport this week that Raducanu has been committing to her new exercises with real purpose. “You see some players looking around or going on their phone while they’re lifting a weight, but Emma is completely tunnel-vision right now. She’s on a mission.”

Another person with insight into the camp said that Raducanu had been reluctant to hire experienced names like Nakamura until her career had established some stability. Only after completing a relatively full season last year – 36 matches across four continents – did she feel ready for that commitment.

Escaping the ‘phenom trap’

On the face of things, Raducanu’s modest results since 2021 might seem like a massive let-down for such a black swan of a player – the first and only man or woman to win a major from qualifying.

If we look a little deeper, however, there are plenty of precedents. Between 2017 and 2021 five women came from relative obscurity to win a slam at a young age. Of those five, Swiatek has gone on to become a powerhouse by every metric, but the other four have all struggled to cope with the aftermath. This “phenom trap” stems from at least two factors: the expectation that follows a dramatic early breakthrough, and the target that suddenly appears on your back.

“I am trying to be as fearless as I was when I was 18, 19.” said Latvia’s Jelena Ostapenko, one member of the group, in an interview with the Tennis Podcast last week. “When you’re 19 or 20 and you already win a grand slam, it’s tough to adapt. I think if I won the grand slam at an older age it would be easy for me to deal with all that stuff.”

Raducanu’s case is by far the most extreme in terms of her ranking, which was an eye-watering 150 at the time of her US Open victory. Plus, as she pointed out on Thursday, she had taken an unusual route to that point. Her parents’ insistence that she complete her A-Levels left her with limited time to practise or compete.

Asked about the contrast in post-breakthrough careers between herself and Swiatek, Raducanu replied: “Of course I’ve seen her win a lot, but I also know that we’ve had very different paths. She was playing since a very young age, and my hours in comparison were probably a bit comical when I was 17, 18 [and] playing six hours a week. I don’t think it was the same trajectory. I think now I’m working on building those foundations, and everyone does things at their own pace.”

Swiatek and the next step up

Raducanu’s third-round meeting with Swiatek has been scheduled for the main court – Rod Laver Arena – at 12.30am GMT on Friday night/Saturday morning.

The oddsmakers say that Swiatek is almost a dead cert to win, and rightly so. She has a 3-0 head-to-head record against Raducanu and looks in fine physical condition, while her opponent is suffering from back pain and was forced to take a medical time-out during the Anisimova match.

And then there is Raducanu’s shaky serve, which has coughed up an alarming 11 breaks in two matches to date. It rather looks as if she was in the middle of tweaking her action when her December back spasm interrupted the rebuilding process, leaving her without optimal confidence in the shot.

If we look hard enough, though, we can find a couple of positives to lean on. Thus far in Melbourne, Raducanu has compensated for her lack of authority on serve by returning brilliantly, winning a massive 61 per cent of her opponents’ service games. She has also played the big points with ruthless, cold-eyed authority.

Even if her road ends in round three, Raducanu has already gone further at an overseas slam than at any time since the 2021 US Open. And she has dealt with niggling physical discomfort along the way – an important ability for any tennis professional, albeit one she has struggled with in the past.

Whisper it, but there are signs that her phase of floating vaguely around the Tour could be over. Backed by a support team with whom she at last feels comfortable, she is beginning to make up for some of her development deficit. If the past week is any guide, Raducanu is emerging from her tennis chrysalis.