MELBOURNE, Australia – In theory, the top 11 players on the WTA Tour to start the 2019 season have a shot at leaving Melbourne with the No. 1 ranking.
A few of them are long shots, involving winning the title and having current No. 1 Simona Halep going out early (see the story on the website).
But still, it’s mathematically possible. And so the permutations of Thursday’s draw obviously took on a little more significance for some of those players.
And so, the draw gods determining that No. 1 Halep and No. 16 Serena Williams would be an on-paper fourth-round match makes things interesting – as does the fact that 2017 finalist Venus Williams – unseeded, could be a third-round opponent.
But it is a game of roulette to even try to predict who might get through.
Many of the players only took part in one tournament before the Australian Open. And many players exited early. Some didn’t didn’t even play one.
Some are carrying injuries over from 2018. There have been multiple coaching changes. There are some dangerous floaters.
And the 2018 champion, Caroline Wozniacki, is defending a major for the first time and is in a section where the most in-form player at the moment, Aussie Ashleigh Barty, could be her fourth-round opponent.
The names that floated to the top during the Tour Finals in Singapore are not necessarily those who are coming into the season riding that momentum.
We’re thinking notably of Elina Svitolina, Kiki Bertens – and even Sloane Stephens, who finished the season beautifully even as she was in the process of splitting up with the coach.
In form, or out?
Here’s how some of the contenders for this year’s women’s singles title are going (to coin the Aussie phrase) leading up to the first major of the season.
 Simona Halep: There are questions to be answered about the back issue that scuttled the end of her fantastic 2018 season. There’s the fact that she is without longtime coach Darren Cahill, although he’s never far away. And there’s the fact that she’s played only four matches since mid-August in Cincinnati – including a straight-sets loss to the in-form Ashleigh Barty in her only match leading up to next week.
 Angelique Kerber: Kerber made a coaching change in the off-season after a not-overly-friendly breakup with veteran coach Wim Fissette. She went with countryman Rainer Schuettler, who had been working with Vasek Pospisil on the ATP Tour.
“He knows how it is to being under pressure, to having the emotions on court. He understands my thinking. You know, on court he is also, like, a hard worker,” Kerber said during her pre-tournament press conference Saturday.
The 2016 champion was beaten in her second match in Sydney by Petra Kvitova in a late night, rain-delayed affair. But she got plenty of tennis in at the Hopman Cup exhibition.
 Caroline Wozniacki: The 2019 Australian Open is going to be a new experience for Wozniacki, who will be defending a Grand Slam title for the first time in her long career. She’ll also – not insignificantly – be defending 2000 ranking points. She also made public a new battle – with rheumatoid arthritis.
Wozniacki got two matches in, at Auckland the first week of the season. She was upset in the second one by Canadian teenager Bianca Andreescu.
 Naomi Osaka: The offseason was a whirlwind for the new darling of women’s tennis – the US Open champion. She signed a number of sponsorship deals (including one announced just Saturday, with an airline).
She is now, officially, a corporate brand. And her every utterance is lapped up by the women’s tennis media as if it comes wrapped in the wisdom of Socrates. She’s on the cover of TIME this week. It’s all a lot to process for the rather shy 21-year-old with the anything-but-shy game.
Osaka got to the semis in Brisbane but was not happy with herself after a 6-2, 6-4 loss to Lesia Tsurenko of Ukraine. She had entered Sydney, but didn’t play.
— NaomiOsaka大坂なおみ (@Naomi_Osaka_) January 12, 2019
 Sloane Stephens: The American finished the season beautifully in Singapore, despite the fact that her team situation was rather uncertain. Gone are longtime coach Kamau Murray as well as traveling coach/hitting partner Othmane Garma. Coach – at least this month – is Sylvester Black. … She comes to Melbourne in question-mark form. Stephens dropped her opener in Brisbane to Johanna Konta. She overcame a first-set bagel to defeat qualifier Ekaterina Alexandrova in a third-set tiebreak. Then, against the feisty Yulia Putintseva, Stephens had the match in hand before losing it 6-0 in the third set.
 Elina Svitolina: The win at the Tour Finals in Singapore seemed to be a big step up for Svitolina, who is always spoken of as a potential Grand Slam champion. So far, though, she has just three quarterfinals in 25 career Slams – two of them at the French Open. But the third came here in Melbourne a year ago.
But Svitolina is another player who has juggled coaching changes. As well, she has just one match in 2019 – an opening loss to Aliaksandra Sasnovich in Brisbane. On the plus side, she looks healthier than she did last year.
 Karolina Pliskova: The former No. 1 seems to have put together an intriguing and potentially fruitful all-female coaching tag-team combo in former players Conchita Martinez (who’s here in Melbourne) and Rennae Stubbs (who is also here, with myriad media commitments).
Pliskova won Brisbane, winning three three-setters and defeating five very good – if not top-ranked – players to take the title. Her form can be considered pretty good coming in.
 Petra Kvitova: The two-time Wimbledon champion tends to struggle with the heat and (sometimes) humidity in Australia. Since reaching the semis in 2012, she has gone past the second round only once. (Of course, she didn’t play it in 2017 after the terrifying home invasion that left her with multiple severed tendons in the fingers of her playing hand.
On Saturday, Kvitova survived (barely) the extreme weather conditions in Sydney to beat Barty in a third-set tiebreak and win the title. That’s a tremendous confidence builder. But it appeared to take everything she had.
Unfortunately, her half of the draw plays Monday at the Australian Open – on what’s expected to be another scorcher. A least, she has an evening match against veteran Slovak Magdalena Rybarikova. She’s 6-1 against Rybarikova, going back to their first pro meeting all the way back in 2007.
When the seeds finally meet for a spot that’s sweet in the second week, the tournament really gets going.
 Simona Halep vs.  Mihaela Buzarnescu – A potential all-Romanian clash although Halep has to get through Kanepi and new titleist Sofia Kenin to get there. You’d expect Venus Williams to oust Buzarnescu in the first round.
 Carla Suárez Navarro vs.  Serena Williams – A good outcome for Serena, who might have to face Genie Bouchard in the second round.
 Daria Kasatkina vs.  Garbiñe Muguruza – Neither of these two are on form. At all. Kasatkina could lose to Bacsinszky in the first round. Muguruza could face Konta or Tomljanovic in the second round. Muguruza beat Suárez Navarro in the first round in Sydney and then withdrew before her match against Kiki Bertens with a GI illness.
 Camila Giorgi vs.  Karolina Pliskova – We expect this one to happen given the players in that quarter. And it’s a dangerous one for Pliskova.
 Naomi Osaka vs.  Hsieh Su-Wei – Victoria Azarenka looms in that section, as a potential second-round opponent for Hsieh.
 Qiang Wang vs.  Anastasija Sevastova – Wang is one of a number of players who made a big splash on the Asian swing last fall. But this is a new year, a new reality. Will she be up to the task?
 Elise Mertens vs.  Madison Keys – Mertens reached the semifinals here a year ago, in her first main-draw appearance in Melbourne. She doesn’t have much tennis in her in 2019, as she came up against a tough draw in Kiki Bertens in the first round in Melbourne. As for Keys – she’s a question mark. She has a new coach in former Tennys Sandgren associate Jim Madrigal. But she has only two actual tennis matches since last September – none this year so far.
 Dominika Cibulkova vs.  Elina Svitolina – It feels as though Cibulkova, a former finalist in Melbourne five years ago, has faded from the landscape a bit even if she made a solid return from injury in 2018. She’ll play her 12th Aussie Open woefully short of match play. Her last tournament was Beijing in early October.
 Petra Kvitova vs.  Barbora Strycova – A meeting of Fed Cup teammates. But we’ll have to see how Kvitova pulls up physically from her Sydney effort Kvitova has won her last six encounters with Strycova in straight sets. Strycova has a tricky little section to navigate that includes Putintseva in the first round and either Siniakova or Bencic in the second round. Odds are she might not get through.
 Lesia Tsurenko vs.  Aryna Sabalenka – A lot is expected of the hard-hitting Sabalenka, who was defeated by Barty in a tight first-round encounter a year ago (her Aussie Open debut). But she could face the always-dangerous Makarova in the second round. And Tsurenko may have to get through promising American teenager Amanda Anisimova.
 Ashleigh Barty vs.  Jelena Ostapenko – Barty had a very good Hopman Cup, and an impressive Sydney, where she lost in the final to Kvitova Saturday night. She beat Ostapenko, Halep, Mertens and Bertens in successful to reach the final. You’d expect her to be there. Ostapenko is a trickier proposition. Ostapenko got just two games against Monica Niculescu in her season opener in Shenzhen. In Sydney, she got six against Barty in her opening loss. And she has a dangerous first-round opponent in Maria Sakkari of Greece.
 Caroline Wozniacki vs.  Maria Sharapova – How often have these two former No. 1s played? Ten times. But not in nearly four years. Sharapova retired down 1-6, 2-4 to Aryna Sabalenka in the quarters in Shenzhen. But she has a draw that might allow her to get into the event if she’s healthy, starting with 22-year-old British qualifier Harriet Dart. If they’re both healthy, they both make it. If.
 Sloane Stephens vs.  Petra Martic – It looks like a very nice section for Stephens, even if there are some hard hitters in there. But her first match is an intriguing one. She plays against fellow American Taylor Townsend, another former pupil of coach Kamau Murray. They’ve never played.
 Anett Kontaveit vs.  Kiki Bertens – A tough section that includes solid players Flipkens, Riske, Pavlyuchenkova, Puig and Sasnovich will be a fight to the end.
 Julia Goerges vs.  Caroline Garcia – Garcia fell right off the charts in 2018, while Goerges, as she was turning 30, had the best season of her career. But Garcia couldn’t ask for a better draw to ease into 2019 with countrywoman Ponchet in the first round, and either Mattek-Sands or Aussie wild card Hives in the second round. Garcia is 2-0 against Goerges.
 Donna Vekic vs.  Angelique Kerber – Watch out for Vekic in 2019, as she seems to be coming into her own a little bit. You’d expect these two to get out of this section even if Vekic drew Kristina Mladenovic in the first round. The two met in the second round in Melbourne last year, with Kerber winning routinely. But Vekic likely would give her a better fight this time.
Pliskova vs. Serena
Osaka vs. Mertens
Kvitova vs. Barty
Kerber vs. Bertens
First-round matches to watch
Monday: Belinda Bencic vs. Katerina Siniakova. … Amanda Anisimova vs. Monica Niculescu … Jelena Ostapenko vs Maria Sakkari …  Maria Sharapova vs. [Q] Harriet Dart …  Sloane Stephens vs. Taylor Townsend.
Tuesday:  Simona Halep vs. Kaia Kanepi …  Mihaela Buzarnescu vs. Venus WIlliams …  Daria Kasatkina vs. [PR] Timea Bacsinszky … Laura Siegemund vs. Victoria Azarenka … [Q] Bianca Andreescu vs. [WC] Whitney Osuigwe.