STUTTGART, Germany - The World No.1 ranking is in play at this week's Porsche Tennis Grand Prix. After No.2 Simona Halep announced her withdrawal due to left hip injury on Tuesday, No.3 Petra Kvitova needs to win the Stuttgart title in order to have a chance to overtake No.1 Naomi Osaka. 

Osaka will open against either Hsieh Su-Wei or Wang Qiang. Kvitova will open against either Dominika Cibulkova or Greet Minnen. 

Here are the No.1 scenarios in Stuttgart:

- If Osaka loses in her opening match, Kvitova must win the title. 

- If Osaka wins her opening match, she secures the No.1 ranking regardless of other results. 

Osaka is making just her second main draw appearance in Stuttgart, with her last coming in 2017, where she successfully qualified and lost in the first round to Johanna Konta. Both Kvitova is a two-time semifinalist in Stuttgart, but has yet to advance to the final.

Osaka has held the No.1 ranking for 13 consecutive weeks since defeating Kvitova in the final of the Australian Open to win her second consecutive major. Halep came within a win from reclaiming the top spot in the semifinals of the Miami Open, where she lost to No.4 Karolina Pliskova. 

The upcoming clay season offers a big opportunity for Osaka to tighten her grip on the No.1 ranking. Halep, the reigning Roland Garros champion, has the most points to defend of any player on the clay. Similarly, Kvitova, the reigning Madrid Open champion, has over 1,400 points to defend before the tour turns to her favored grass. 

In contrast, Osaka has just 200 points to defend on clay, meaning a good series of results could give her some distance from the peloton.