Our stats analyst Omair is already famous for his statistical articles and now he's inspired Ludolf, another reader of Women's Tennis Blog and fan of tennis numbers, to contribute his take on the WTA rankings, i.e. he compared the actual rankings with the performance of players at the biggest events – Grand Slams and WTA Championships. Enjoy!

The WTA ranking does not rank properly the strength of players in the sense of the ability to win a match or a tournament. The main reason is that it is cumulative and therefore underestimates players without a sufficient number of tournaments. We need to compute an average to avoid this. Moreover, the WTA ranking considers tournaments with weights not depending on the quality of players on them.

To achive the above-mentioned goal it seems to be more appropriate to take the average result from majors and the WTA Championships, the tournaments where the best players are almost always present. By the result of a player we mean the number of her losses (including the rounds which she did not achieve), i.e. 0 for the winner, 1 for the defeated finalist, 2 for defeated semifinalists, and so on. The results for the last 52 weeks are presented in the table, completed by the WTA ranking (after the Australian Open) for comparison. (FO: French Open, W: Wimbledon, USO: US Open, WTA: WTA Championships, AO: Australian Open)

It is not a surprise that Serena Williams and Kim Clijsters reached much better position than their WTA ranking. It should be noted that the average results of these players (and some others, too) are not relevant in the same degree as of the other players due to a small number of tournaments they took part in. For instance, had Kim Clijsters reached the next round at the French Open, she would have taken the 6th position with the average of 3.50. Also, Samantha Stosur and Agnieszka Radwanska got significantly worse result than their WTA ranking.

We can conclude that the first three players are significantly better than others, except maybe Serena Williams and Kim Clijsters. This is in a good correlation with the WTA ranking, which need not be true in general.

There are some weak points of this average result. First, rather small number of tournaments is considered, hence the average has a rather big deviation. This has been already pointed out for Kim Clijsters. Let us also note that the first three players have the smallest possible differences. Also, it does not describe the actual level of players but an average in past 52 weeks.

What do you think of this perspective? It's nice to have one more approach, but as Ludolf himself stated, it still has many flaws and the fact that only five tournaments are taken into account, it's pretty limited. Plus, almost all the best players showed up at the tournaments analyzed, but still it's "almost". (photo: © Neal Trousdale)

Other than those two events, Li decided to rest at home and stay away from the limelight.

Since I have returned, I have tried my best to not go out if I can help it and just stay at home. Perhaps everyone's recognition of me is greater and their expectations will be higher, but to me I don't want to change the life I have been leading.

Li’s husband Jiang Shan was also present at the Beijing homecoming ceremony. They've been married for almost five and a half years.

Li's win over Francesca Schiavone in the final of Roland Garros was the most-watched sporting event in China this year and the most-watched tennis match ever in the country.

You can see more nice photos from the event in WTA's gallery. (via ESPN)

China's Li Na has been sponsored by Nike and the sportswear company was quick to celebrate the Roland Garros victory of their tennis partner. Nike featured Li's photo in their Paris store and organized an event with the Asia's first Grand Slam singles champion giving autographs, posing for the pictures with fans and talking to the press.

In addition, together with Maria Sharapova, Li Na will be part of a Nike ad campaign shot by Annie Leibovitz. Nike is aware of the publicity they can gain, only in China the 2011 Roland Garros final was watched by 110 million people.

You can see more photos from the Paris Nike store event in the WTA gallery.

China’s Li Na yesterday became the first player from an Asian nation to win a Grand Slam singles title and it means a lot not only to China but to the entire tennis world as Li’s success is expected to fuel the sport's rapid growth in the most populous country.

In the above video you can see the final moments of the 2011 Roland Garros championship match in which Li defeated Italy's holder Francesca Schiavone 6-4 7-6(0).

And here's Li's post-match interview.

Chinese language lessons could be useful now. Therefore, check out Li herself teaching us how to say 40-0, 30-0 and 15-0 in Chinese. The video was filmed by the WTA Tour during Roland Garros.

Here's Li and her French Open trophy with the Eiffel Tower in the back.

Clothing brand in charge of Li's on-court appearance, Nike, has already prepared a tribute for the champion.

And last but not least, here's a video tribute to Roland Garros 2011 created by our loyal reader Leo Jamorin. If you remember, he won Wilson a tennis racquet signed by Justine Henin in one of contests here on Women's Tennis Blog.

It was a fulfilling tournament and congratulations to Li Na, who will now climb to No.4 in the rankings, from her current No.7, and equal Kimiko Date-Krumm's mark for highest-ranked Asian in WTA history. (photos via WTA Tour, Down the Line)

China's Li Na has just made a tennis revolution – the 29-year-old defeated last year's winner Francesca Schiavone in the final of Roland Garros and the sport not so popular in China is now expected to bloom, or at least to start blooming, and when you have a population of so many people in question than it's a really big deal. As for the very championship match, Li was solid, had precise shots and was in charge more or less throughout the match, which can be described as one calm Grand Slam final, without much fuss and excessively expressed emotions.

The world No.7 Li had a straightforward win in the first set. In 39 minutes the Chinese sixth seed faced no break points, took Schiavone's serve in the fifth game and simply marched on to take the set 6-4. The second set Li continued in the similar fashion, breaking Schiavone's serve in the very beginning and at 3-1 Li had a great opportunity to bring the match too close to an end, but she netted a clear shot and the world No.5 Schiavone slowly managed to get back into the match when she leveled at 4-4. Then both players held their serves until the tiebreak in which Li started shining again and actually won it without losing a point! Final score: 6-4 7-6(0).

Li was playing aggressively and her shots were mostly landing where she wanted them to land, so her number of winners totaled 31 to her opponent's only 12.

En route to the title match at the 2011 French Open Li defeated Barbora Zahlavova Strycova of the Czech Republic in the first round, Silvia Soler-Espinosa of Spain in the second, Sorana Cirstea of Romania in the third, ninth seed Petra Kvitova of the Czech Republic in the fourth, seed No.4 Victoria Azarenka of Belarus in the quarterfinals and seventh-seeded Maria Sharapova of Russia in the semis.

In case you forgot, this French Open final was actually Li's second Grand Slam singles final. Her first one she played this year, at the Australian Open. As for her WTA titles, Li has four: Guangzhou (2004), Gold Coast (2008), Birmingham (2010), Sydney (2011).

Regarding the 2011 French Open prize money, the Nike-clad Li Na earned an astonishing 1.2 million euros, which is about 1,750,000 US dollars. As a runner-up Schiavone earned 600,000 euros, i.e. almost 900,000 US dollars.

I'd also like to mention a nice factbox Reuters compiled about the rise of China's tennis (they published it before Li won Roland Garros). (photos: francetvsport)

Here we go again, two players pretty much no one was talking about in the lead-up to the French Open are now in the final of the claycourt Grand Slam –

Before anything I'd like to repeat that Schiavone and Li are playing the final of the French Open and Caroline Wozniacki, Kim Clijsters, Vera Zvonareva, Victoria Azarenka, Samantha Stosur, Jelena Jankovic, Petra Kvitova, Julia Goerges are all gone. Many of them long gone!

The world No.5 Schiavone made a big statement by reaching the final again. Even if the Italian doesn't win the remaining match, she has proved that her last year's success wasn't just an incidence, and even though people will always argue and mention the circumstances or whatever, I think the 30-year-old Schiavone has a solid proof that she can rock. Her quarterfinal against Anastasia Pavlyuchekova this week was one of best showcases for Schiavone's physical and mental capabilities.

Every now and then the seventh-ranked Li becomes "the first Chinese player who ________". In January she played the Australian Open final as the first Chinese Grand Slam finalist in women's singles, and now, just a day after becoming the first Chinese to reach the singles semifinals at Roland Garros, she's become the first Chinese to play the finals, by ousting three-time Grand Slam champion Maria Sharapova 6-4 7-5. Li made twice more winners than the Russian (24 to 12), five less unforced errors (23 to 28), seven double faults less (3 to 10), and hit one ace to her opponent's zero.

Schiavone and Li have a 2-2 career head-to-head record. Their last and only match on clay was at last year's Roland Garros and Schiavone won 6-4 6-2 in the third round. Although, as unpredictable as women's tennis is, this statistical point doesn't mean much. (photos: chascow, Stephane Martinache)

Maria Sharapova is not a good slider on clay and four years ago at the very same tournament she famously compared her movement with a "cow on ice", but now, with a different setting in women’s tennis, she’s a title favorite and today she had a straightforward 6-0 6-3 win over Andrea Petkovic to reach the semifinals. The three-time Grand Slam champion, seeded seventh this year, is now only two wins away from completing a career slam. Just to mention, Sharapova did play the semifinals of Roland Garros in 2007 and lost to Ana Ivanovic. She lost in the quarters three times.

Sharapova’s opponent in the 2011 semifinal will be China’s Li Na, who used to think of Roland Garros as the last place where she could go that far. The sixth-seeded Li has had a change of mind after her 7-5 6-2 quarterfinal victory over Victoria Azarenka. Li believes her success will give extra confidence to other Asian players, whose flat shots are more compatible with grass and hardcourts.

Li is used to writing the tennis history of her country and now she’s become the first Chinese player to reach the semis of Roland Garros in singles. Actually, the only other Grand Slam where Li went this far is the Australian Open where she finished runner-up this year.

Women’s tennis is so unpredictable nowadays that even players themselves are sometimes caught in surprise.

The other semifinal will feature home favorite Marion Bartoli vs. holder Francesca Schiavone. (photos courtesy of Tony)

First-time Grand Slam quarterfinalist Anastasia Pavlyuchenkova looked to be following up her upset of world No.3 Vera Zvonareva with an upset of defending champion Francesca Schiavone when the score was 6-1 4-1 for the 19-year-old Russian.

However, Schiavone, 11 years older than her opponent, dragged out a 7-5 second-set win and in the third set she raced to a 5-1 lead. Even though Pavlyuchenkova managed to level at 5-5, the fifth-seeded Italian was determined to finish the job, and on her third match point defeated the 14th-seeded Russian 1-6 7-5 7-5.

In the semis Schiavone will play the winner of the Marion Bartoli vs. Svetlana Kuznetsova quarterfinal. (photo by our reader Tony)

Maria Sharapova

The three-time Grand Slam champion Sharapova, who has a chance to complete a career slam this week, came back from 4-1 down in the first set, leveled to 4-4, then both players held their serves to take the set to a tiebreak. In the second set Sharapova faced set points, but saved all five of them and finished the job in that set.

It’s interesting to compare Sharapova’s and Radwanska’s stats because of contrasts in most departments. Sharapova hit 7 aces to Radwanska’s 1, but also 7 double faults to Radwanska’s 0. When it comes to winners and unforced errors the situation is equally unbalanced. Sharapova hit almost 4 times more unforced errors (44 to Radwanska's 12), but also much more winners, 47 to 13.

Andrea Petkovic, who defeated Maria Kirilenko 6-2 2-6 6-4 in the fourth round, will be next Sharapova's opponent. Other quarterfinal pairs are: Svetlana Kuznetsova vs. Marion Bartoli, Anastasia Pavlyuchenkova vs. Francesca Schiavone, and Li Na vs. Victoria Azarenka. (via Sharapova's official website, photo courtesy of our reader Tony)

World No.1 Caroline Wozniacki brought nothing new to the fashion table of Roland Garros – the 20-year-old Dane, who bowed out of the tournament in the third round already, wore the adidas by Stella McCartney Ruffle Dress which she debuted at Indian Wells in March.

Adidas impressed with an array of bright colors that perfectly contrast/match the red clay of Roland Garros. Above you can see the variety of pink, orange and green combinations on Daniela Hantuchova, Sorana Cirstea, Andrea Petkovic, Maria Kirilenko and Arantxa Rus. Here you can read more about Adidas' French Open collection.

And now that we mentioned Arantxa Rus, let's proceed with Kim Clijsters. The Belgian sported a special vintage Monica Seles-inspired ensemble, which Fila made for her based on her childhood tennis outfit from the 80s. It's refreshing, something out of the ordinary for the usually classic Clijsters.

Compare this year's tennis fashion to what players were wearing at Roland Garros 2010.

Lacoste, represented by Samantha Stosur and Gisela Dulko, opted for stripes in red and black. Adidas' Adipure line, which Dulko's doubles partner Flavia Pennetta is wearing, also has stripes.

Vera Zvonareva, the most prominent representative of K-Swiss, wore a nicely-shaped black skirt and a cute red tank.

When it comes to Nike, they prepared a dress specifically for Serena Williams, even though she hasn't played competitive tennis in almost a year, but Maria Sharapova and her yellow Eiffel Tower-inspired dress are giving plenty of exposure to the brand. Julia Goerges was in the similar color palette, wearing Nike Statement tank and skort.

Victoria Azarenka is sporting a purple Nike Flirty Set Point dress, while Li Na is wearing a Nike Summer Smash Classic Top and Skort. Nike can be satisfied with three representatives in the quarterfinals.

Ellesse considerably tuned down their fashion expression for Nadia Petrova. That's less interesting for us, but good news for Nadia. Defending champion Francesca Schiavone is also wearing simple clothes, a Lotto outfit in neutral colors.

Jelena Jankovic and her always-colorful Anta, this time in pink. Jelena also had a matching bag.

And last but not least, Bethanie Mattek Sands. The American had a number of looks at the French Open, some more moderate than the others, but of course she stayed faithful to herself – with her long socks, under-eye makeup and tattoos. I don't know yet what happened to the release of her Lady Gaga craziness, though.

My favorite of all the outfits is without a doubt the Adidas Summer Adizero dress, and the entire current Barricade and Adizero collection. Nothing else really impresses me. What about you? Which Roland Garros 2011 outfit is your favorite? (photos: y.caradec, Cedric Fischer, tsavoja, krissaconnection, Paul Auther, Diario Informe, Julien (Quelques-notes.com), francetvsport, Yahoo, Roland Garros)