*On Monday our guest poster and stats lover Omair dug us into the numbers of his detailed analysis about the number of wins year-end Top 10 players scored over Top 10 players in 2011 and their best tournaments. Now it's time for Part 2 and a different perspective – results of the Top 10 stars approached through their losses.*

First have a look at the table showing **average rank of players who defeated each of the year-end Top 10 players** and the** lowest-ranked player to beat year-end Top 10 players during 2011**.

**Vera Zvonareva needs to be mentioned here for her consistency as she is the only one of the Top 10 who was not beaten by a player ranked outside Top 35, while the rest of her colleagues from this elite group were beaten at least twice. **The lowest-ranked player to defeat Zvonareva during 2011 was Tsvetana Pironkova, ranked 33rd (seeded 32nd) during the third round of Wimbledon.

Of Zvonareva's 22 losses only three came at the hands of players ranked between 30 and 35 and interestingly they came at the hands of players ranked 31, 32, and 33. Also, a total of only three losses came at the hands of players ranked between 21 and 29, while the rest of 16 came at the hands of Top 20 players. **Average rank of Zvonareva's conquerors was 15, while the average rank of the conquerors of all the remaining Top 10 players was not even within Top 20.**

**Victoria Azarenka also needs to be mentioned here, because only five of her 17 losses came at the hands of players ranked outside Top 20**, and of those five losses two came at the hands of Serena Williams who had low ranking due to her health problems and lack of play. Average rank of Azarenka's conquerors in 2011 was 23.

Let's continue with more specific tables, one for each of the Top 10 players, containing:

1) names of tournaments where players lost a match;

2) rank of the player that defeated them;

3) name of the player who defeated them.

Players who have beaten a Top 10 player in question twice or more in 2011 are highlighted in the tables.

Interestingly, three players have beaten** Caroline Wozniacki** twice this year, only one of them being a Top 10 player. **Petra Kvitova** has been beaten twice by only two players in 2011 – Andrea Petkovic and Vera Zvonareva – both the year-end Top 10 players. However, Petkovic was ranked 11th when she defeated Kvitova in Cincinnati.

It's interesting to note that Kvitova, who can be considered the player of the year especially for her Wimbledon and WTA Championships titles, played two events on the ITF Women's Circuit in 2011 – Nassau she exited in the opening round, while Prague 2 she lost in the final. Also **note that six of Kvitova's 13 losses (almost 50%) came at the hands of players ranked below 40**.

**SUMMARY STATS FOR WOZNIACKI**

Total rank of players who defeated her: 465

Number of defeats: 17

Average rank: 27.4

**SUMMARY STATS FOR KVITOVA**

Total rank of players who defeated her: 474

Number of defeats: 13

Average rank: 36.5

**Victoria Azarenka **has been beaten twice or more by three players – Li (both times at Grand Slams), Kvitova (three times) and Serena Williams (twice). **Maria Sharapova **was beaten twice by two players – Kvitova and Li, both Top 10 players.

Flavia Pennetta needs to be mentioned here since she was the one who spoiled the perfect record of Sharapova in three-set matches during 2011. Before the US Open Sharapova had won all the matches during 2011 that went to the third set, however Pennetta changed all that at US Open when she beat Sharapova 6-3 3-6 6-4 in the third round of US Open.

**SUMMARY STATS FOR AZARENKA**

Total rank of players who defeated her: 398

Number of defeats: 17

Average rank: 23.4

**SUMMARY STATS FOR SHARAPOVA**

Total rank of players who defeated her: 603

Number of defeats: 14

Average rank: 43.1

Lisicki and Stosur have been able to defeat **Li Na **twice or more this year, with Stosur beating her on four ocassions. **Samantha Stosur** has been beaten by Sharapova (three times), Kirilenko (twice), Bartoli (twice) and Kvitova (twice).

Of all the Top 10 players, the US Open champion **Stosur suffered the biggest loss in terms of how low her opponent was ranked, falling to No.262 Melinda Czink in the first round of Wimbledon**.

**SUMMARY STATS FOR LI**

Total rank of players who defeated her: 624

Number of defeats: 17

Average rank: 36.7

**SUMMARY STATS FOR STOSUR**

Total rank of players who defeated her: 865

Number of defeats: 23

Average rank: 37.6

**In the beginning of this analysis I've already said so much about Vera Zvonareva's consistency, but there were two players against whom the Russian was weak: Agnieszka Radwanska defeated her four times in 2011, Samantha Stosur three times.**

**Agnieszka Radwanska** also had her fair share of unwelcome opponents: Petra Cetkovska, Lucie Safarova, and Top 10 players Wozniacki and Kvitova all defeated Radwanska twice this year.

**SUMMARY STATS FOR ZVONAREVA**

Total rank of players who defeated her: 338

Number of defeats: 22

Average rank: 15.4

**SUMMARY STATS FOR RADWANSKA**

Total rank of players who defeated her: 453

Number of defeats: 18

Average rank: 25.2

**Marion Bartoli** has the unwelcome title in the elite 10, **falling to the lowest-ranked opponents on average. **Bartoli also has the unlikely honour of being the** only Top 10 player who was beaten four times by players ranked outside Top 100 during 2011**. However, she also played the most tournaments – 29, while no other Top 10 player played more than 22.

Andrea Petkovic and Caroline Wozniacki were the only players to beat **Marion Bartoli **twice or more this year. Wozniacki, Sharapova and Radwanska handed **Andrea Petkovic **two or more losses this year.

**SUMMARY STATS FOR BARTOLI**

Total rank of players who defeated her: 1310

Number of defeats: 25

Average rank: 52.4

**SUMMARY STATS FOR PETKOVIC**

Total rank of players who defeated her: 461

Number of defeats: 17

Average rank: 27.1

So far we've featured numerous Omair's analytic tables covering the following topics:

- Comparative analysis of Top 10 players and their performance at big tournaments in 2011;
- Top 10 players in 2011 – how they scored against fellow big opponents; and now
- Top 10 players in 2011 – what do their losses suggest?

* Did all these analyses help you draw some conclusions or direct your attention to specific data which you didn't realize before? Did some specific numbers maybe only strengthen some of your theories about certain players? *(photos: © Neal Trousdale)

Thx Marija for giving me this opportunity

I hope your readers like this

I guess these analyses did bring up some interesting facts, esp the one about Kvitova beating 3 or more top 10 players in one tournament twice and Li Na beating 4 top 10 players en-route to her first Grand Slam. Another interesting thing that I found out was the consistency of Zvonareva and that she never lost to a player ranked outside top 35.

Lets see what 2012 brings for us

Keep up the good work

Thanks once again Omair for another great article!!

Vera has been a very steady player in 2011. Your stats really shows why and exactly how steady. Thinking about my top 10 for 2012, six of these players – Caroline, Petra, Victoria, Vera, Agnieska, and Andrea would seem to be better bets than the other 4. Of course there are some other details including subjective factors that must be taken into account in any predictions.

I still can't agree with you that Petra should automatically be player of the year. Caroline beats her in these, your part II stats. Caroline repeated for the second year in a row and beat Petra in the only stat that counts – the WTA points leader for 2011. My vote is for co-players of the year.

This is a very good list. It's illustrative of players actual records, and not our perception of them. Good stuff again. A few tidbits:

Though Zvonareva should be commended for losing to the highest ranked average of players; we shouldn't celebrate too much.

Zvonareva had a healthy 22 loses. That means that Vera had almost twice the losses of some one like Kvitova, though she seemingly always played well in the earlier rounds of a tournament against inferior opponents. That's nothing to break about. It just reinforces the fact the Vera is a "Pretender" and not legitimate "contender".

As far as Wozniaki and the commenter above; this chart actually exposes the fact that Wozniaki is not nearly as "consistent" as some of her biggest fans claims her to be. She's very close to Kvitova in "consistency" (though slightly ahead). That's not much to brag about; really. More importantly Kvitova has only 13 loses to Wozniaki's 17 (and a clear better winning percentage) with her 60 vs Wozniaki's 63.

Add up all the other stuff Kvitova has done vs Wozniaki (I'm not going to re-hash it; but it's well known), and it's clear why Petra was the overwhelming player of the year. They're no areas where Wozniaki blows her away, but they're several areas where Petra blows Wozniaki away. This chart actually reinforces that Petra is better, and that Wozniaki's alleged consistency over Petra is negligible (and probably worse with 5 more loses and a poorer winning percentage).

Bartoli with 25 loses. Wow!

Wow, Omair this is a great piece of work! This really shows that ranking system is not incorrect as many people say. It is a result of both the highs and the lows.

Thanks John and Marine for the appreciation

Well! We did not say that Petra should be the player of the year, we referred to the Player of the year Award that she had won :), and yes Caroline does beat her in part – II of stats but whats important to note is Caroline does not top here, whereas Petra did in the previous analysis. However, Wozniaki did earn her no.1 spot over everyone, end of story

and yes Marine you are right, players are humans, they too have bad days, days when you are unable to feel the ball, you are unable to execute your game the way you want to, so it is a result and a combination of all those highs and lows

Very interesting analysis once again, Omair! Zvonareva didn't rate so highly in some of your previous articles, but this one really shows why she is in the top 10. I'm not a big fan of Vera but credit to her for the consistency she has shown over the last year. I'm still not convinced whether she can keep this up and still be in the top 10 at the end of 2012… only time will tell!

Thanks James

Yes, Zvonareva was not that consistent in my previous analysis but this one really shows how consistent she has been during 2011. I think she will keep her level up and be at the YEC again at the end of 2012.

I love Omair's analyses because they show how many players were shining in certain categories, even though they were not so good in the others, and vice versa. They show that we should not focus on one type of losses, wins, or whatever and claim that that player is good/bad.

I agree, this really shows that Vera has had a great season. It's a shame that she still seems to have that mental block at the big occassions and loses tight matches.

@ MSL

Wow man! Very true indeed

These were a few things that I had not taken into account but you are right.

We have not been talking about Vera being the legitimate contender, yes she did not step it up when needed but she also did not let herself loose to lower ranked players, and that's how everyone wants a top player to be, but yes you are right its almost double the amount of looses as compared to Kvitova.

As far as Wozniaki is concerned, if we compare both players (wozniaki and Kvitova) several things have to be taken into account. and yes I agree with you, Kvitova has literally blown her out when it comes to no. of wins against top players, or wins at big stages, where Wozniaki has mostly choked, here Wozniaki does have edge, but again as you pointed out she has 4 more looses, yes she has but she also has 3 more tournaments she played. But all in all Wozniaki did enough to remain no.1 for 2nd year in a row. Hopefully Kvitova will take the no.1 sport by February… Lets hope for a better 2012…

@ Marija

Yes, I completely agree with you here, where one player outshone the other in one respect, the other did the same in some other area and perspective, proving that no1 has really been dominant or been able to step it up consistently at the big stages.

@Omair

Yes. I don't want to give Vera too much grief, cause her consistency is admirable. She's an excellent Top Level Pro.

If Petra or Woz had her consistency, the other would be number one, and Woz wouldn't be so close/ in danger of losing it to Petra soon? And it's not like Vera hasn't or can't get offensive and aggressive when she needs to. She has; and does. It's just that it comes and goes, or she tenses up when in finals (I think she's 1/9 or something to that effect)?

As far as next season, yes there are a lot of things on the Agenda to watch for in 2012, And as you stated, watching Woz and Petra will be one of them indeed.

You brought up a good point, by mentioning that Woz's 3 extra tournaments, added to her 17 loses (though she'd still have one more loss than Petra, and less wins if she didn't) vs Petra's 13. But it's also those three extra tournaments she played, and their points that kept her number one, as well. It goes both ways for her. Lol

Nonetheless, I liked your two list. One addressed high level encounters, and number of deep penetration in tournaments. And this one generally covers consistency.

You covered both ends, and basically summarized in the data, the laborious work that many of us would have to do on our own (or printed out, what was already in our minds). Lol

Thanks

loved the stats marija… <3

Thanks for all stats (IMO the most iteresting is the win/loss stat of top 10). I have an objection against the "average rank of players who defeted her" computed as arithmetic mean. Arithmetic mean is suitable for linear relations, however the player quality is not a linear function of ranking. There is a "pyramid" situation – a lot of players of level quality and with increasing quality smaller number of players. Hence the average should be (for diferent values) smaller than the arithmetic mean. Moreover, if a top player has a bad day, she can lose against a rank 40 as well as for 80 – this makes a substantial difference in arithmetic mean but the actual rank is only a coincidence.

I think that it is better to use a "p-mean" defined as p-th root of the arithmetic mean of p-th powers for a suitable p<1 (p=1 gives arithmetic mean, p=0 given by limit gives geometric mean – n-th root of product of n values).

Let's have 4 players with 10 losses, 1st 10 times against rank 5, 2nd 5 times against 1 and 5 times against 9, 3rd 9 times against 1 ad 1 times against 91, 4th 9 times against 1 and 1 times against 191. IMO 2nd should have better average than 1st and 4th not too much higer average then 3. The averages for p = 1, 1/2, 0 are: 5/5/10/20,

5/4/3.4/5.2, 5/3/1.6/1.7. maybe p=1/2 is the most appropriate.

To my previous post: Another problem is with players whose ranking does not correspond to their level due to small number of tournaments – e.g. Serena Williams has too high ranking and therefore a big negative influence to players which lose to her (80 for Azarenka and Stosur and even 169 for Bartolli!). This is another reason for suppressing the influence of high rankings.

@ ludolf

Yup your point is very valid, the average rank of player who defeated her should not be caluclated as a linear mean. I did not get the idea of the p thing you mentioned, I am not a good mathematician actually so… But I will for sure look into it and try to put it in some other way….

Thanks alot for going through the article

Top stuff Omair….

Thanks Hasnain