Article - A Trading Deconstruction of Radwanska vs Cibulkova

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Dominika Cibulkova's Rolling Projected Hold varied significantly based on game state against Agnieszka Radwanska...

I've chatted with several people in depth on Twitter recently about the statistics behind a couple of matches in the Miami quarter-finals - notably the women's quarter-finals between Agnieszka Radwanska and Dominika Cibulkova, and the men's clash between Tomas Berdych and Alexandr Dolgopolov.

This article will focus on the first mentioned match between Radwanska and Cibulkova, with a future article looking at the ATP match.  This WTA quarter-final match was won by Cibulkova 3-6, 7-6, 6-3.

Prior to the match starting, I commented in the daily match preview that "I think this is a match where Rolling Projected Holds come into their own - if there are early breaks I can see this being a bit of a break-fest.  Assessing the game state in-play is crucial here."

Many readers at this point may be a little confused and ask what is a Rolling Projected Hold?

Put simply, my research showed that the scoreline of a previous service game has a big impact on future service game scorelines.  This can affect basic pre-match projected holds (how likely the player is to hold serve on average) by around 20% - either in a positive or a negative way.  

A superb example of this is the clash between Lauren Davis and Klara Zakopalova in the first round of the Cincinnati Premier event in August last year, won by Davis (a 3.44 underdog) 7-6, 7-6.  Regular readers of the website and regular traders will be fully aware of Zakopalova's tendencies - she has an awful record protecting a break lead, and a strong record of recovering deficits.  This is fairly unsurprising considering her stats - 57.1% holds in the last 12 months is 6.2% below the 63.3% current WTA mean, and 48.2% breaks in the same time period is a huge 11.5% above the WTA average.

Furthermore, current break-back stats show that the Czech gives up a break lead 58.2% (9.6% above top 100 WTA mean) and recovers a break deficit 58.5% (8.0% above top 100 WTA mean) which illustrate that she loses break leads and recovers deficits much more than the average player.

Her match with Davis was incredible with 20 out of 24 service games broken, including all 12 in the first set!  One of the most prevalent things with the Rolling Projected Holds is that breaks statistically tend to lead to more breaks, and whilst I don't want to reveal exact formulas, it became likely that both players would struggle to hold over 50% of the time when broken in the previous service games.

Radwanska vs Cibulkova - A Tale of the tape:-

WTA Mean Radwanska Cibulkova Radwanska Cibulkova
12 month 12 month 2014 2014
Service Hold 63.3 70.3 67 64.2 67
Service Break 36.7 46.8 44.6 49.5 52
Combined 100 117.1 111.6 113.7 119

Those who read the match preview will also note that I wrote "Over 12 months, it's Radwanska with the better stats but interestingly Cibulkova has the better win percentage and also hold/break stats in 2014.".

This is borne out with the above table indicating that Cibulkova has dramatically improved her stats to top 5-10 level in 2014 but Radwanska's have declined to about 10-12 in the world level.

Starting prices made Radwanska the marginal underdog, which looks value based on the 12 month stats.  However, 2014 stats and the fact that Radwanska looked to be struggling with fitness in recent matches indicates that Cibulkova's status as favourite was justified - certainly backers of either player could have decent arguments to their case.  For the purpose of this article I will assume that the starting price was correct.

As I use 12 month stats for my projected hold model calculations, this gave Radwanska the edge with a 61.8% projected hold to Cibulkova's 56.3%.  

However, there are situations based on the Rolling Projected Holds that the player who has the lower projected hold pre-match actually turns out to have a higher Rolling Projected Hold in play.  As the information and figures are pretty sensitive I don't want to post it specifically on here, but what I can say is that despite having a 5.5% projected hold deficit pre-match, Cibulkova actually would have a higher Rolling Projected hold should have held to any score in her previous service game when Radwanska was broken in her previous service game.  

The match started in incredible fashion.  Eight out of the nine opening service games were breaks, with Radwanska's solitary hold being the reason that she took the opening set 6-3.  

Whilst 12 month break-back stats (combined scores of 104.9 and 102.0 on Cibulkova and Radwanska respectively) only showed a slight edge to laying either player a break up, projected holds would have been so low on either player when broken in succession that at scores of 0-0 (Cibulkova serving with an initial low projected hold), 1-1 and 2-2 there would have been huge advantages laying the Slovak's serve based on Rolling Projected Holds and the market expectation.

According to the Tier Two Daily Spreadsheet, these should have been the only trades performed in the first set, and they would have all been winners.

After taking the first set but being broken in her final service game of the set, laying Radwanska's serve at 0-0 in the second set would have been mandatory.  She was broken.  A similar story applied prior to Radwanska being broken in the third game of the second set - again she failed to hold serve.

Eight out of 12 service games in the second set were broken, with winning trades laying Radwanska at 0-0, 1-1, 3-3.  Only at 4-4 would we have had a losing trade opposing her serve (although she was 0-40 down so there were opportunities to trade out with significant profit), and at 5-5 she would not have been laid as she held serve in the previous service game.

We could only have laid Cibulkova's serve once in the second set as she was a break up in all other situations except for *4-5 (as previously mentioned the break-back stats did not provide enough edge to lay her a break up as they were below the 105 threshold to give this trade enough positive expectation).  As she was broken the service game prior to this, it would definitely have been a statistically viable trade (except for her price being too high to lay at a set down and on serve in the second set) and she actually faced three break points in this service game despite holding.

Both players were broken in the last two service games of the set, leading Cibulkova to take the set 7-6 on a tiebreak, 7-5.

Further viable lay points in the third set came when Cibulkova was serving at 0-0 and 2-2, with both being losers.  However she could not have been laid when a break up as discussed above, or at 3-3, as she held to love in the previous service game, making her projected hold much higher than if she was broken in the previous service game.

Overall, you will be able to see that the Rolling Projected Holds allowed us to win six out of nine trades, with one of the three losing trades being where Radwanska held despite being 0-40 down (where it could have been traded out with significant profit).

Finally, you may recall that earlier I specified that Radwanska's prematch hold was 61.8% with Cibulkova's being 56.3%, and I also spoke about how Cibulkova's in-play Rolling Projected Hold could turn out to be higher than Radwanska's depending on the game state.

I calculated the average projected hold for either player in-play based on Rolling Projected Holds and the following figures were generated:-

Set 1:  Radwanska 57.8%, Cibulkova 48.1%
Set 2:  Radwanska 59.2%, Cibulkova 51.4%
Set 3:  Radwanska 59.9%, Cibulkova 60.3%

You can see that because of the game state in the third set, Cibulkova's projected hold was actually 0.4% higher than Radwanska's - despite having a 5.5% lower pre-match projected hold.  Not only this, it was significantly higher than in the previous sets, where she had more issues holding serve.  

Furthermore, Cibulkova's average Rolling Projected Hold in the third set was 4.0% higher than her pre-match projected hold, whilst Radwanska's was 1.9% less.

These stats illustrate exactly how Rolling Projected Holds alter due to game state, and how useful they can be in-play to traders.

As always, if you have any questions, please get in touch via email at:

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