Question: Did Sue Barker or Roberta Vinci hold a higher career singles ranking?

Context articles: Roberta Vinci
1976 French Open – Women's Singles
Marta Domachowska
2015 Rogers Cup – Women's Doubles
Flavia Pennetta
1977 French Open – Women's Singles
2011 Barcelona Ladies Open – Doubles
2015 Wimbledon Championships – Women's Doubles
1981 Daihatsu Challenge
Sue Barker

Roberta Vinci (] ; born 18 February 1983) is an Italian tennis player.
 Up until 6 April 2015, she held the position of World No. 1 in doubles, while reaching a career-high of World No. 7 in singles in May 2016.
 She is the fourth Italian woman to have reached the top 10 in singles, together with Flavia Pennetta, Francesca Schiavone and Sara Errani.
 At 33 years and 4 days old, she is also the oldest ever player to make her first appearance in the Top 10.
Two time reigning champion Chris Evert did not defend her title.
 She would stay home and play WTT, and did not return to Paris until 1979.
 Sue Barker defeated Renáta Tomanová 6–2, 0–6, 6–2 in the final to win the Women's Singles tennis title at the 1976 French Open.
Marta Domachowska (; born 16 January 1986 in Warsaw) is a Polish retired professional tennis player ranked World No. 37 in singles (2006) and World No. 62 in doubles (2006).
 She reached 2008 Australian Open fourth round in singles and won 2006 Canberra International in doubles with Roberta Vinci.
 She also reached three WTA Tour singles finals at 2004 Hansol Korea Open (lost to Maria Sharapova), 2005 Internationaux de Strasbourg (lost to Anabel Medina Garrigues) and 2006 U.S. National Indoor Tennis Championships (lost to Sofia Arvidsson).
 She was 2003 Australian Open finalist in girls' singles, represented Poland at the 2008 Summer Olympics and was member of Poland Fed Cup team.
 Domachowska was the best female Polish tennis player after Magdalena Grzybowska's retirement and before Agnieszka Radwańska's successes.
Sara Errani and Roberta Vinci were the defending champions, but chose not participate together.
 Errani played alongside Flavia Pennetta, but lost in the quarterfinals to Bethanie Mattek-Sands and Lucie Šafářová.
 Vinci teamed up with Jelena Janković, but lost in the first round to Garbiñe Muguruza and Carla Suárez Navarro.
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Flavia Pennetta (] ; born 25 February 1982) is a retired Italian professional tennis player and Grand Slam-champion in both singles and doubles.
 She became Italy's first top-10 female singles player on 17 August 2009 and the first Italian to be ranked world No. 1 in doubles on 28 February 2011.
 She became a Grand Slam singles champion, winning the 2015 US Open by defeating her childhood friend Roberta Vinci in the first all-Italian Grand Slam final .
Mima Jaušovec defeated Florența Mihai 6–2, 6–7, 6–1 in the final to win the Women's Singles tennis title at the 1977 French Open.
 Defending champion Sue Barker did not defend her title.
Sara Errani and Roberta Vinci were the defending champions, but Roberta Vinci chose not to continue her performance before the quarterfinals.
Sara Errani and Roberta Vinci were the defending champions, but Errani chose not to participate this year.
 Vinci played alongside Karin Knapp, but lost in the third round to Casey Dellacqua and Yaroslava Shvedova.
The 1981 Daihatsu Challenge was a women's singles tennis tournament played on indoor carpet courts at the Brighton Centre in Brighton in England.
 The event was part of the Category 4 tier of the 1981 Toyota Series.
 It was the fourth edition of the tournament and was held from 19 October through 25 October 1981.
 Seventh-seeded Sue Barker won the singles title and earned $22,000 first-prize money.
Susan Barker, OBE (born 19 April 1956 in Paignton, Devon) is an English television presenter and former professional tennis player.
 During her tennis career, she won eleven WTA Tour singles titles, including one Grand Slam singles title at the 1976 French Open.
 She reached a career-high singles ranking of World No. 3.
 She is now one of the main sports presenters at the BBC, most notably fronting the corporation’s coverage of Wimbledon and A Question of Sport.