More than that, Williams has lost only four matches, taken her career earnings past US$50 million, and become the oldest woman to hold the world number one ranking.

She claims not to be mindful of such records, but nevertheless volunteered that: “I’m excited about the possibilities.”

Retaining the title this week will be a great momentum builder for her off-season work – increasingly important as Williams gets older – just as it was, she says, when she regained the title at the 2012 WTA Championships.

Williams is probably a stronger favourite now than then, partly because of the absence of Maria Sharapova, who is in rehabilitation because of her vulnerable shoulder.

The player most capable of upsetting Williams is Victoria Azarenka, who has no doubt over where the American stands in the history of the sport.

“She can be the greatest of all time,” Azarenka reckoned after losing to Williams in the longest US Open women’s singles final in 30 years last month. ”Serena’s still not done.”

The Belarusian also suggested the American now focuses more intensely, and raises her level more dangerously when it really matters.

Judging from the grand slam wins in Paris and New York, that level is sometimes higher than ever. On the evidence of setbacks at Melbourne and Wimbledon it can also be variable.

Williams has lost twice to Azarenka this year – in Doha in February the day after having regained the number one ranking from her rival – and in Cincinnati in August after leading for most of the match.

Azarenka, at her best, has a chance of repeating these successes, because she has a big game and the boldness to try to impose it.

“Against her you have to take risks,” Azarenka says, “because she will [do that], and she will do that really well.”

But Azarenka will need to recover from a disappointing build-up to the WTA Championships. The world number two lost in the second round in Tokyo, where she had been feeling unwell, and in the first round in Beijing, where she served 15 double faults.

The other six qualifiers in an eight-player field are Agnieszka Radwanska, the former Wimbledon finalist from Poland, Li Na, the Chinese pioneer who reached her third grand slam final in Melbourne this year and Petra Kvitova, the 2011 WTA Championships winner.

The field is made up of Sara Errani, the Italian who also tops the world rankings in doubles, Jelena Jankovic, the former world number one from Serbia, and Angelique Kerber, the German who won her first title of the year immediately after becoming the last player to qualify.