Australia in summertime is traditionally a happy hunting ground for Serena Williams: five times in her career she has held aloft the Daphne Akhurst Memorial Cup, awarded to the winner of the Australian Open women’s singles, on the final Saturday in Melbourne.

But with 2015 only 10 days old, the year already has an unusually portentous feel for the American, who was beaten for the second time in a week as a three-set defeat to Agnieszka Radwanska helped Poland beat the United States in Perth to lift the Hopman Cup for the first time.

In claiming her first victory over Williams in nine attempts, Radwanska – evidently buoyed by the addition of 18-time grand slam champion Martina Navratilova to her coaching team – emerged as a genuine contender for the Australian Open, where she reached the semi-finals last year.

The Pole’s delight at claiming the scalp of an opponent who denied her the 2012 Wimbledon title was plain. She said of her 6-4, 6-7, 6-1 win: “When you play against her, you have nothing really to lose, she is No 1 in the world and a great champion. It doesn’t matter what the score is. It’s never over, she’s a great fighter.

“I’m just very happy that I could come back after that second set and play my good game in the third set. Wins like this always give a lot of confidence.”

It would be unwise to read too much into Williams’ results in the mixed team event, which is ostensibly little more than a light-hearted warm-up for the more serious business ahead at the year’s first major.

Yet the fact remains that the American – who, in tandem with John Isner, suffered a second defeat in the mixed when Radwanska partnered Jerzy Janowicz to a straight-sets win that ended US hopes, after Isner had beaten Janowicz in the singles – has been strangely out of sorts all week. On Monday she lost the opening set 6-0 to Italy’s Flavia Pennetta before calling for an espresso; duly caffeinated, she hit back for an ultimately decisive win. The following day, though, she could claim only three games against Canada’s Eugenie Bouchard.

If Williams is to overtake Chris Evert and Navratilova in the all-time grand slam winners’ list by taking her to tally to 19 in Melbourne, the practice courts – and, no doubt, plenty of coffee – beckon.