Labor Leader Bill Shorten wants to focus on ordinary people rather than “silly political games” after putting leadership speculation to bed with formidable wins in four by-elections.

Mr Shorten was dogged by persistent questions about his position throughout the gruelling campaign, based largely on seat-by-seat polls that turned out to be wildly inaccurate.

His main leadership rival, Anthony Albanese, was also highly visible in the lead-up to Super Saturday, delivering a speech widely viewed as an effort to position himself for the top job in the event of poor results.

Labor won four of five seats up for grabs, including contests in two crucial marginal electorates that were framed as litmus tests for Mr Shorten.

The opposition leader said the thousands of people he spoke to on the by-election campaign trail had no interest in politicians talking about themselves.

“What really matters to voters is how their family is going and how is their health,” Mr Shorten told reporters in Longman on Sunday.

“If your family is okay and your health is okay then you can start to have dreams and aspirations.”

He said “the real world is happening” regardless of chatter among the Canberra commentariat, and Labor’s policies were focused on people’s lives.

“They want to know when the waiting list for their surgery will be reduced. They want to know if we can improve the cancer treatment locally. They want to know if their local school can be properly funded.”

Labor deputy leader Tanya Plibersek is confident the leadership speculation will dissipate after the strong by-election results.

“I don’t think there was ever a genuine problem,” Ms Plibersek told the ABC.

Ms Plibersek singled out News Corp for fuelling the leadership speculation, claiming the organisation wanted Labor talking about itself so it would lose the next election.

“We didn’t succumb to that temptation to talk about ourselves,” she said.

Incoming Labor president Wayne Swan described the by-election results as an “emphatic rejection” of the prime minister, and an endorsement of Bill Shorten’s policies.

“The pleasing thing about the result last night was that there was a pretty big tick for Bill Shorten’s program, for his tenacity and his grit in sticking to the issues, unlike the prime minister,” Mr Swan said.

“I don’t think there was any validity in that (leadership) chatter before the by-election. There’s certainly no validity in it now.”