The makers of the Power Balance bracelet worn by footballer David Beckham have admitted there is no evidence that the wildly popular wristbands boost sporting prowess.

The admission came after Australia's consumer watchdog said the California-based company behind the wristbands and pendants had no business claiming that the colourful silicone bands improved balance, strength and flexibility.

After an agreement with the Australian Competition and Consumer Commission last month, Power Balance wrote: "We admit that there is no credible scientific evidence that supports our claims."

It also agreed to give refunds to customers who believe they were cheated.

Critics railed against the company on Twitter and those who had believed in the bracelet's power and the company unleashed a torrent of its own tweets, playing on the word "admit".

In one, it said: "Power Balance Admits products have been worn during the last world series, nba finals and super bowl champions!"

US basketball star Shaquille O'Neal swears by the bracelet, which he says gives him a competitive edge on the court. And fans insist the bands have helped their game.

"Our trainers swear by it," Phoenix Suns basketball forward Jared Dudley wrote on his Twitter page.

The company began selling bracelets in 2007 embedded with holograms purportedly designed to interact with the body's natural energy flow.

Since then, the wristbands, which sell for just over £19, have become ubiquitous, donned by Los Angeles Lakers' Lamar Odom and former England captain Beckham.

They have also been worn by celebrities including actors Robert De Niro and Gerard Butler.

Power Balance expects to have made more than £22.5 million in sales for 2010.

Adam Selwyn, a spokesman for the company, based in Laguna Niguel, California, said Power Balance did not claim to have science on its side, but relied on testimonials from famous athletes and users to tout the products' effects.

The company says it pays some athletes for the right to use their images wearing the bracelets, including O'Neal and Odom.

Josh Rodarmel, one of the company's co-founders, said he knew there may be sceptics. "We're not trying to win over every person in the world," he said.

Ralph Reiff, programme director at St Vincent Sports Performance in Indianapolis, said maybe a third of the hundreds of professional and amateur athletes who trained there wore the wristband or an imitation.

The programme even thought about putting its logo on the products and handing them out, he said.

But officials decided against that because they could not find enough reliable research to back up the company's claims about giving a biological boost to performance, he said.

"I couldn't look in the mirror and 100% say (it's) a product I can put my brand reputation behind," said Mr Reiff, a qualified athletic trainer.

He said he believed any benefit was purely psychological.

"It's just like a pair of lucky socks," he said. "It's a lucky charm, and if you believe in it, then it's excellent."

On its website, Power Balance features video footage of athletes holding their arms out and resisting downward pressure in trials with and without the bands.

But a Wisconsin professor ran similar tests comparing the performance of 42 athletes wearing Power Balance wristbands and silicon versions from Wal-Mart and said he found no difference.

Athletes were more likely to perform better wearing the second bracelet they put on, largely because they knew what to expect from the trial, said John Porcari, professor of exercise and sport science at University of Wisconsin-La Crosse.

"I think it is a scam," he said. "It has absolutely nothing to do with the bracelets. It is all in people's heads."