The revelation that more than a third of competitors at this summer's Olympics may have arrived in Rio without being drugs tested once in 2016 was branded "alarming" by the president of the World Anti-Doping Agency.

Sir Craig Reedie spoke out after a damning report revealed the staggering number of athletes who came to the Games with no record of having taken a dope test during the year.

The Wada-commissioned report by a team of independent observers found this applied to 4,125 of the 11,470 entrants for the Olympics, 1,913 of them in the 10 sports deemed to present the highest risk of cheating, such as athletics, swimming and cycling.

Attempts to rectify the oversight were then hindered by a shambolic anti-doping programme during the Games itself, during which almost 500 fewer tests were conducted than planned, including less than one in 10 scheduled collections of athlete biological passport samples.

Many tests had to be abandoned because competitors could not be located amid swingeing budget cuts, staff shortages and appalling planning. But it was data relating to the pre-Games period that was arguably the most shocking revelation from the independent observer (IO) report.

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"If what you say is true, yes, it is alarming," Reedie told The Daily Telegraph about the figures, collated for the first time following the recommendation of the IO team from the Sochi Winter Olympics in 2014.

To make matters worse, the information was compiled by a taskforce led by UK Anti-Doping which had earlier identified 1,333 athletes who were deemed to warrant target-testing. The report found fewer than 40 per cent of the required tests were actioned in full by the relevant international federation (IF) or national anti-doping organisation (NADO).

It is widely accepted that most dopers do not take drugs during a major event but do so in the months leading up to it, making regular out-of-competition testing vital.

The effectiveness of the tests which did take place was demonstrated by the fact they produced 15 adverse findings.

"Some NADOs and IFs weren't as efficient, it would appear, as we had hoped," Reedie said. "The leadership of ABCD, which was the Brazilian NADO, changed and a number of tests that should have been done in Brazil were not done. We chased that as best we could to get federations to do it at test events."

Richard Ings, the former chief executive of the Australian Sports Anti-Doping Authority, described the lack of pre-Games testing on athletes as "terrible".

"Many of the Russian athletes were barred from competing in Rio because they couldn't prove that they had been satisfactorily tested before going into the Games," Ings said. "There are athletes in countries around the world whose dream is not to win a medal but just to make the b----- team. If there's no testing going on, you are potentially denying clean athletes the chance to fulfil that dream."

Games organisers did virtually manage to ensure all medal winners were tested but Ings was dismissive of the relevance of that.

"Once you get to the business end of competition, you know you're going to be subject to testing, and you're much more careful in terms of what you're taking," he said. "Even if they were tested, they're not going to get caught."

The IO report said: "While the pre-Games intelligence taskforce was a successful initiative, Olympic IFs and NADOs should be undertaking this type of gap analysis and testing themselves in the 12 months leading into the Games."

The International Olympic Committee ran anti-doping at Rio 2016 and its medical and scientific director sought to gloss over the unprecedented problems faced there, many of which were exclusively revealed at the time by The Telegraph.

Dr Richard Budgett said: "The IO report shows that it was a successful Olympic Games with a successful anti-doping programme. The integrity of the programme was ensured despite some challenges the organising committee had to overcome.

"The IO recommendations for future Olympic Games will be carefully studied and considered by the IOC and passed on to the new independent testing authority, which is planned to be in place before the next Olympic Winter Games PyeongChang 2018."