“Of course it has an effect,” said Dmitrii Trunenkov, a member of the Russian crew that won a gold medal in the four-man event at the Sochi Games. “He’s the president, after all.”

Mr. Bedzhamov is not the first Russian sports federation official to be embroiled in scandal. A former vice president of the nation’s biathlon union was convicted of arranging a murder in 2007, and the head of Russia’s curling federation has been accused of abusing state construction contracts. More recently, the head of Russia’s track and field federation received a lifetime ban from his sport for extorting athletes in return for covering up their doping.

The frequency of such scandals may be attributable to the peculiar closeness of sports to politics and business in Russia, where many federations are sponsored by large state companies and led by powerful businessmen.

Mr. Bedzhamov was typical. He had interests in several companies, including one of Russia’s largest shipping lines, and he and his sister shared a powerful connection in Nikolai Tokarev. Mr. Tokarev is a longtime friend of Mr. Putin, who served with him as a K.G.B. agent in the former East Germany. Transneft, the huge state oil firm led by Mr. Tokarev, was one of Vneshprombank’s core clients and was also a sponsor of the bobsled federation.

Such networks reflect how sports have become a patronage-infested domain in the Putin era, with major companies expected to support Russian teams, and businesses seeing sports as an arena in which they can earn official favor and build ties.

Sports have become loaded with prestige as the Kremlin has come to identify them as ways to showcase Russian power. Vast sums have been directed to overhauling the country’s sports infrastructure, and that movement has created lucrative opportunities for Mr. Putin’s allies. Ahead of the Sochi Olympics, companies owned by friends of Mr. Putin’s received huge construction contracts.

At the same time, it is understood that supporting sports will attract favorable notice from the government.