With its talented players with little money, Ghana is one of the countries that fixers frequently target at international tournaments, Mr. Nyantakyi said. So he was not surprised when, in 2007, it was discovered that there had been an attempt to fix an international match involving Ghana’s celebrated goalkeeping coach, Abukari Damba, who was working with the Singaporean fixers.

After some players turned him in, Mr. Damba confessed and said in a Ghana Football Association hearing that he had worked with the Singaporean fixers for 10 years.

Enter the Croatians

Mr. Perumal joined the international match-fixing group in 2008. In his interrogation cell in 2011, he charted the syndicate’s organization for Mr. Granat and other Finnish police officers. It had European partners and Chinese backers who supplied money allegedly laundered through casinos in Macau.

The match-fixing syndicate was a criminal network, according to European police investigators. Europeans supplied compliant referees, players and coaches; Mr. Tan and the Singaporeans provided access to the vast, unregulated sports gambling market in Asia.

If the match fixers had only the referee on the take, they would say it was a one-star fix. In this case, the Asian syndicate would bet a smaller amount. If the local fixers had the entire team and the officiating crew on the take, it was called a five-star fix, and the syndicate would wager far more.

This system was devised at a meeting in a hotel room in Vienna in September 2008 between the Asian syndicate run by Mr. Tan and Ante and Milan Sapina, two Berlin-based Croatian brothers who had a vast network of corrupt soccer players, referees and coaches. The Sapinas have twice been convicted of match fixing in Germany and are in prison there.

Together, they fixed hundreds of soccer matches around the world, targeting nearly every league — from the prestigious Champions League and World Cup qualifying matches to obscure, low-level matches. Once the Sapina brothers had persuaded their contacts to fix matches, Mr. Tan could then place bets on the Asian sports gambling market, the biggest in the world. Because much of the Asian market is underground, estimates of its size vary greatly. Patrick Jay, a senior executive of the Hong Kong Jockey Club, one of the largest government-controlled gambling companies in the world, estimated that the Asian market handled $1 trillion in wagering.