Before the 1988 Olympics, Massimo Costantini was playing for Italy in the European qualifying tournament when he encountered Ding Yi, a player who had moved from China to Austria. Costantini, now the coach of the United States team, lost to Ding that day, and he remembered the other players, coaches and fans feeling bewildered about what had happened.

“We were shocked, actually, to be playing against someone Chinese,” said Costantini, who was later added to the Olympics as a wild-card entrant.

Ding played in four Olympics for Austria, and the trend only grew. Players facing dim prospects in China have increasingly sought to extend their careers as both players and coaches in other countries eager to host them.

“After I lost my opportunity to get into the Chinese national team, I was still young; I still had my dream,” said Eugene Wang, 30, who was offered a spot on the Canadian team shortly before the 2012 Games. “At the same time, I had this invitation. I just went for it.”

Marcos Madrid, a player from Mexico, sighed and smiled when asked how players felt about the spread of Chinese players worldwide. “It’s complicated,” he said, echoing the sentiments of many players in the game.

Everyone acknowledges how far ahead China remains in terms of training and skill. The thinking for many national federations, then, has been that having such skilled players and coaches around — beyond giving them a chance to win competitions in the short term — will raise the skill levels of those countries’ other players.

“I know in my mind I need to practice more because they are there,” Madrid said.

In most parts of the world, there are simply not enough good players to measure oneself against. Chinese players often double as coaches and valuable sparring partners for players in their adopted countries.