BEIJING—To understand why China has such a tough time producing world-class innovations, take a look at how the Chinese play games.

Ping pong tables are everywhere in public spaces and open to all comers, from kids to agile retirees, producing a reservoir of talent that has made China a ping pong innovator and champion. By contrast, basketball courts in China are generally locked up. Entrance is controlled by the state—in this case, school officials—shrinking the talent pool and the chance for youngsters to hone their moves....