Béla Ordódy was initially a football player of note. The midfielder played for three clubs from Budapest, BTC in 1901 and 1902, BEAC 1903-05, and Ferencváros in 1905. With BTC he was Hungarian Champion in both seasons. He also earned two caps representing Hungary in 1904. In 1902, he was one of the earliest Footballers-of-the-Year in Hungary. He also acted as a football referee. In 1918 and 1919 Ordódy was a member of the Ferencváros Championship water polo team. He later switched to ice hockey as a goaltender for BKE Budapest, representing Hungary at the 1927 European Championships and the 1928 Olympic Winter Games. During the time of the Olympics, he was the oldest ice hockey player ever to compete in an Olympic tournament (through 2016), at 48 years, 29 days. Ordódy was a chemical engineer by trade.