Kóczán participated at the 1912 Summer Olympics under the pseudonym Mór Kovács to avoid conflicts with the church, which opposed his sporting activities. In the qualyfing round of his main event, the javelin throw, Kóczán topped his group and achieved third best overall result with 54.99 metres. In the final round he improved it to 55.50 but could not match defending champion Eric Lemming (60.64) and Julius Saaristo (58.66), and eventually won the bronze medal thus becoming the first non-Scandinavian to win a medal in the javelin throw at the Olympic Games as well as the first Hungarian to win an Olympic medal in athletics. In the two handed javelin throw competition Kóczán finished 12th and in the discus throw event he came 33rd.