He began training athletics during his high school years and in 1900 he was already a member of Budapesti TC. An all-around athlete, Kóczán competed in the discus throw, the shot put and the javelin throw, achieving his best results in the latter one. In 1908 he was invited to an athletics competition in Budapest, which he won with a throw of 57.05 metres – a result better than the then World record –, and made into the Olympic team as well. Between 1909 and 1911 he broke his own record further three times, however, the IAAF officially ratified the World record since 1912, therefore these results remained unofficial. Kóczán competed at the 1908 Summer Olympics in the discus throw event, the Greek discus competition, the freestyle javelin event, and the shot put competition, but remained without any success.