Dávidík won silver and bronze at the Junior World Championships in 1996 and 1997 with the Slovak relay. 1997 also another bronze medal on the long distance behind the Swede Johan Modig and the Czech Vladimir Lucan . In the same year he made his debut at the World Championships for active athletes in Grimstad, Norway, and was 46th on the short distance. Two years later in Scotland he was World Cup 14. on the long distance. Dávidík had the greatest single success in 2000 in Ukraine at the re-introduced European Championships. In the long distance he came in second behind the Russian Valentin Novikov . A day later he was eleventh on the short distance. In 2001 he reached his first top ten place at world championships with a tenth place in the sprint. Others followed in 2003 in Switzerland (6th place on the middle distance), 2005 in Japan (9th place in the sprint) and 2008 in the Czech Republic (6th place on the long distance). With the Slovak relay he achieved seventh place as the best result in 2005.
Dávidík's Slovak association is Kobra Bratislava . He has already run internationally for Modum O-Lag , Halden SK and Tampereen Pyrintö . With Halden he won the Tiomila in Sweden in 2003 and 2006 .
