[1][3] Stäbler trains at TSV Musberg in Leinfelden-Echterdingen, Germany, coached by Janis Zamanduridis from the national wrestling team.

Stäbler represented Germany at the 2012 Summer Olympics in London, where he competed in the 66 kg class in men's Greco-Roman wrestling.

[4] Because his opponent advanced further into the final match, Stäbler offered another shot for the bronze medal by successfully defeating United States' Justin Lester in the repechage bout.

However, he lost the bronze medal match to Georgia's Manuchar Tskhadaia, who pushed him out of the wrestling mat in the third period, with a score of 1–3.

[5] (only Senior) Stäbler's logo, which appears on the official merchandise, his video diary and printed media, is a jumping squirrel.