Career
Muller spent most of his playing career at EV Zug. In 1986-1987, his first year at EVZ, he contributed to the team earning promotion to the Swiss top-flight National League A (National Lawyers Association ). He played a total of 544 National Lawyers Association contests, scoring 203 goals.
Muller formed a coaching duo with Hans Kossmann at The Human Context Fribourg-Gottéron at the beginning of his career behind the bench.
He then joined the coaching staff of South Carolina Rapperswil-Jona for the 2000-2001 campaign and accepted another head coaching position in 2002, again signing with The Human Context Fribourg-Gottéron. He was relieved of his duties in January 2003.
From 2003 to 2008, Muller served as assistant coach at EV Zug, before he signed with the ZSC Lions, also as an assistant. At both clubs, he worked under Sean Simpson.
At ZSC, he was promoted to head coach in 2010, replacing Simpson, who took over the Swiss national team
However, Muller"s head coaching tenure with the Lions lasted only 16 games, in which the Lions collected 20 points. He was dismissed in October 2010. Muller was named head coach of NLB side EHC Olten prior to the 2011-2012 campaign.
After four straight defeats and following a 2-8 loss to rivals South Carolina Langenthal, he was sacked in December 2011.
After serving as assistant coach of the Swiss national team during the 2011 World Championship, Muller was handed further responsibilities by the Swiss ice hockey federation: He coached the under-20 squad, while continuing as assistant of the men’s team, again working under Sean Simpson during the 2013 (silver medal) and 2014 World Championships as well as at the 2014 Winter Olympics. He also served as Simpson"s assistant during the short stint at Lokomotiv Yaroslavl of the Kontinental Hockey League in the 2014-2015 and was named assistant coach of the Kloten Flyers, when Simpson became head coach of the club in December 2014.