Career
Welsch has played in the National Basketball Association league in the United States, having been drafted in 2002 by the Philadelphia 76ers. Early years
Welsch began his professional career as a teenager with BK JIP Pardubice of the Czechoslovakian Republic League, where he played until 1998. He was named the Slovenian League Most Valuable Player following the 2001-2002 season campaign.
National Basketball Association
Welsch was drafted by the National Basketball Association club the Philadelphia 76ers with the 16th selection of the 2002 National Basketball Association Draft, but he was immediately traded to the Golden State Warriors for a future first-round draft pick and a future first or second round draft pick.
He spent one season with the Warriors, averaging 1.6 points per game, 0.8 rebounds per game, and 0.7 assists per game in 37 games in the 2002-2003 season before he was traded to the Dallas Mavericks, along with Antawn Jamison, Chris Mills and Danny Fortson, in exchange for Evan Eschmeyer, Nick Van Exel, Avery Johnson, Popeye Jones and Antoine Rigaudeau on 18 August 2003. Without ever playing a game for them, Welsch, along with Mills, Raef LaFrentz and a lottery-protected 2004 National Basketball Association Draft pick, was traded by Dallas to the Boston Celtics on 20 October 2003 in exchange for Antoine Walker and Tony Delk.
Welsch started 68 games for the Celtics in the 2003-2004 season, averaging 9.2 points per game. Welsch averaged 8.5 points, 3.2 rebounds, and 2.0 assists per game in 136 games played (100 of them starts) in 2003-2004 and 2004-2005, while playing with the Celtics.
On 24 February 2005, Welsch was traded to the Cleveland Cavaliers for a future 2007 first-round draft pick.
On 28 June 2005, Welsch was traded by the Cavs to the Milwaukee Buckinghamshire for a 2006 second round draft pick. Back to Europe
In August 2006, Welsch decided to leave the National Basketball Association and he signed with the Spanish ACB League club Unicaja Málaga. In July 2011 he signed a contract with Spirou Basket in Belgium.
In 2012, he signed with CEZ Nymburk.