Stoudt attended Oberlin High School, where he played quarterback. He also was one of the state's top prep golfers. Stoudt accepted a football scholarship from Youngstown State University, where he became a four-year starter. As a sophomore, he led the team to an 8-1 regular season record and the school's first appearance at the NCAA Division II playoffs, where they lost against the University of Delaware. As a junior, he posted 1,022 passing yards and 406 rushing yards. As a senior, he started all 10 games, passing for 1,259 yards and 5 touchdowns, while also rushing for 307 yards and 7 touchdowns. He finished his college career with 303 completions out of 637 attempts for 4,387 yards, 5,459 total yards and 16 touchdowns. In 1987, he was inducted into the YSU Athletics Hall of Fame.
Professional career
Pittsburgh Steelers
Stoudt was selected by the Pittsburgh Steelers in the fifth round of the 1977 NFL Draft. Stoudt was the third-string quarterback to Terry Bradshaw from 1977 to 1979. At the time he set an NFL record, after spending the first 56 games of his career as an active roster member without appearing in an official game. In 1980, he was promoted to the backup quarterback role. His first career start came against the Cleveland Browns. In 1983, he took over as the starter at quarterback during Bradshaw's injury-plagued final season in 1983. He led the Steelers to a 9–2 start, but the team melted down late in the season. Steeler fans, accustomed to Bradshaw's late game heroics, turned viciously on Stoudt. The Steelers won the AFC Central with a 10–6 record and stumbled into the playoffs, but were quickly dispatched by the Los Angeles Raiders.
Birmingham Stallions
In 1984, Stoudt left the NFL and signed with the Birmingham Stallions of the United States Football League. During the third game of the season which was the home opener for the Pittsburgh Maulers on March 11 at Three Rivers Stadium, Stoudt was heckled and pelted with snowballs by the fans. It would turn out to be the only sellout in the one season history of the Maulers. Stoudt started every game, registering 3,121 passing yards, 26 passing touchdown, 400 rushing yards, 9 rushing touchdowns and 7 interceptions, while leading the team to a division championship and ranking No. 2 overall in quarterback rating. In 1985, he had 3,358 passing yards, 34 passing touchdowns, 437 rushing yards, 5 rushing touchdowns and 19 interceptions, repeating as division champion and the No. 2 overall quarterback rating. He led the Stallions to a two-year record of 27-9, while passing for 6,479 yards, 60 touchdowns and 26 interceptions. In 1986, the league ceased operations after losing most of its claims in an antitrust suit against the National Football League, with its top talent absorbed by the NFL in a dispersal draft conducted in the aftermath.
St. Louis Cardinals / Phoenix Cardinals
Because the Pittsburgh Steelers still owned the rights to Stoudt, on September 1, 1986, he was traded to the St. Louis Cardinals in exchange for a conditional draft choice. He served as Neil Lomax's backup and was also the team holder on kicks. He had 2 starts each in 1986 and 1988. In 1989, Stoudt asked for his release after the team acquired free agentGary Hogeboom. He was cut in March 1989.
Miami Dolphins
On April 14, 1989, he was signed as a free agent by the Miami Dolphins. Although he performed well during most of training camp, he was released on September 3, after he had 2 interceptions returned for touchdowns in the Dolphins' 20-10 preseason loss against the Philadelphia Eagles and Scott Secules was promoted as the backup to Dan Marino. On September 7, he was re-signed when Marino suffered a right bruised elbow on his throwing arm. He appeared in 3 games and didn't attempt a pass. He was cut on August 28, 1990.
Dallas Cowboys
On December 24, 1990, he was signed by the Dallas Cowboys, to be an emergency back-up quarterback to Babe Laufenberg for the season's final game against the Atlanta Falcons, after Troy Aikman suffered a right shoulder injury in Week 15. In 1991, he went into training camp with Aikman, Laufenberg, and fourth-round draft choice Bill Musgrave at quarterback. On August 25, the Cowboys traded for Steve Beuerlein to improve the backup position and released Stoudt the next day, opting to keep just 2 quarterbacks.
