[1] Nagy attended Roger Ludlowe High School in Fairfield, Connecticut,[2] where he starred in baseball and football.

[4] He was the first Huskies player drafted in the first round[5] and the first to be named the BIG EAST Pitcher of the Year, which he won twice (for the 1987 and 1988 seasons).

[7][8] Nagy was a member of the Team USA Baseball that competed in the 1988 Summer Olympics in Seoul, South Korea as a demonstration sport.

Nagy was the second of three first round picks selected by the Indians, sandwiched between SS Mark Lewis and pitcher Jeff Mutis.

Being a successful college pitcher, Nagy skipped several levels and was assigned to the Kinston Indians, the Cleveland "High A" affiliate in the Carolina League.

On August 8, 1992, he threw a complete game one-hitter against the Baltimore Orioles, giving up just a single in the seventh inning, while allowing two walks.

1992 was possibly Nagy's best year statistically as he finished the season with an impressive 2.96 ERA and a career high 252 innings pitched.

Nagy hit an infield single off Doug Jones while wearing a Texas Rangers batting helmet.

In 1999, Nagy batted twice in a game against Toronto, after a mistake with the initial lineup card cost the Indians their designated hitter.

During this period from 1995 through 1999, Nagy was the workhorse of the Tribe pitching staff, amassing 15 or more wins each season, a feat only matched by Greg Maddux.

However, Nagy was placed on the disabled list (DL) on May 16, 2000, snapping a streak of 192 consecutive starts dating back to October 3, 1993.

[19][20] He was fired by general manager Kevin Towers on October 7, 2013 partly for refusing to instruct pitchers to hit players on opposing teams.

[22] In February 2015, Nagy was hired again by the Cleveland Indians as Special Assistant to Player Development along with Travis Hafner and John McDonald.