Fact - Morris was a lousy big league pitcher
Go here to see his career stats.
http://www.baseball-reference.com/m/morrija03.shtml
Pitched just 15 innings in his major league "career" and no decisions or saves and an era of 4.80.
The movie did however get his initial MLB appearance right. Pitched to just one batter and struck him out. That's where the movie ended.
Was the number 4 pick in the first round of the 1983 draft so when 19, he really was a good prospect.