How bad is bad? As in, possibly the worst game in the post World War II era.
Coming in to start the third inning with the Royals trailing the Indians 3-1, Mazzaro pitched a scoreless third inning. He then gave up TEN runs in the fourth inning. He gave up one more run in the fifth, when he was finally, mercifully taken out with one out and the bases loaded. All three inherited runners scored. The Indians went on to win 19-1. (Box score)
2.1 Innings Pitched. 14 earned runs allowed.
Using Baseball-Reference's Play Index tool, I was able to find all of the pitchers who have allowed 14 runs (none have allowed more) in the last 66 years.
On August 3, 1998, Mike Oquist of the Oakland A's allowed 14 runs in 5 innings. 13 of those runs came in the first three innings, so I guess you could say Oquist settled down.
On August 14, 1977, Bill Travers of the Milwaukee Brewers gave up 14 runs in 7.2 innings. It should be noted that this was in the second game of a doubleheader.
On June 28, 1947, Al Jurisich of the Phillies gave up 14 runs against the Giants in an 8 inning complete game, presumably because manager Ben Chapman wasn't aware he could use a relief pitcher. Jurisich, 25 years old and 15-16 in his career to that point, never won another major league game. Hopefully Mazzaro has a better fate.
EDIT: Looking at the game logs, it appears the Phillies had a doubleheader scheduled for the following day. So that at least gives some insight into what Chapman's thinking might have been.