Texas lore holds that the legendary UT football coach Darrell Royal (1924-2012) said that there are three things that can happen when you pass the football, and “two of them are bad.” There are claims that this was said by other college football coaches (University of Tennessee coach Robert Neyland, Ohio State coach Woody Hayes, Michigan State coach Duffy Daugherty). Royal definitely used the saying by at least 1962. In 2006, Royal credited Woody Hayes with saying it previously.
   
“We like to run, because when you pass there are three things that can happen to you and only one of them is good” was said by Washington and Lee football coach Lee McLaughlin in November 1961.
     
 
Wikipedia: Woody Hayes
Wayne Woodrow “Woody” Hayes (February 14, 1913 – March 12, 1987) was an American football player and coach. He served as the head coach at Denison University (1946–1948), Miami University (1949–1950), and Ohio State University (1951–1978), compiling a career college football record of 238 wins, 72 losses, and 10 ties. 
 
Wikipedia: Darrell Royal
Darrell K Royal (July 6, 1924 – November 7, 2012) was an American football player and coach. He served as the head coach at Mississippi State University (1954–1955), the University of Washington (1956), and the University of Texas at Austin (1957–1976), compiling a career college football record of 184–60–5. In his 20 seasons at Texas, Royal’s teams won three national championships (1963, 1969, 1970), 11 Southwest Conference titles, and amassed a record of 167–47–5. He won more games than any other coach in Texas Longhorns football history. Royal also coached the Edmonton Eskimos of the Canadian Football League for one season in 1953. Royal never had a losing season as a head coach for his entire career. He played football at the University of Oklahoma from 1946 to 1949. Royal was inducted into the College Football Hall of Fame as a coach in 1983. Darrell K Royal – Texas Memorial Stadium in Austin, Texas, where the Longhorns play their home games, was renamed in his honor in 1996.   

ESPN.com
I want to set the record straight about something. It was General Neyland who said, “When you throw the ball, three things can happen—and two of them are bad.” He doesn’t always get credit for the quote, as it is often attributed to Woody Hayes. But it was Neyland.
 
12 November 1961, Richmond (VA) Times-Dispatch, “Generals Roll In Second Half To Win, 26-8,” pg. C-3, col. 1:
The (Washington and Lee University—ed.) Generals’ coach, Lee McLaughlin, had his aerial attack held in reserve as is his custom. “We like to run,” he said, “because when you pass there are three things that can happen to you and only one of them is good.”
 
16 November 1961, East Liverpool (OH) Review, “Purely Personal” by Truman Twill, pg. 4, col. 7:
I can’t remember who said this but no one said it better than the football coach who explained his reluctance to use pass plays by saying that three things can happen when you throw a football and two of them ain’t good.
   
Newspapers.com
18 November 1961, Moline (IL) Dispatch, “Sports Seen” by Paul Carlson, pg. 20, col. 8:
Woody Hayes, Ohio State’s successful coach, once said, “When you star throwing the ball in the air, only three things can happen—and two of them are bad.”
 
Newspapers.com
4 February 1962, San Antonio (TX) Express and News, “Don’t Quote Me” by Johnny Janes, pg. 2-D, col. 2:
The Royal Theory
Darrell Royal, the University of Texas football coach who has been somewhat more than successful in his five seasons at Austin, probably never will admit that there is a place in football for the forward pass.
 
More than likely that is because the 37-year-old coach has been one to study statistics before making plans and he has this to say about the figures on passing:
 
“Every time you throw the ball only three things can happen and two of them are bad.”
 
That is, the odds are 2-1 that there will be an interception or an incompletion instead of a completion.
 
11 October 1962, The Daily Ardmoreite (Ardmore, OK), “Cougars’ Line Rated Best Since ‘58” by Ernest Thompson, pg. 12-A, col. 3:
Added to that is McBroom’s dictum that only three things can happen when the football is passed and only one of them is good for the offensive team.
(Ada Cougars football coach Craig McBroom.—ed.)
 
16 October 1962, San Antonio (TX) Express, “Don’t Quote Me” by Johnny Janes, pg. 1-B, col. 1:
Coach Darrell Royal of the Longhorns has said often that when a team throws a forward pass only three things can happen and two of them are bad.
 
2 November 1962, Cedar Rapids (IA) Gazette, “Red Peppers” by Gus Schrader, pg. 17, col. 6:
“When you pass the football, only three things can happen, and two of them are bad.”—W. W. Hayes.
 
23 November 1962, Dallas (TX) Morning News, “Texas Presents Something New?” by Bud Shrake, sec. 2, pg. 2:
You could almost hear Royal repeating his maxim: “When you throw a pass three things can happen to it, and two of them are bad.”
 
31 July 1963, Indiana (PA) Evening Gazette, “Change Style of Attack” by Chuck Mills, head football coach, Indiana State College, pg. 22:
A controlled passing game is a safe method of keeping possession of the football. As one coach said, “when you pass three things can happen and two of them are bad.” Well, this is certainly over-simplification. We feel we will have the potential for a good passing attack on the one hand and on the other feel we still will lack a top break-away threat for the long run.
 
9 January 1964, New York Times, “Royal Is Chosen Coach of Year,” pg. 24:
Royal’s teams stress defense and a running rather than a passing offense. He has said three things can happen when a team throws a pass—one good, two bad.
 
“You complete the pass, that’s good,” he repeated yesterday. “You don’t complete it, that’s bad. Or the other team intercepts it and that’s very bad.”
 
15 January 1964, Frederick (MD) Post, pg. 6:
Darrell Royal of Texas, coach of the year: “There are three things that can happen to you on a field goal and two of them are bad. There are also three things that can happen on a run, punt or pass, and two of them are bad. You can see that I talk pretty conservative. I’m sort of the Barry Goldwater of football. The fact that we passed for a touchdown on first down from our own 37 against Navy is just one of those things.”
 
5 October 1964, Indiana (PA) Evening Gazette, pg. 14:
Chuck Klausing has been quoted many times as saying, “When you pass three things can happen, and two of them are bad.”
 
23 September 1965, Lincoln (NE) Star, pg. 25:
Devaney, who takes the positive approach to passing rather than the approach that says anytime you throw the ball only three things can happen and two of them are bad, noted “Each week we try to mix our passing and running game to its best advantage.”
 
12 October 1969, New York Times, “Texas Rally Topples Oklahoma by 27-17 With Aerial Attack,” pg. S1:
Trailing, 14-0, late in the first quarter and forced to justify an offense that had thrown only 27 passes in three games, Texas rebounded for its fourth straight triumph in 13 games for Coach Darrell Royal against his alma mater.
 
It was Royal, one of college football’s most successful coaches, who once said that three things can happen when you throw the ball and two of them are bad.
     
28 November 1973, Richmond (VA) Times-Dispatch, “Sportview: Woody ‘n’ The Pass” by Chauncey Durden, pg. B-5, col. 1:
IN WOODY HAYES’ coaching scheme, the most obscene thing in football is the forward pass. The Ohio State coach agree 110 per cent with the late Bob Neyland’s words about throwing the ball: “When you pass the ball three things can happen and two of them are bad.”
 
2006 September 9, Columbus (OH) Dispatch, “Royal took Longhorns from oblivion to No. 1″ by Todd Jones, pg. 7E:
“Now, you can hear some stuff in a barbershop. You can pick up some wisdom there. I’m just a model of the people I’ve been around in my life, and Woody was one of those people.”

Royal credits Ohio State’s Hayes, his contemporary and friend, with being the first one to say three things can happen on a pass play and two of them are bad.