In 2003, Koetter's recommendation persuaded Houston Nutt to hire Wittke as his offensive coordinator at Arkansas.
This offseason, Koetter revisited his endorsement of Wittke when his longtime offensive coordinator, Mark Helfrich, left to become offensive coordinator at Colorado. At the same time, Arkansas ushered Wittke out of town in favor of Springdale (Ark.) High School coach Gus Malzahn.
"He asked me who I would recommend as a top-flight quarterbacks coach," Koetter said of his conversation with Nutt in 2003. "I thought Roy was bright and a good recruiter who knew the passing game. He's a guy I've been interested in a long time."
Wittke's change of scenery is much more than the 1,200-plus miles from Fayetteville, Ark., to Tempe, Ariz.
It's a drastic change in styles.
During Wittke's three seasons with the Razorbacks, Arkansas was the SEC's most productive running team. The Hogs ran the ball at least 62 percent of the time and never finished out of the national top 25 in rushing during Wittke's tenure.
During the same time at Arizona State, the Sun Devils were among the nation's top passing teams. In 2004 and '05, Arizona State finished in the top five nationally in passing offense. ASU was ranked 25th in 2003.
Wittke will have an interesting choice at quarterback, but for different reasons. At Arkansas, Robert Johnson and Casey Dick split starting duties with limited success last season.
The pair combined to complete 142 passes for 1,460 yards and 12 touchdowns – less than either of Arizona State's two quarterbacks, Sam Keller and Rudy Carpenter.
Keller passed for 2,165 yards and 20 touchdowns in the first seven games before being sidelined by a thumb injury. Carpenter took over and became the nation's most efficient passer.
The Keller-Carpenter situation at quarterback will give Wittke his most high-profile decision, but as Koetter has said since the end of last season - it's a predicament Wittke said he can live with.
"Anytime you're blessed with the situation we have at quarterback, it makes (the move) better," said Wittke, who ran a pass-first system while the offensive coordinator at Division I-AA Eastern Illinois from 1990-2002.
Play selection for Arkansas and Arizona State over the last three seasons:
Despite the differing offensive styles at Arkansas and Arizona State, Koetter is looking less for new ideas than a new approach to his offense.
Arizona State's previous offensive coordinator, Helfrich, had worked with Koetter since 1997 when they were both at Oregon. Helfrich had been the coordinator for Koetter's entire tenure.
When Helfrich left for Colorado, Koetter hoped to bring a fresh perspective to his offense - a system which guided the careers of Andrew Walter at Arizona State, Ryan Dinwiddie at Boise State and Joey Harrington at Oregon.
In his first three seasons Koetter replaced only one assistant. This season he replaced two offensive assistants, with John Wrenn being named line coach.
The turnover has turned coaching meetings into question-and answer sessions.
"I've asked 'why' more times than I have anywhere else," Wittke said. "It's forced us to look at what we do and why we do them. We've gone through a thorough examination of the system."
In his short tenure in Tempe, Wittke has been briefed on the details of recruiting a new Sun Devils quarterback, how plays are called, and the way terminology is used.
But don't expect Arizona State to turn to Arkansas' grinding, run-first style. Koetter said the minor changes made to the offense and the additions to the coaching staff have helped the offense "to stay cutting edge."
"As far as the impact on the team, it's hard to say what that will be until you get into a real season," Koetter said. "It made me go back and explain why we do things. It's been a refreshing eye-opener."