The N.C.A.A. allows a student to move to a new university and play immediately if he has completed his undergraduate degree. Although there are exceptions, many students who transfer without degrees are allowed to play only after sitting out a year.

For this season, No. 4 Oklahoma, home of the last two Heisman Trophy winners, brought in Hurts, who spent three years at Alabama. No. 6 Louisiana State has Joe Burrow, and Mississippi State, Texas Christian and Maryland are among the teams that have entrusted their offenses to graduate transfers. When West Virginia goes to Missouri on Saturday, each team’s first string is expected to include a degree-bearing quarterback: Kelly Bryant, formerly of Clemson, for Missouri; and Austin Kendall, who played at Oklahoma, for the Mountaineers.

“You have to be invested in the program you’re going to because these guys are taking a chance on you,” Kendall, who predicted that the trend of graduate transfers would continue, said in an interview on Tuesday.

The season’s first weekend showed mixed performances for graduate transfer quarterbacks. Bryant’s 423 passing yards accounted for close to 80 percent of Missouri’s offense in a humiliating loss at Wyoming. Kendall was responsible for an even greater share of West Virginia’s yards when it beat James Madison .

Tommy Stevens, who moved to Mississippi State from Penn State, used his first career start to throw for 236 yards and two touchdowns. Arkansas’s graduate transfers, Ben Hicks and Nick Starkel, mustered just 191 passing yards against Portland State, and Riley Neal of Vanderbilt did not even make it to triple-digit yardage.

But Hurts — and there is perhaps no current player whose highs and lows have been more public — used Sunday night’s game against Houston to open a viable Heisman campaign. He passed for 332 yards and rushed for 176 , assembling a personal record for total offense. His first possession as a Sooner lasted all of three plays, ending with a touchdown throw.

“Playing at a school like Alabama and playing at a school like Oklahoma, there ain’t many people in the world who can say they’ve done that,” Hurts, seemingly averse to the spotlight, said softly after the game. “It’s just all unprecedented, but I’m focused on the now. We’re focused on the now.”