Redshirt-freshman quarterback J.T. Barrett waits for the snap during a game against Cincinnati on Sept. 27 at Ohio Stadium. OSU won, 50-28, behind 409 yards of total offense from Barrett.Credit: Mark Batke / Photo editorWhen senior quarterback Braxton Miller went down with an injury during fall camp, the Ohio State football team turned to a redshirt-freshman who hadn’t taken a meaningful snap since high school.While there have been bumps in the road, that young quarterback — J.T. Barrett — has already accomplished things Miller never did for the Scarlet and Gray. Miller’s name could nearly fill its own record book, but Barrett ranks ahead of the veteran on multiple fronts just four games into his career.OSU coach Urban Meyer left some credit for the coaching staff when it comes to Barrett’s quick improvement, but also praised the signal caller’s ability to learn.“I think (I’m) not surprised by his development,” Meyer said after OSU’s 50-28 win against Cincinnati on Saturday. “I think (co-offensive coordinator and quarterbacks coach Tom Herman) is an excellent coach and he’s a very good student.”Barrett tied the school record for touchdown passes in a game when he threw six against Kent State — and had more than 300 yards in the air — before adding to his accomplishments with another record-setting night against Cincinnati. The Wichita Falls, Texas, native threw for 330 yards and four touchdowns and added 79 yards on the ground.That makes two consecutive games Barrett has thrown for more than 300 yards — something Miller hasn’t done in three seasons. Barrett’s 409 yards of total offense rank as the second-best in school history behind Art Schlichter’s 412 yards gained against Florida State in 1981. He also led the OSU offense to a school-record 45 first downs and the third best total output in OSU history of 710 yards.After his record-setting night, Barrett saved more of the praise for his offensive line, which gave him time in the pocket to complete 26 passes out of 36 attempts.“All the credit goes to the offensive line,” he said after the game. “They got it started for us and that’s what coach Meyer always talks about in relying on them to keep the offensive going.”Barrett said he still has a room for improvement, but recognized the strides he has made since first taking the field against Navy on Aug. 30.“I think coming into Navy I was trying to make sure everything was right,” he said after the Cincinnati game. “Knowing I make mistakes and then just learning from them throughout the game.”He went on to say he’s more worried about trusting his instincts instead of worrying about making mistakes, something Herman said he wanted the quarterback to focus on in practice before taking on the Bearcats.“Trusting what you see and pulling the trigger, it’s better to be early than to be late,” Herman said after the game. “I thought he did — just from my vantage point — better, (but) still could probably get better at that.”Barrett set personal career-highs for passing attempts, pass completions and passing yards in the game, and did it all without throwing an interception for the first time in his career.Regardless of those numbers, Herman said Barrett can improve on making quicker decisions, but added he saw a “vast improvement” in another part of the quarterback’s game.Herman said given Barrett’s 6-foot-1 frame, the signal-caller needs to hang back in the pocket more in order to be able to see over the line and make the correct decisions.“So we really worked on keeping him a little bit deeper in the pocket on some of our drop-back throws and I thought he did that tonight,” Herman said.Despite his big day, Barrett said he recognized the spots where he needs to improve, and added he is ready to get back to work to keep getting better.“There’s certain things that you know you need to execute on during the game and so you think about those more than the big plays,” he said. “Definitely going in (to practice Sunday) trying to correct the mistakes we made.”Through four games, Barrett has completed 70 passes out of 110 attempts for 1,087 yards and 13 touchdowns. He’s thrown five interceptions — three of which came against Virginia Tech on Sept. 6 — and gained another 205 yards on the ground with one additional touchdown.After a bye week before the Cincinnati game, the Buckeyes are set for a typical game week before taking the field again. OSU is scheduled to play Maryland next Saturday in College Park, Md., and kickoff is set for noon.