The potential to make history is on the line for Baker Mayfield on Saturday night at Ohio State.

It's only Week 2, and making any definitive statements about the Heisman Trophy race this early in the season has proven to be foolish time and time again. Nevertheless, No. 5 Oklahoma's trip to Columbus to meet the No. 2 Buckeyes can't help but feel like a pivotal moment for both the College Football Playoff hopes of the Sooners and the Heisman hopes of Mayfield, their star senior quarterback who has already made admirable pushes for the Heisman twice.

Last September, Ohio State visited Oklahoma and won easily, 45-24. The Sooners had already lost to Houston in the opener, and at home against the Buckeyes, Mayfield completed 17 of 32 passes for 226 yards, two TDs and two INTs. Remarkably, it was the only game out of 13 in which he did not average over nine yards per pass attempt, and it was the only time he didn't complete 60 percent of his passes.

Mayfield set the single-season FBS passer rating record and finished third in the Heisman vote, throwing for 3,965 yards and 40 touchdowns. Despite going undefeated with enormous numbers in Big 12 play, the performance against the Buckeyes, and the 1-2 hole Oklahoma started in, made catching up to Lamar Jackson and Deshaun Watson impossible. Mayfield finished a distant third, although both he and his top receiver, Dede Westbrook, were invited to New York as finalists. This came after Mayfield had a fourth-place season in 2015, when the Sooners did make the playoff and he threw for 3,700 yards and 36 TDs.

In earning his trip to New York last year, Mayfield became the 59th player to finish in the top five of the Heisman race twice. Thanks to a ruling in 2016 that allowed Mayfield to regain an extra year of eligibility after transferring to Oklahoma from Texas Tech, where he walked on, he now has a chance to do it three times after he returned for his senior season.

That raises a question: Can Mayfield become just the seventh player in the history of the Heisman Trophy to finish in the top five of the vote three times?

Fifteen players have earned top-10 finishes three times. The only players to finish in the top five three times are Doc Blanchard, Glenn Davis, Doak Walker, Archie Griffin, Herschel Walker and Tim Tebow, a who's who of all-time college football greats. All six of those players won the award in one of those seasons (Griffin won it twice), and Mayfield is trying to join an exclusive club of legends of the sport.

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Special thanks to Sports-Reference's Heisman voting data.

Not many players have had such an opportunity. Mayfield is only the 18th two-time top-10 finisher in the vote to return for another season of college football. That list includes the 15 in the above chart, plus Saint Mary's -- and future "Hawaii Five-O" -- star Herman Wedemeyer and Ohio State's Braxton Miller, neither of whom finished in the top 10 in their final season. Injuries played a role for both: Wedemeyer was banged-up during the Gaels' fall to 3-7 in 1947. Miller, who finished fifth as a sophomore and ninth as a junior, missed the 2014 season with an injury, then returned in 2015 but mostly as a receiver after Cardale Jones and J.T. Barrett took over at quarterback.

Mayfield's hopes of joining the three-time Heisman top-10 club got off to a strong start in Week 1, as Oklahoma dominated an overmatched UTEP squad, winning 56-7. Mayfield played only the first half, and he completed 19 of 20 passes for 329 yards and three touchdowns in the first game without his head coach (Bob Stoops), Heisman finalist receiver (Westbrook) and two thousand-yard rushers (Samaje Perine and Joe Mixon).

Despite Oklahoma's attrition, Mayfield is still paired with the same play-caller, Lincoln Riley, who was promoted to head coach after overseeing Mayfield's prolific past two seasons. He's also playing behind arguably the nation's best offensive line, an experienced group headlined by star left tackle Orlando Brown. Questions remain at the skill positions as the competition stiffens, but against the Miners, Mayfield got a huge game from his most proven weapon, tight end Mark Andrews (seven catches, 134 yards, one TD).

There are, of course, few conclusions to be made from one half of football against UTEP. The perception of Mayfield and Oklahoma going forward will be shaped by what happens in Columbus on Saturday night against the Buckeyes, who have lingering questions on offense and in the secondary but boast a ton of talent, especially on an absurdly loaded defensive line. (There will be few better matchups in college football this year than the Oklahoma offensive line vs. the Ohio State defensive line.)

Thanks to Mayfield, Oklahoma has what should be a substantial edge in the passing game. Ohio State's J.T. Barrett finished fifth in the Heisman race as a redshirt freshman in 2014, but in 2015-16, he averaged just 6.7 yards per pass attempt (10.9 per completion). Mayfield averaged 10.2 yards per attempt (14.7 per completion) in those two seasons. The Buckeyes have plenty of talent and speed, but we're still waiting to see evidence that they can attack opponents downfield. Oklahoma does that as well as just about anybody, and Ohio State's new-look secondary appeared vulnerable against Indiana last week, giving Mayfield a chance to do some damage and build an early case in the Heisman conversation against players like defending winner Lamar Jackson, Penn State tailback Saquon Barkley, USC quarterback Sam Darnold and UCLA quarterback Josh Rosen, among many others.

Given the lingering stigma associated with Big 12 defenses -- last week's Texas loss to Maryland and Baylor loss to Liberty didn't help -- Mayfield needs a big high-profile nonconference performance against a team like Ohio State to build momentum and avoid having to play catch-up in the race again. As someone who's been a top-four Heisman finisher twice, he has the name recognition to be a slam-dunk candidate; getting actual first-place votes is another matter, one likely to require a signature nonconference win on top of success against the Big 12.

A win this time against Ohio State would significantly increase the chances of Mayfield joining the club of five Oklahoma Sooners who have won the Heisman. It isn't the only exclusive company that he has a chance to join, either.

Heismans are won't in September, but for Mayfield, this week's game could help open up historic possibilities.

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Contact Matt at matt.brown5082@gmail.com and follow him on Twitter @MattBrownCFB and Facebook.