A few weeks ago, 538 wrote an excellent article looking at density curves for NFL quarterbacks. They found some common trends in these QB density curves and identified ten different types of NFL quarterbacks, from the elites, to the game managers, to the "uh-ohs."
Since you may have heard that Ohio State will have a quarterback "problem" next season in that the team has three highly-capable challengers for the single starting spot, I thought that it might be possible to produce QBR density curves for Cardale Jones, J.T. Barrett, and Braxton Miller to see who statistically had the edge based on past performance.
So, before going in to the methods here, it's worth saying that past performance might not matter in the upcoming quarterback race. Even though it's unlikely at this point, one of the contenders may transfer, one may switch positions, or injuries may make past performance a bad predictor of future ability. Then there's the fact that ESPN's College QBR ranking definitely isn't a perfect measure of quarterback ability. In any case, I thought it might be interesting all the same. To the data!
I used ESPN's Adjusted QBR rankings for the each quarterback's last full season of play. I only included games where the player either started or threw at least ten passes. Braxton (2013) and J.T. (2014) each had twelve games, while Cardale had three -- Jones threw nine passes against Illinois this year, but that performance didn't make the cut. Adjusted QBR is adjusted for the opposing defense.
While the 538 article was dealing with a large amount of data, I was working with 12 observations per quarterback. Instead of calculating density curves exactly like they did, I collected frequencies of QBR scores by every ten points (i.e., Barrett had five 90+ Adj. QBR games). Charting these out, with the QBRs on the x-axis and frequencies on the y-axis, you're able to get a rough quarterback curve. Like in the 538 article, you want the tail of the curve to go up at the end and not have a low frequency near the graph origin.
QBR Frequency Charts
It's hard to take too much away from a quantitative analysis of Cardale's play considering he only started three games last season. Braxton had the highest mean QBR, but he also had the highest standard deviation, too.
From left to right is Jones, Barrett, and Miller, with QBR in the x-axis and frequency of QBR scores in the y-axis.
It's a little difficult to compare these three, but the biggest takeaway from the beginning is that both Braxton and J.T. have far more excellent games (90+ QBR) than bad games. J.T. had two games in the 50s, while Braxton had one poor performance in the 30s (and two in the 60s), but both players had far more excellent performances than mediocre ones. Cardale's density curve looks crazy with only three data points, but essentially Cardale had two decent games (one with a QBR in the 60s and one in the 70s), and one excellent game (the 90.4 Adjusted QBR performance against Wisconsin). I'll also say that Braxton's bad performance (a 30.4 Adjusted QBR against Northwestern) is a little deceiving -- his QBR was only that low because he didn't account for any touchdowns himself.
QBR scores and defensive rankings
That wasn't as revealing as I hoped. All three quarterbacks are capable of excellent performances against excellent competition, and their curves were exactly what you'd hope for in a quarterback: a greater number of excellent performances than poor or mediocre ones. So I then plotted Adjusted QBR scores by game and compared those with Opponent Defensive F/+ rankings to see how the quarterbacks did against their opponents. While Adjusted QBR is adjusted for opponent already, as you'll see, there were still wild variations in how the quarterbacks performed against good and bad opponents:
Cardale's QBR scores vs. Defensive F/+ rankings
J.T.'s QBR scores vs. Defensive F/+ rankings
Braxton's QBR scores vs. Defensive F/+ rankings
Any quarterback would theoretically want to play well all the time, but particularly against the best opponents (when Opp. F/+ Rank is very low, and QBR is very high). In his third season at Ohio State, Braxton had four games against top-25 Defensive F/+ defenses and averaged a 78.9 Adjusted QBR. In J.T.'s redshirt freshman season, he had three games against top-25 Defensive F/+ teams and averaged a 72.4 Adjusted QBR. All three of Cardale's starts were against top-25 Defensive F/+ teams, and he averaged a 76.0 Adjusted QBR.
Against lesser competition (Defensive F/+ rankings above 60), J.T. averaged a 77.2 Adjusted QBR, while Braxton averaged 80.6.
I also ran a simple correlation between Opponent Defensive F/+ Rank and QBR for both quarterbacks. Both Braxton and J.T. had a slightly positive but weak relationship between the two variables (R = .104 and .086). In short, we don't have sufficient evidence across just 12 games to say that either quarterback plays better or worse against better (or worse competition). Sometimes they step up in big games, sometimes they don't.
Essentially, these results just fan the flames of what should be a very interesting summer for Ohio State quarterbacks. It's tough to compare performances between a mostly-finished product in junior Braxton and redshirt freshman J.T. Barrett (and redshirt sophomore Cardale), but all three quarterbacks have fairly equal claims to be the starter based on individual performance according to QBR.