# Mariota’s Still Human (And a Rookie)

By Kurt Bullard

If you’ve seen or read any coverage on the Tennessee Titans this preseason, you’re familiar with the leading story that Marcus Mariota has yet to throw an interception in his 186 attempts 7-on-7 drills. Any fan of the NFL knows how poorly the Titans have performed over the past few years, and the fan base is justifiably looking for any sign of hope from its potential franchise quarterback. But is Mariota’s ball protection in practice worthy of all of this coverage?

The main goal here is to figure out how much 186 throws without an interception should affect the expectations of the Flyin’ Hawaiian going into the regular season – a task perfectly suited for Bayesian statisticians. Doing so simply requires utilizing the concept of conjugate priors – a statistical method that allows you to take into account prior expectations and empirical data by combining two distributions.

Prior to any hooplah surrounding Mariota in camp, a decent predictor of Mariota’s interception rate would be to take the average of the interception rate of rookies in recent history. First-year signal-callers since 2008 have thrown on average 3.94 interceptions per 100 throws. Using the interception rates of these rookies, I was also able to form a prior distribution by fitting the data to a beta distribution through Method of Moments inference, which returned parameters of a = 0.55 and b = 13.49

I could then combine the prior distribution with a simple binomial distribution to form a posterior distribution that could then be used to best estimate Mariota’s “true” interception rate. This makes the assumption that an interception in practice is as common as an interception in a full-speed NFL game – an assumption that probably will underestimate Mariota’s true ability to maintain possession. Combining a beta distribution with a binomial distribution yields another beta distribution with the following parameters:

Apost = Aprior + interceptions in practice = 0.55
Bpost = Bprior + attempts – interceptions = 199.49

With the posterior distribution having been found, one can use the maximum likelihood estimator – the maximum of the likelihood function – to pinpoint the most probable interception rate. For the beta distribution, this calculation is simply (Apost)/(Apost +Bpost), which yields an interception rate of 2.76%, more than 1%-point better than the average rookie has performed over the past seven years.

Sure, Mariota is projected to be better with the ball than most rookies; but then again, he was the No. 2 pick in the draft, so he should be. The real question is how that rate stacks up against NFL starters.

Last year, 42 QBs attempted at least 100 passes. Here is how Mariota’s projection would rank last year among qualifying quarterbacks.

 QB Int. Rate Rank Aaron Rodgers 0.96% 1 Charlie Whitehurst 1.08% 2 Alex Smith 1.29% 3 Carson Palmer 1.34% 4 Ben Roethlisberger 1.48% 5 Tom Brady 1.55% 6 Russell Wilson 1.55% 7 Michael Vick 1.65% 8 Matthew Stafford 1.99% 9 Derek Carr 2.00% 10 Ryan Tannehill 2.03% 11 Tony Romo 2.07% 12 Drew Stanton 2.08% 13 Colin Kaepernick 2.09% 14 Joe Flacco 2.17% 15 Matt Ryan 2.23% 16 Kyle Orton 2.24% 17 EJ Manuel 2.29% 18 Eli Manning 2.33% 19 Colt McCoy 2.34% 20 Peyton Manning 2.51% 21 Ryan Fitzpatrick 2.56% 22 Drew Brees 2.58% 23 Andrew Luck 2.60% 24 Cam Newton 2.68% 25 Marcus Mariota 2.76% 26 Robert Griffin 2.80% 27 Mike Glennon 2.96% 28 Brian Hoyer 2.97% 29 Teddy Bridgewater 2.99% 30 Shaun Hill 3.06% 31 Philip Rivers 3.16% 32 Austin Davis 3.17% 33 Jay Cutler 3.21% 34 Nick Foles 3.22% 35 Andy Dalton 3.53% 36 Geno Smith 3.54% 37 Mark Sanchez 3.56% 38 Blake Bortles 3.58% 39 Zach Mettenberger 3.91% 40 Josh McCown 4.28% 41 Kirk Cousins 4.41% 42 Jake Locker 4.79% 43

Mariota ranks 26th in the NFL, just in front of the much-maligned Robert Griffin III, showing that his streak in practice is rather meaningless. To be fair, interception rate is just one aspect of a quarterback’s performance – no one would argue that Charlie Whitehurst is the second best quarterback in the league except for maybe the man himself. But considering that the leading story out of Titans’ camp every day is that Mariota didn’t throw an interception, it’s definitely being read into too much.

So, while Titans fans need some sign of hope to keep moving forward, a few days of practice without an interception is not one of those signs. Mariota is showing signs of being a good rookie, but at the end of the day, he is still just a rookie.