Zack Cozart has only played 222 major league innings. Even though any number over 100 still sounds like a lot to me, we don't have a sample remotely big enough to match a reasonable number to his defensive value. And that's setting aside that the question of whether the task is even possible.
If it matters, Cozart has already been worth 5.6 fielding runs over two very small slices of a season according to FanGraphs, with a 29.6 UZR/150. That looks more like a decimal place error than a number we should trust.
I don't think we're at a point yet where you can quantify fielding reliably to even an integer, though defensive metrics can certainly be an instructive baseline over multiple seasons. I thought we could try something a little more anecdotal.
Cozart has had enough reps in the major leagues to make an initial impression, while having been a professional long enough to have an established reputation. He was judged the best defensive infielder in the Reds' system in 2007 and 2008 by Baseball America. He kept his reputation as a plus defender as he rose in the ranks. Early this season, John Sickels was very complimentary of Cozart's defense: "He's reliable and steady with the glove, showing above-average range and an accurate, if average, arm."
But I'm curious what your impressions have been to Zack Cozart, Major League Short Stop. At Age 26, his defensive skills have some room for refinement and adjustment to the challenges of playing in the big league talent pool, but they are very nearly a finished product after 5.5 seasons as a professional.
Below is a pretty informal poll to gauge Cozart's fielding. It's premature to pass any final judgment on what he offers this season, but the wisdom of the crowds has proven pretty reliable with fan ratings. Try set aside his pedigree and the tug of homerism and think just about the plays you've seen him make. If you've watched him in the minors, try to use recent (2011 and beyond) recollections to inform your judgment.
We'll check back in on Zack and other Reds' defenders to see if this helps flesh out our picture of the run savers.