I had an overly long post devoted to Cozart's hitting. I like Cozart and hope his hitting can improve. I've cut out some of the detail because it was way over long. But here are the high points -
Cozart makes a lot of contact. He struck out 18.8% of the time, which is relatively low. He walked about 5% of the time, which is quite low. His rate of homers per fly ball is 8.8%, also low.
In other words, Zack puts a lot of balls in play. Few homers, walks, Ks per plate appearance. High contact rate.
Zach doesn't swing at too many bad pitches. Fangraphs shows us this in its plate discipline chart. So his problem is not swinging out of the zone, although his walk total is low.
So what's the problem?
Two things I see. First, bad luck. Cozart had a .282 BABIP which is quite low. No Red regular (except Rolen, who tied Cozart) had such a low BABIP last year.
Secondly, Cozart hits too many fly balls. Phillips, the most comparable hitter in some respects, had 32.3% fly balls. Cozart had 38.3% fly balls.
Since Cozart has a low homer to fly ball ratio, he can't hit so many fly balls. They mostly die out there. More line drives and ground balls would be better. (His line drive rate of 20 percent last year was similar to Phillips and Bruce, all could improve a bit. Phillips hits too many grounders, Bruce too many flies.)
Hopefully, Cozart will overcome the bad luck part. Also, since he doesn't swing at that many bad pitches, his walk rate will hopefully improve. The major area for hitting improvement IMO is to stop hitting quite so many fly balls. Cozart's fly balls don't result in enough homers to justify the high rate.
Still pretty long, but originally much worse.