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Forbath was 3/4 during preseason, the one miss being that shank from over 50 yards. Darn, he shanked a kick that is only a 50-50 proposition for most kickers even when they hit it well. Barth was 2/2. He didn't miss in preseason, but unfortunately didn't get as many opportunities either. While I don't know the totals, nor have the time to search every day of media tweets for kicks during training camp, I remember it being pretty clear that Forbath had the edge.
Here is a link to a good article after the open media days.
In Saints kicking battle, Kai Forbath, Connor Barth have similar backgrounds | NOLA.com
From that article, Forbath was 13/13 during that period while Barth was 9/12, building a strong lead. I do remember reports coming after in which Forbath missed on or two, but in every one of those reports, I payed attention to Barth's numbers to see if he was catching up - which, unfortunately, he wasn't. The theme I remember was this, any time Barth managed to miss fewer in practice, Forbath would then nail a 50+ yarder.