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I think the problem here is just one of player frustration caused by unlucky dice rolls. I get it. A streak of bad rolls can be really annoying.
But it has nothing to do with the feat. Like several in this thread, I had a great experience with Nimble Dodge. It saved my Rogue from a round 1 crit that would have resulted in a desperate situation. The difference with the OP is pure luck of the dice.
The math calculation is correct but unconvincing. A 20% chance to make a difference is great. In fact, I don't think many feats usable every round provide more than a 20% improvement of anything. Most feats that provide a bonus give a +1. Some give more, but are situational (compare with You're Next, the other level 1 Rogue feat that provides a reaction).
As others have mentioned, Nimble Dodge is a fine choice for a level 1 feat, for a class that doesn't have a built-in reaction. At higher levels, it can be upgraded with Nimble Roll, or it can be retrained when stronger reactions become available.
I think the OP has a point, however, when it comes to the Swashbuckler. That class is built for reactions, so it would be a much greater cost for the Swashbuckler to declare Nimble Dodge against his opponent's first attack, making Opportune Riposte unavailable for the rest of the round.
Now, the Swashbuckler is in the playtest phase. Now is the time to provide that feedback, so the designers can consider a new version of Nimble Dodge more appropriate for the Swashbuckler.
My other takeaway is that keeping a log of dice rolls is a bad idea. If the dice have been bad, it's just depressing. It proves exactly nothing. Worse, it gives rise to the false impression that you're somehow "due" better luck in the future.