It's subjective, I have to admit. I would say a search is accurate if most people find what they are looking for in their dataset in the first try.
Distance definitions such as the Levenshtein and Damerau-Levenshtein distances provide a solid basis for discussions on accuracy. However, they are costly to compute and hence not widely adopted in fuzzy search libraries.
I started by using the known filter equation for the Levenshtein distance and computed a quality score with a leightweight formula. Then, I realized that the filter equation can be extended to the Damerau-Levenshtein distance by sorting the characters of the 3-grams.
In my tests, this implementation worked well. Please let me know how it works for you if you test it.