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Faceted navigation (and other) counts in Funnelback are estimates based on the number of results found when a search query is executed.
The accuracy of the estimates can vary depending on how large the index is and the number of results that are returned.
The counts can also change when you select a category because the counts are re-estimated when the new query containing the applied facet runs.
Funnelback v12+ has a default query processing mode known as document at a time (DAAT) - this mode is much more efficient when retrieving relevant results, but it produces estimates for all counts.
This will result in the counts being inaccurate, and possibly changing when you select them (as a new estimate is produced on a smaller result set).
Improving count accuracy
When query runs in DAAT mode the query execution stops once the DAAT limit is reached. By default this occurs when 5000 matching results have been found. The totals found - then all counts are extrapolated from this result set.
You can increase the accuracy of counts by increasing the DAAT limit, but the trade off is performance.
To increase the DAAT limit on a collection you set a query processor option of -daat=N where N is the size (eg. default is -daat=5000).
Note: using -service_volume=low or -daat=0 turns DAAT mode off (making the counts accurate) however this is not recommended because many newer features within Funnelback will not function if DAAT mode is turned off.