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Description
The majority of the logic in StatsValuesFactory for dealing with stats over fields just uses the ValueSource API. There's very little reason we can't generalize this to support computing aggregate stats over any arbitrary function (or the scores from an arbitrary query).
Example...
stats.field={!func key=mean_rating mean=true}prod(user_rating,pow(editor_rating,2))
...would mean that we can compute a conceptual "rating" for each doc by multiplying the user_rating field by the square of the editor_rating field, and then we'd compute the mean of that "rating" across all docs in the set and return it as "mean_rating"
Issue Links
 is blocked by

SOLR6507 various bugs using localparams with stats.field
 Closed
 is related to

LUCENE5961 FunctionValues.exist(int) isn't returning false in cases where it should for many "math" based value sources
 Closed

SOLR6540 strdist() causes NPE if doc is missing field
 Closed
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Bulk close after 5.0 release.