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Does a metric exist that quantifies morphological richness in languages? Either a numerical score, or at least a ranking of languages would suffice.

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    What kind of morphology do you mean, general, derivational, inflectional, any other? Every word root is a morpheme, do you know that? – Yellow Sky Feb 8 '17 at 1:05
  • Generally if there is a lot of inflection, there is a lot of derivation to go with it. I would say the average number of frequent words (assuming "word" has a good definition in the language) that come from a particular root -- for derivation, combined with parameters about the number, size, and shape of relevant paradigms -- for inflection (those parameters could distinguish between fusional and agglutinative inflectoin) would do for both. We can consider root compounds to be syntax, if there's no bound forms necessarily involved. – jlawler Feb 9 '17 at 0:48
  • What do you mean by "derivation"? In Bantu languages there is a vast amount of inflection, and not much derivation (depending on what your definitional criterion is for "derivation"). – user6726 Feb 9 '17 at 0:57
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No, but as contrasted with the related notion of morphological complexity, it seems at least a bit more possible to define and count it. When people say a language has a "rich" morphological system, that usually means that there are very many non-lexical morphemes. It might also mean that there is the possibility of combining affixes, but I don't think that is inherent in the notion of richness. If a language has 200 affixes (a reasonably rich morphology), it would be unusual if e.g. there were 200 cases or mood suffixes, and no other morphemes. Simple counting would be a good measure of "richness".

Complexity is much harder to define, since it necessarily involves rules of combination. For example, instead of just saying "the past tense marker is -ile", you might have to say "the past tense marker is -ita after the causative -ʃ and -ile otherwise", which makes the system more complex. The problem is that there is no scientific utility to having a metric of "richness", that is, unlike water which boils when it reaches a specific temperature, languages don't have properties that depend on having a particular quantity of richness.

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    "Richness" involves multi-layered structures and lots of available construction techniques; "complexity", on the other hand, involves a significant degree of irregularity and asymmetry, with enough richness to be confusing. – jlawler Feb 9 '17 at 0:51

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