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Information in digital libraries and information systems frequently refers to locations or objects in geographic space. Digital gazetteers are commonly employed to match the referred placenames with actual locations in information integration and data cleaning procedures. This process may fail due to missing information in the gazetteer, multiple matches, or false positive matches. We have analyzed the cases of success and reasons for failure of the mapping process to a gazetteer. Based on these, we present a statistical model that permits estimating 1) the completeness of a gazetteer with respect to the specific target area and application, 2) the expected precision and recall of one-to-one mappings of source placenames to the gazetteer, 3) the semantic inconsistency that remains in one-to-one mappings, and 4) the degree to which the precision and recall are improved under knowledge of the identity of higher levels in a hierarchy of places. The presented model is based on statistical analysis of the mapping process of a large set of placenames itself and does not require any other background data. The statistical model assumes that a gazetteer is populated by a stochastic process. The paper discusses how future work could take deviations from this assumption into account. The method has been applied to a real case.