The author-affiliation links are the essential elements used for multiple purposes, such as the disambiguation of authors, the attribution of credits of a publication and fractional counting, the analysis of scientific networks, etc. In this article we analyzed the author-affiliation link quality in the Web of Science (WoS) database between 2000 and 2021. We analyzed the link completeness for 32,676,914 scientific publications under different angles: WoS index, document type and the number of authors per publication. The analysis showed that the author-affiliation link begins to be well informed from 2008. The share of publications for which all addresses and all authors are linked is close to 100% from 2016. The results show a strong variability according to the WoS index, the document type and the number of authors per publication. AHCI is the index with the highest completeness rate, unlike the SCI. For the document type, these are the Conference proceedings where the completeness rate is better and/or can be completed. Regarding the number of authors, statistics show that the higher the number, the more addresses and unlinked authors there are. Finally, the analysis of a random sample of 100 publications showed that in more than 50% of the cases, the author-address links do not exist in the original publication, and the WoS reproduced only the available information provided by the editor.