The quality, position of visitor, notably where that is a title:(noun)
Attendance, number of visitors attending an event, etc.(noun)
Wiktionary.org : Text is available under the Creative Commons Attribution-ShareAlike License
Use "visitorship" in a sentence
"* Getting back for a moment to the increasing visitorship of the Whatever, I do want to note that I very strongly suspect that, in addition to whatever I may blatherate about here, another very strong component to growing the visitorship is the comment threads, which are sometimes oh, okay, often more interesting than the entries to which they are attached."
"Its visitorship last year exceeded that of the Solomon R."
"Despite the growing pains, the museum maintained visitorship through the downturn, says Mr. Eng."