Visitors and the ‘hotel problem’

A common mistake in content analytics is improperly adding visitor totals over a period of time.

Web analysts call this the “hotel problem“: You cannot add visitor totals for a range of dates in a period and have that total equal the actual number of visitors in the period.

For example, summing up visitor totals from Monday, Tuesday, and Wednesday will not equal the correct visitor total for the 3 days as a whole. Similarly, adding visitors from every day in a month will not match the correct total visitors for the month.

This is called the hotel problem, because it’s often best illustrated with a chart of hotel guests:

	Monday	Tuesday	Wednesday
Guest 1	x	x
Guest 2		x
Guest 3	x	x	x
Daily visitors	2	3	1

Adding the number of hotel visitors from each day above results in 6:

2 + 3 + 1 = 6

But from Monday-Wednesday, 3 visitors stayed at the hotel, not 6. You cannot add the daily totals and get the accurate total for the full date range.

As another example, here are daily visitor totals for a small site tracked by Parse.ly:

	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday	Sunday
Daily site visitors	423	257	181	228	168	166	148

Adding the site visitors from each day results in a total of 1,571:

423 + 257 + 181 + 228 + 168 + 166 + 148 = 1571

But the actual total number of site visitors, when looking at a report for the entire week, is 1,231. Some visitors came to the site more than once during the week — adding the total from each day means you count those return visitors multiple times instead of once.

You cannot add visitor numbers from individual dates in a period to get the correct total. You must run a report for an entire period to get the correct visitor total, be it a week, month, quarter, or year.