The Hotel Problem

The hotel problem is generally the first problem encountered by a user of web analytics. The problem is that the unique visitors for each day in a month do not add up to the same total as the unique visitors for that month. This appears to an inexperienced user to be a problem in whatever analytics software they are using. In fact it is a simple property of the metric definitions.

The way to picture the situation is by imagining a hotel. The hotel has two rooms (Room A and Room B).

Day 01Day 02Day 03Total
Room AJohnJohnMark2 Unique Users
Room BMarkAnneAnne2 Unique Users
Total222?

As the table shows, the hotel has two unique users each day over three days. The sum of the totals with respect to the days is therefore six.

During the period each room has had two unique users. The sum of the totals with respect to the rooms is therefore four.

Actually only three visitors have been in the hotel over this period. The problem is that a person who stays in a room for two nights will get counted twice if they are counted once on each day, but are only counted once if the total for the period is looked at. Any software for web analytics will sum these correctly for the chosen time period, thus leading to the problem when a user tries to compare the totals.

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