The “Hotel Problem” – Revisited

One of the things that I always find that people have difficulties with when starting off on their Web Analytics journey is when they discover what’s known as “The Hotel Problem”. Wikipedia’s has a good explanation about it, and also notes its origins.

The Problem:
Unique Visitors for each day in a period of time DO NOT add up to the same total as Unique Visitors for that entire period of time.

Let’s say you kept a daily track of all of the Unique Visitors to your website for every day of this week. Here’s what that would look like:

Sunday: 5 Unique Visitors
Monday: 10 Unique Visitors
Tuesday: 5 Unique Visitors
Wednesday: 10 Unique Visitors
Thursday: 5 Unique Visitors
Friday: 10 Unique Visitors
Saturday: 15 Unique Visitors

So, that’s 5+10+5+10+5+10+15 = 60 Unique Visitors (Don’t be afraid to double-check that math, lol )

But then let’s say that you go back in your Web Analytics program and look at the Unique Visitors for that same week that you kept track of (So, instead of looking at Unique Visitors only by that single day, you’re now looking at Unique Visitors by that whole entire week). Chances are extremely high that you will see something like this:

Unique Visitors: 37

Common Reactions:
- “Huh???”
- “Which number is correct?”
- “My Web Analytics system must be broken…”

The Solution:
None.

Explanation:
Most every Web Analytics program tabulates statistics based upon your date-range. Even though you added up 60 Unique Visitors to your website manually, your Web Analytics system won’t, when showing you the Unique Visitors for that entire week combined. The reason? Because during that week, you probably received repeat unique visitors to your website on separate days, and your Web Analytics program won’t show you those “repeat unique visitors” when looking at that week combined.

The best possible explanation available is thinking about it as a Hotel, hence the term “The Hotel Problem”. Let’s say that I’m a guest at your Hotel. I stay on Monday (1 Unique Visitor on Monday), I stay on Wednesday (1 Unique Visitor on Wednesday), and I also stay on Friday (1 Unique Visitor on Friday). If you add them up manually, that’s 3 Unique Visitors total…but there can only be one of me, so looking at that week as a whole, you’d only see 1 Unique Visitor total.

So, which one is “right”? They both are. But you’ll need to know why you’re looking at your Unique Visitors in the first place, and then go from there.

Again, I recommend checking out the Wikipedia Article on it, as it has a nice table that visually explains it the best.