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Mathematics of Blog Traffic: Model and Tips for High Traffic

Over the last few days I finally did what I long had planned and worked out a mathematical model for blog traffic. Here are the results. First we’ll take a look at the most general form and then use it to derive a practical, easily applicable formula.

We need some quantities as inputs. The time (in days), starting from the first blog entry, is denoted by t. We number the blog posts with the variable k. So k = 1 refers to the first post published, k = 2 to the second, etc … We’ll refer to the day on which entry k is published by t(k).

The initial number of visits entry k draws from the feed is symbolized by i(k), the average number of views per day entry k draws from search engines by s(k). Assuming that the number of feed views declines exponentially for each article with a factor b (my observations put the value for this at around 0.4 – 0.6), this is the number of views V the blog receives on day t:

V(t) = Σ[k] ( s(k) + i(k) · bt – t(k))

Σ[k] means that we sum over all k. This is the most general form. For it to be of any practical use, we need to make simplifying assumptions. We assume that the entries are published at a constant frequency f (entries per day) and that each article has the same popularity, that is:

i(k) = i = const.
s(k) = s = const.

After a long calculation you can arrive at this formula. It provides the expected number of daily views given that the above assumptions hold true and that the blog consists of n entries in total:

V = s · n + i / ( 1 – b1/f )

Note that according to this formula, blog traffic increases linearly with the number of entries published. Let’s apply the formula. Assume we publish articles at a frequency f = 1 per day and they draw i = 5 views on the first day from the feed and s = 0.1 views per day from search engines. With b = 0.5, this leads to:

V = 0.1 · n + 10

So once we gathered n = 20 entries with this setup, we can expect V = 12 views per day, at n = 40 entries this grows to V = 14 views per day, etc … The theoretical growth of this blog with number of entries is shown below:

viewsentries

How does the frequency at which entries are being published affect the number of views? You can see this dependency in the graph below (I set n = 40):

viewsfrequency

The formula is very clear about what to do for higher traffic: get more attention in the feed (good titles, good tagging and a large number of followers all lead to high i and possibly reduced b), optimize the entries for search engines (high s), publish at high frequency (obviously high f) and do this for a long time (high n).

We’ll draw two more conclusions. As you can see the formula neatly separates the search engine traffic (left term) and feed traffic (right term). And while the feed traffic reaches a constant level after a while of constant publishing, it is the search engine traffic that keeps on growing. At a critical number of entries N, the search engine traffic will overtake the feed traffic:

N = i / ( s · ( 1 – b1/f ) )

In the above blog setup, this happens at N = 100 entries. At this point both the search engines as well as the feed will provide 10 views per day.

Here’s one more conclusion: the daily increase in the average number of views is just the product of the daily search engine views per entry s and the publishing frequency f:

V / t = s · f

Thus, our example blog will experience an increase of 0.1 · 1 = 0.1 views per day or 1 additional view per 10 days. If we publish entries at twice the frequency, the blog would grow with 0.1 · 2 = 0.2 views per day or 1 additional view every 5 days.

Increase Views per Visit by Linking Within your Blog

One of the most basic and useful performance indicator for blogs is the average number of views per visit. If it is high, that means visitors stick around to explore the blog after reading a post. They value the blog for being well-written and informative. But in the fast paced, content saturated online world, achieving a lot of views per visit is not easy.

You can help out a little by making exploring your blog easier for readers. A good way to do this is to link within your blog, that is, to provide internal links. Keep in mind though that random links won’t help much. If you link one of your blog post to another, they should be connected in a meaningful way, for example by covering the same topic or giving relevant additional information to what a visitor just read.

Being mathematically curious, I wanted to find a way to judge what impact such internal links have on the overall views per visit. Assume you start with no internal links and observe a current number views per visitor of x. Now you add n internal links in your blog, which has in total a number of m entries. Given that the probability for a visitor to make use of an internal link is p, what will the overall number of views per visit change to? Yesterday night I derived a formula for that:

x’ = x + (n / m) · (1 / (1-p) – 1)

For example, my blog (which has as of now very few internal links) has an average of x = 2.3 views per visit and m = 42 entries. If I were to add n = 30 internal links and assuming a reader makes use of an internal link with the probability p = 20 % = 0.2, this should theoretically change into:

x’ = 2.3 + (30 / 42) · (1 / 0.8 – 1) = 2.5 views per visit

A solid 9 % increase in views per visit and this just by providing visitors a simple way to explore. So make sure to go over your blog and connect articles that are relevant to each other. The higher the relevancy of the links, the higher the probability that readers will end up using them. For example, if I only added n = 10 internal links instead of thirty, but had them at such a level of relevancy that the probability of them being used increases to p = 40 % = 0.4, I would end up with the same overall views per visit:

x’ = 2.3 + (10 / 42) · (1 / 0.6 – 1) = 2.5 views per visit

So it’s about relevancy as much as it is about amount. And in the spirit of not spamming, I’d prefer adding a few high-relevancy internal links that a lot low-relevancy ones.

If you’d like to know more on how to optimize your blog, check out: Setting the Order for your WordPress Blog Posts and Keywords: How To Use Them Properly On a Website or Blog.