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) · b^{t – 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 – b^{1/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:

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):

**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 – b^{1/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.