## Wednesday, July 15, 2009

### Peak Posting

As is true for most things there is a point where quality and quantity of blog posts combine to make for an optimum flow of readers. In general you need volume of posts in order to draw readers but you need quality of posts in order to make them come back. But since my posts tend to have neither quality nor quantity I suppose this question is (like most everything else on this blog) purely academic.

The simplest model I can think up is that you have a quality index q between 0 and 1 which represents the likely hood of someone who stumbles upon the blog to return in the future and a quantity index p between 0 and infinity which represents how many posts you make per unit time and should sort of be vaguely help determine the number of readers you pull with those posts. I would say that probably the number of readers you pull varies something like log(p+1) Let us furthermore assume that a person has a total amount of time that they can devote to the blog and therefore the total quality of all the posts is constant so Q_total = p*q the last part of our model is how to use these factors to model reader flow. Since we attract C*log(p+1) random readers in a unit time and of those readers q of them come back we have a recurrence relation. The expected number of readers R_t+1 = qR_t + C*log(p+1). Letting L = C*log(p+1) we have R_t+1 = qR_t + L Now suppose there is a limiting number R_l = qR_l + L Solving we get R_l = L/(1-q) which is because the amount is a geometric series in q (I thought it was should have just trusted myself). So if we take the time limit we see that to maximize the number of readers that we have over the long term we should make our quality as high as possible at the cost of quantity.

Of course this was based on the assumption that quality of a post was directly proportional to the amount of time spent on it when in reality I suppose the quality is more like the logarithm of the amount of time you spend on it. Sure you can always make a post better but only perhaps if you are willing to spend some fraction again of all the time you have spent on it up to this point.

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