Suppose that we want to know the average body-mass index (BMI) of American teenagers. Since it is extremely difficult even to count every single teenager in the country, sampling is necessary. So we try to find N typical teenagers, measure and weigh them, and then compute their average BMI with the standard statistical formula
population mean ≈ ∑ᵢ BMIᵢ / (N + 1)
Now we all learned averages in junior high. Where did the “+ 1″ come from? This is in fact a simple trick that every statistician has to learn on day 1. When we estimate a population mean from a small sample, there will inevitably be an error, typically on the high side. As a useful rule of thumb, we get a better estimate when dividing by (N + 1) instead of by N. Note that, as N gets large, N ≈ (N + 1); and so we do converge to the population mean in the limit.
A semantic dictionary is nothing more than millions of averages of term frequencies in documents, and most of them are based on only a fairly small number of occurrences of a given term. To get good results here, we have to do more than just junior high math.
Our situation is actually much more complicated than that of estimating a simple population mean, but we have to do a similar kind of data smoothing. This is all to provide you with the highest quality numbers for your web app.