To understand Ball’s accomplishments, you might start with the problem of counting rattlesnakes.And then he goes on to describe how one can estimate how many rattlesnakes are in a population by marking ones that you find and then counting how many times you refind one you have marked previously. This is a method generally known as mark-release-recapture (e.g., see the Wikipedia entry here, which seems OK but I have not read too carefully).
Apparently, Ball uses a similar type of statistic to estimate the number of murders and/or deaths in particular areas, by looking for overlap among different reports of deaths.
What you say does this have to do with microbial ecology? Well, everything. Because one of the most common methods for estimating the number of microbial species in a sample is to use a gene survey method where one isolates DNA from environmental samples and then one looks in the DNA for multiple versions of a gene found in all species (the gene most commonly used is known as small subunit rRNA). The gene survey method is needed because appearance is not a robust method of identifying microbial species.
From the gene sampling data, one then compares each version of the gene to the others and counts how many times one sees the same form of the gene (suggesting that one has found two different cells of the same species). If one keeps seeing the same forms of the gene even with only a few samples, one would estimate there are few species in the sample. If one keeps seeing different forms of the gene, one would estimate there are many species in the sample.
Things that seem to be hidden - be the murders or populations of rattlesnakes or microbes - can still be studied with what the Times perfectly refers to as
"A statistical sleight of hand"