I think the issue with the math is that it doesn't read well.

For example, the paragraphs around the paragraph with "compute the exact Poisson tail (or use a Chernoff bound)" and that paragraph itself could be better illustrated with lines of math instead of mostly language.

I think you do need some math if you want to approach this probabilistically, but I agree that might not be the most accessible approach, and a hard threshold calculation is more accessible and maybe just as good.