I've never heard it referred to as the law of large numbers (which I also associate with stats). But I still remember a discussion I had with an exec at a large systems company a number of years back when I was a consultant. I don't remember the exact context but it was around the potential for some new initiative or other. The gist of his remark was to the effect of "If it won't be a minimum $1 billion a year business for us, it's in the noise and uninteresting."

I think the connection is that when you're 100% of the pie, you're, by definition, average. You cannot be exceptional when you so dominate the market segment.