At what point do you hire someone just to keep track of things, versus fix the process instead?

I keep meeting people running one or two service based businesses who reach the same fork in the road. Hire an ops person to catch what is slipping, or find a better way to catch it themselves first. I went the second route out of necessity, cash was tight and a hire felt too early. Curious where others draw that line, is it revenue, headcount, or just how much you personally cannot hold in your head anymore?