I recently ran the Hedgehog for a group of founders at an event, and the third circle tripped them up the way it usually does.
Most of them heard "profit per X" as a division problem. Pick a denominator, divide, track it. One KPI.
A conversation with one of the founders helped me see it from the other side. Collins's example is Southwest Airlines: profit per plane in the air. Turn it around. A plane on the ground makes no money, and the airline built its strategy around that fact. The denominator exists because planes were at the center.
So the X says what sits in the middle of your business. If you divide by clients or contracts, ask what a client stands for. One you changed something for? One who is satisfied? One who went through your process and reached a good result? Each answer points to a different strategy.
What would you put in your denominator, and what does it say about what you are building around?