So here's the quandry--
We've got our house with a long distance of water pipe between the water heater and the faucet. Each morning, we make ourselves some tea, and need to boil some water to do so.
It's nice to simply heat hot water from the water heater instead of boiling cold water from the tap. But in order to get the hot water, we need to run the tap for a couple of minutes, and all that cold water just goes down the drain, wasting all the energy it took to pump it there to the tap in the first place.
We know that providing water and sewage treatment has an energy cost.
We also know that water heating itself is an energy cost.
Depending on the efficiency of the water heater-- between 30-60 gallons of water down the drain to be equivalent of the water heating energy needed to raise the water temperature to 130 (equivalent to the output of the water heater).
Note: You may notice that I'm implicitly assuming that the heat from the water heater would be otherwise "wasted" which of course, it isn't all. So, it's a bit of a simplistic calculation. At least it gives a little order of magnitude.