The common statistics I've heard is 30% of household energy usage goes to keeping the hot water heater at temp. How much of your power usage is water heating?
Looked at my natural gas usage. In the summer it only used for water heating/keeping it hot at 10 therms/month. Total annual gas usage is 700+ therms. 12*10/700 = 17%. And this includes both heating and keeping it hot.
This site [1] quotes 0.0113 therms to heat a gallon of water. 120 therms / 0.0113 / 365 = 29 gals of hot water per day. This place [2] estimates 41 gallons of hot water per day used during peak demand. My estimate is that we use more for showers, less for washers/dishwashers, same for faucets. Looks like I would spend all of my BTUs on heating these 29 gals of water every day. Most likely close to single digits %% for keeping it hot.