I have an all-electric condo which we rent with Airbnb, it is equipped with a Stream Labs water use monitor. We made two changes that saved hot water with no complaints from the guests. I installed a different flow restrictor in the shower, down from 2.5 GPM to 1.5 and a 1.75 GPM one on the hot water line to the washing machine.
The washer defaults to warm water in the regular cycle. By adding the restrictor I changed the ratio of hot/cold while still leaving the hot water option intact. Guests use the washer a surprising amount. I presume they don’t spend much time selecting the water temperature.
The average shower, per multiple web sources, is 8 minutes. For a couple this is a monthly savings of 480 gallons of water a month. At 1.5 GPM the shower is still refreshing. I used the existing showerhead with a new restrictor. This has the added benefit of keeping me in the lower pricing tier for water.
Humans shower at a predicable temperature (105 degrees) to get the hot/cold ratio you need the average inlet (cold water) temperature. You can find the average on the web or simply measure it. Once you have that it is easy to calculate the hot water saved. Here are my cost to heat water calculations
It takes .000293 Kwh to raise 1 pound of water 1° F
A gallon of water weighs 8.34 lbs.
Average temp tap water in my area is 72 degrees
Water heater set at 120 degrees for us that is 48 degrees of rise
Efficiency of heater .95 (95%) For 2015 and later models .90 pre 2015
Ave price of electricity .105 KwH
Formula: .000293 X 8.34 X 48 X .90 X .105 + .110841 cents per gallon or .1055628 KwH per gallon or 9.473034 gallons per KwH