Here are numbers from the last time I turned my tub down for a four day absence:
Starting at 104F (weather in mid 40's with light and variable winds)
Turned set point down to minimum (80F)
When I got back, 96 hours later, my 215 gallon tub was at 87F
That works out to about 36 kWh saved
Heating the tub back up took about 8 hours, at 1500W, that is 12 kWh.
I pay 8.5 cents per kWh, so that saved me $2.04. That number only increases the more days the tub is left without heat input. At some point the thermostat would kick in at 80F to maintain that, but again, less heat is lost to the environment at lower temperature differences. Also, the 24hr circulation pump throws this off a bit... That is 70W, but that also ultimately ended up as waste heat in the water. In the summer, HS tubs have a summer mode which disables the circ pump for 8 hours a day, allowing me to save a nickel a day.
These may not sound like impressive savings, but in this modern world we have lots of little things that nickel and dime us and add up to hundreds, if not thousands of dollars a year. I make the relatively small effort to reduce recurring expenses like that when it doesn't impact me much... $2 saved say 25 times a year is $50. Easy. That is a nice dinner out!
I should add a couple, er, number of things here:
1) when in doubt, always follow the recommendations in your tub's manual
2) your mileage may vary... I have a very well insulated tub, moderate weather, and inexpensive electric rates.
3) I use a conversion factor of 2.44 to derive Watt-hours saved per gallon per degree of temperature drop (Fahrenheit) per day. Multiply times 1000 for kWh. I came up with that one day crunching number of BTU and raising temperature of one pound of water, etc, etc. So far my logs pass the sanity test and match up with what I observe on my power usage meter.
4) Check out WattVision and The Energy Detective for ways your can monitor your home electricity consumption. I use WattVision which seems to work well enough for this purpose. TED looks more sophisticated, but required space in the panel for installation, which I don't have enough of. Even cheaper and just as effective is to learn to read your electric meter and track kWh over time. You can do pretty darn well with just keeping a simple log or spreadsheet.
5) I could be wrong. Wear safety glasses.
[edited to correct units]