On constantly only works out cheaper if you have your heating on a lot usually. We're talking hours and hours every day. I did this as an experiment one year - a month of constantly on but adjusting thermostats etc, and a month just putting it on when we actually needed it on. We definitely used fewer gas units just putting it on as needed. But then we don't tend to use our heating much - unless it's really a harsh winter it's usually only on an hour or so in the morning and a couple/few hours at night.
I have done a bit of research into this and found very mixed opinions. Many in the industry say it is a misconception that it is cheaper to leave it on all the time, but some disagreed with this.
Try the experiment, it's easy to do!