The problem is that at 50 my furnace runs like 3 times a day because the house is built to be comfy down to -30, probably much worse (since it did OK at -20 last week). So you end up saving 25% of very little.
This mathematical model would work for a poorly insulated house in an area that never gets cold. So if in Atlanta the furnace is struggling at 50F outside, then this would mathematically work out. The problem of course is total annual heating bills in Atlanta probably aren't very impressive, so saving even 10% on them still wouldn't amount to much.
The broader point is that the average heating season temperature at the location is more interesting than the coldest temperature experienced during a given decade.
That still ends up being something like (1-8/50)/100 for a lot of people, so an easy opportunity for 15% during away times (and 70->62 isn't an absurd night setting...).
This mathematical model would work for a poorly insulated house in an area that never gets cold. So if in Atlanta the furnace is struggling at 50F outside, then this would mathematically work out. The problem of course is total annual heating bills in Atlanta probably aren't very impressive, so saving even 10% on them still wouldn't amount to much.