The variables are (W)eather, (D)ebt, (d) monthly salary, (T)ime since Christmas, time since failure to (Q)uit a bad habit, low (M)otivational levels and (NA), the need to take action.
"All these elements converge to make for a very unhappy day on the 23rd of January," says Arnall.
He said his formula holds true for the United States as well as Britain, except perhaps in places such as Texas, Florida, or California where better weather could help lift the day's depressing mood.
But Arnall said there are ways to beat the late January blues. Instead of trying to turn over the same old new leaf every New Year's Day, he suggested, why not resolve to make a change in a different month, such as March or April?
"I also advise people to do the unusual every January," he said. "Go for a walk in the woods or just get out and about."
Arnall suggested groups of friends could throw parties to celebrate the 23rd, since being around people you like can boost your spirits. People also could resolve to make a budget for their holiday spending next December.
Leslie Godwin, a Los Angeles-based author and life transition coach, agreed that January is a tough time of the year. She encouraged people to exercise, whether the weather's bad or not.
"Exercise releases hormones that give us a sense of well-being, and it should be seen as an antidote to feeling down or blue," she said.