Blue Monday, which falls on the third Monday of January, is allegedly the most depressing day of the year. Understandably, tightened purse strings following the festive splurge, time passed since Christmas and failed new year resolutions is not a combination for happiness – but why is the third Monday in January apparently the worst day of the year?

The theory was first published in 2005 a press released under the name of Cliff Arnall, who at the time was a tutor at the Centre for Lifelong Learning – a Further Education centre associated with Cardiff University. Later, however, the Guardian printed a statement from the university distancing itself from the psychology professor: "Cardiff University asked us to point out that Cliff Arnall... was a former part-time tutor at the university but left in February."

It turns out the concept started as a publicity campaign by travel agents Sky Travel to sell last-minute holidays. So while the January blues is nothing new, Blue Monday is largely considered a PR stunt backed by pseudoscience.

But, according to Arnall, the date can be calculated using several factors. Debt level, pay time since Christmas, the abandon of new year's resolutions, low motivation levels and cold weather are all to blame for the most depressing day of the year.

According to a press release by a mental health organisation Beat Blue Monday, there is a formula to calculate the day – although units of measurement are not defined. It is broken down as follows: W = weather, D = debt, d = monthly salary, M = low motivational levels, Na = the feeling of a need to take action. The formula is {[W + (D-d)] x T^Q} ÷ [M x N_a].

Most people are unconvinced there is one specific day for misery, however. In 2011, British physician and journalist Ben Goldacre said Blue Monday could lead to serious issues concerning the perception of mental health: "It's also worth thinking about the wider consequences when we indulge, deploy, and therefore normalise, nonsense... This does not feel like a constructive contribution to stigma, or the perception of serious mental illnesses."

Writing in the Guardian in 2014, Michael Marshall said: "Keener observers have spotted that today isn't actually the most depressing day of the year at all, but merely the day a particular travel company wanted to nudge you into booking a winter blues-alleviating holiday, hiring a media-friendly scientist-type along the way to add a veil of legitimacy to their advert."