An amateur mathematician and tech pundit has figured out that playing the video game Angry Birds at work cost U.S. employers $1.5 billion in productivity.

Alexis Madrigal, a visiting scholar at the University of California, used as his starting point a survey that found people across the country play 200 million minutes of Angry Birds a day.

What Madrigal didn’t mention was the studies showing that playing video games at work is good for you.

The two things – wasted time and good mental health – are not mutually exclusive.

And a few commenters found gaping holes and redid the math for Madrigal’s back-of-the-envelope calculations in The Atlantic – and pointed out that they had wasted a bunch of work time recalculating his math.

Madrigal used a formula similar to the one a reputable Chicago consulting firm, Challenger, Gray and Christmas, employs each year to generate headlines based on work time squandered watching NCAA basketball tournaments.

He figured 5 per cent of Americans might be playing Angry Birds, the world’s most popular video game, at work. Then he figured $35 was the hourly pay of American smartphone owners. Voila: $1,516,666,667 down the toilet in productivity.

But where did the 200 million minutes figure come from? Digital market researchers at Ask Your Target Market Research had whipped together an infographic on Angry Birds and the global addiction it has inspired. The data were based on AYTM interviews with 500 adults. Half said playing the game relaxed them, improved their mood and gave them joy.

Which could be said to corroborate a 2009 study by Leonard Reinecke of the University of Hamburg published in CyberPsychology and Behaviour.

Reinecke found that “individuals with higher levels of work-related fatigue reported stronger recovery experience during gameplay.”

He also found that “persons receiving less social support from colleagues and supervisors played games at work more frequently.”

Of the 833 people who told the German researcher they played online games at work, one-quarter said they did it daily or several times a week.

No less a collective of innovative tall foreheads than the TED conference last year invited Jane McGonigal to present her findings that video gamers will save the world, as outlined in her book Reality is Broken: Why Games Make Us Better and How They Can Change the World.

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McGonigal’s theory is that games such as World of Warcraft teach skills vital to the 21st century.

Then again, McGonigal is a video-game designer.