Ever suffered from a limp wrist, or been on the receiving end of a painfully iron grip? Car manufacturer Chevrolet know all about the importance of a good handshake, which is why they’ve developed a complex mathematical equation for their new staff training guide, as that well known science journal the Daily Mail reports.

It’s been a while since I covered this kind of dodgy maths, so let’s go over the basics. “Formula for” stories are seen by PR agencies as a great way to get free press coverage for whatever product they are shilling because the equations can be dressed up as real research. Attaching a “Dr” or “Prof” to your news story is a great way to gain legitimacy, and the media lap it up as another example of what those crazy boffins are up to.

While this is all great for the PR agencies and their clients, it’s terrible for science. These formulas tend to be based on extremely dodgy assumptions and contain variables which can’t be objectively measured. What’s worse, even a simple mathematical analysis usually reveals problems such as division by zero, which can lead to things like cold and lumpy but infinitely perfect pancakes.

With these problems in mind, let’s take a look at the formula for the perfect handshake. It was created by Geoff Beattie, head of Psychological Sciences at the University of Manchester, and is detailed in this the press release:

(vi + t + te)² + {(4<c>2)(4<du>2)}²

I’ve broken it over two lines because the thing is so long, and I think that square root is meant to cover the entire equation, not just the first term, but the press release isn’t very clear. We’ve also got a definition for the many variables, along with what I assume is their optimal values:

(e) is eye contact (1=none; 5=direct) 5;

(ve) is verbal greeting (1=totally inappropriate; 5=totally appropriate) 5;

(d) is Duchenne smile – smiling in eyes and mouth, plus symmetry on both sides of face, and slower offset (1=totally non-Duchenne smile (false smile); 5=totally Duchenne) 5;

(cg) completeness of grip (1=very incomplete; 5=full) 5;

(dr) is dryness of hand (1=damp; 5=dry) 4;

(s) is strength (1= weak; 5=strong) 3;

(p) is position of hand (1=back towards own body; 5=other person’s bodily zone) 3;

(vi) is vigour (1=too low/too high; 5=mid) 3;

(t) is temperature of hands (1=too cold/too hot; 5=mid) 3;

(te) is texture of hands (5=mid; 1=too rough/too smooth) 3;

(c) is control (1=low; 5=high) 3;

(du) is duration (1= brief; 5=long) 3.

Both the formula and its variables are looking really dodgy. I’ve literally no idea what terms like {(4<c>2)(4<du>2)}² are meant to mean. I can only think that the angular brackets denote some kind of average, but then why do they only apply to some of the variables? Are those 2s actually meant to be ²? In which case you can rewrite the whole term as (2<c><du>)^{4}, which is at least a little bit simpler.

I also take issue with using two letters to stand in for one variable, because they can be confused for two separate variables multiplied together. Measuring “verbal greeting” and “vigour” doesn’t mean that both of your variables have to start with a v – real mathematical equations make extensive use of Greek letters in an effort to solve this exact problem. But even if this equation was beautifully formatted, it would still be rubbish.

All the measurements are completely subjective, and the scales of 1 to 5 indicate the data behind the equation was probably collected from a survey. This even includes variables such as temperature, which can easily be measured scientifically. Remember, subjective measurements are one of the hallmarks of a “formula for”.

I emailed Beattie yesterday to ask how the formula was created, but as he is yet to reply I can only speculate. I think what he has done is ask people a bunch of questions about handshakes, and then tried to fit their answers to some kind of least-squares model, as indicated by the squares and square root in the formula. This method gives you a great equation for “explaining” the data you’ve gathered, but doesn’t necessarily tell you anything about the phenomena you’re examining.

If that is the case, I still don’t understand how the formula is meant to work. You’d expect that the perfect handshake would have a maximum value of PH, and since there is no division or subtraction involve, that just means slotting in the maximum values for all your variables. The optimal values in the press release include a few 3s and 4s though, so PH isn’t going to be maximum. Hmm.

As with all “formula for” stories the maths behind the perfect handshake formula just doesn’t add up, yet it’s being interpreted as a serious piece of research. Comments on the Mail story such as these two show just how much damage this can do to people’s impressions of science:

“So, most of the country is out of work desperately trying to survive and these idiots are getting paid, what – to study handshakes? Sack these people immediately!”

How much time did the nutty professor spend on this useless bit of information?

Mathematical models and equations are a fantastical tool for understanding the natural world around us, but they have to be based on sound assumptions and decent science – things that “formula for” stories such as this almost invariably lack.