# Geometric mean and sales performance ranking

When in school, statistics is easily the most mind-numbing subject we had to learn. Remember being bored to tears while the professor gleefully demonstrated on the blackboard how to calculate a “geometric mean?” You might have asked yourself, “Why do I need to learn this?” For many of us, finding the average of a set of numbers through the n-th root of their product was nothing more than an ostentatious display of math skills that serves no practical purpose.

This all came back to us on a project we did for a medical device company, which tasked us to come up with a performance ranking mechanism for their field sales representatives. Our initial analysis showed that some reps’ quota attainment fluctuated dramatically year-to-year. A rep who attained 140% of quota in 2010 may have ended up achieving only 60% in 2011. Even though that rep’s two-year average is 100%, he performed less consistently than a rep who attained 100% in both years. And consistency counts!

At this point, most consultants would have stopped thinking and started ranking reps by arithmetic averages, using standard deviation as a tie-breaker. We went one step further to find an intuitive metric that combines average and consistency into one – by using the geometric mean. Looking at our hypothetical rep above, we see that the geometric mean of 140% and 60% is 91.7%, while the geometric mean of 100% and 100% is, still, 100%.

In the end, we were able to provide a more scientific measure for sales reps multi-year performance, and therefore provide a more meaningful recommendation to our client. Obviously, the selection of statistical tools is a tiny portion of any AGI consulting project. Taking the time to pick the most suitable measure, though, gives us the most intuitive and powerful story to tell a VP of Sales. That’s what we strive for.