As you might have noticed we don’t use a simple average rating formula (so avg=positive ratings / total ratings) to rank agents in the chat and ticket satisfaction reports.
Instead, we use Wilson score, which lets us calculate the probability of getting a positive rating, taking into account both the number of positive and negative ratings in relation to all ratings.
Why we use Wilson score![Link icon](data:image/svg+xml;base64,PHN2ZyBmaWxsPSJub25lIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHZpZXdCb3g9IjAgMCAyNCAyNCI+CiAgPHBhdGggZD0iTTEwIDE0YTMuNSAzLjUgMCAwMDUgMGw0LTRhMy41MzYgMy41MzYgMCAwMC01LTVsLS41LjUiIHN0cm9rZT0iIzAwMCIgc3Ryb2tlLXdpZHRoPSIyIiBzdHJva2UtbGluZWNhcD0icm91bmQiIHN0cm9rZS1saW5lam9pbj0icm91bmQiLz4KICA8cGF0aCBkPSJNMTQgMTBhMy41IDMuNSAwIDAwLTUgMGwtNCA0YTMuNTM1IDMuNTM1IDAgMTA1IDVsLjUtLjUiIHN0cm9rZT0iIzAwMCIgc3Ryb2tlLXdpZHRoPSIyIiBzdHJva2UtbGluZWNhcD0icm91bmQiIHN0cm9rZS1saW5lam9pbj0icm91bmQiLz4KPC9zdmc+Cg==)
Still not sure why we chose some complicated formula instead of the average?
Let’s look at an example:
Jake has 2 positive ratings and 0 negative ratings, while Anna has 10 positive ratings and 2 negative ratings. Who do you think should be ranked first? I bet you said Anna.
If we used the average to calculate rankings, it would be Jake that is ranked higher than Anna. Because 100% of his ratings are positive in comparison to Anna’s 83%.
That’s why we use Wilson score (you can see the exact formula for calculating it below). It calculates the probability of getting a positive rating: which is 52% for Anna and 33% for Jake. Meaning that Anna is ranked higher than Jake. Which makes things fair.
Calculate Wilson score for your agents![Link icon](data:image/svg+xml;base64,PHN2ZyBmaWxsPSJub25lIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHZpZXdCb3g9IjAgMCAyNCAyNCI+CiAgPHBhdGggZD0iTTEwIDE0YTMuNSAzLjUgMCAwMDUgMGw0LTRhMy41MzYgMy41MzYgMCAwMC01LTVsLS41LjUiIHN0cm9rZT0iIzAwMCIgc3Ryb2tlLXdpZHRoPSIyIiBzdHJva2UtbGluZWNhcD0icm91bmQiIHN0cm9rZS1saW5lam9pbj0icm91bmQiLz4KICA8cGF0aCBkPSJNMTQgMTBhMy41IDMuNSAwIDAwLTUgMGwtNCA0YTMuNTM1IDMuNTM1IDAgMTA1IDVsLjUtLjUiIHN0cm9rZT0iIzAwMCIgc3Ryb2tlLXdpZHRoPSIyIiBzdHJva2UtbGluZWNhcD0icm91bmQiIHN0cm9rZS1saW5lam9pbj0icm91bmQiLz4KPC9zdmc+Cg==)
Have some spare time on your hands? Check if Wilson score actually works. Here is the formula we use to calculate it:
Constants:
Z=2.69 (confidence level)
Pre-calculated values:
n=number of positive ratings + number of negative ratings (total number of ratings)
p=number of positive ratings / n (probability of a positive rating)
zznf=Z Z/(4 n) (constant for keeping the formula short)
Formula:
Wilson score = (p + 2 zzfn - Z √ ((zzfn / n + p (1 - p)) / n)) / (1 + 4 zzfn)
And an example:
Jake: 2 positive, 0 negative
Anna: 10 positive, 2 negative
Wilson score for each agent using the formula provided above:
Anna: 0.5194200469 (52%)
Jake: 0.3312764381 (33%)
The higher the score, the higher the probability of getting a positive rating. Which translates to a higher ranking of the agent.
Don’t have time to do the maths by yourself? Not a problem. We prepared a Google Sheets document, that you can copy and fill in with your agents’ ratings. The score will be calculated automatically.