How we calculate agent rankings

Alicja Pawliczak
2 min read
updated: Nov 4, 2019

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.

LiveChat agent ranking

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

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

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.

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