A mean is a shape you cannot see

The star is the most-read mark on a gambling page and the least informative on its own. Sample 2 has 1,940 reviews at a mean of 4.4 - a figure consistent both with a well-run operator and with one that is loved by most of its customers and hated by a sixth of them.

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Mark stub

Reviews: 1,940
Mean: 4.4
To move to 4.3: +59 one-star
To move to 3.9: +335 one-star

the issuerThe company or body that put the mark there - a testing house, an association, a review platform or a media brand

the scopeWhat the examination covered: a process, a system, a game type, one entity or one market

the recourseWhat the issuer does when the operator fails - the question almost no mark answers

Direct answerA star rating is a summary of a distribution, and the summary throws the distribution away. In this sample 1,940 reviews give a mean of 4.4, which is equally consistent with 85% five-star and 15% one-star as with a spread of threes and fours. Read the reviews under the number, or read the shape.

The same mean, two businesses

A mean of 4.4 over 1,940 reviews is a sum of 8,536 stars. That sum can be made in very different ways, and the ways correspond to different businesses. Both columns below are the same mean over the same number of reviews.

Sample 2 - one mean, two shapesa well-run operation      spread of mostly 4s and 5s, few 1s
                           1,940 reviews, sum 8,536, mean 4.4
a polarising operation    only 5s and 1s, nothing in between
                           1,649 five-star + 291 one-star = 1,940
                           (8,245 + 291) / 1,940 = 4.4
the 1s in that shape      291 / 1,940 = 15.0% of all reviewers
what the number says      nothing that separates the two

Why the second shape matters more. A polarising operator is not a worse operator on average; it is an operator with a group of customers who had a serious problem - usually a withdrawal, a check or a closed account. The mean hides exactly the group whose experience a reader most needs to know about.

How little it takes to move a star

Because a mean is a division, adding a small number of bad reviews to a large number of good ones moves it very little - and the amount it takes is worth knowing, because it sets a floor under how seriously the star should be read.

Sample 2 - what it takes to move the starstarting point                    1,940 reviews, mean 4.4, sum 8,536

first 0.1 of a star:  +59 one-stars  ->  8,595 / 1,999 = 4.30
next  0.4 of a star: +276 one-stars  ->  8,871 / 2,275 = 3.90
   335 one-star reviews in total     ->  14.7% of 2,275 reviewers

a single one-star moves the mean by       (4.4 - x) / 1,941
the last 100 reviewers as a block        about 0.05 of a star

Three hundred and thirty-five bad reviews, on a base of nearly two thousand, is what it takes to lose half a star. That is why a star that moves is news, and why a star that has not moved for a year may simply mean nobody has written recently.

marks whose issuer examined the site - 32.8%marks that were bought - 21.9%the remainder are logos and awards, neither examined nor bought

What to read instead of the star

The distribution

How many one-star reviews, and when they were written. A cluster of one-stars in one month describes an incident; a steady trickle describes a process, and the process is usually withdrawals or verification.

The verified share

Whether the platform confirms that reviewers held accounts. An unverified review can be written by anybody, and both glowing and furious unverified reviews are worth less than a smaller number of confirmed ones.

The response pattern

Whether the operator replies, whether replies are templated, and whether the reply describes an outcome. A public trail of unresolved complaints is more informative than the mean that summarises them.

The volume against the customer base

Two hundred reviews from a customer base of a million is not a sample. The star is a summary of whoever chose to write, which is never the same population as the people who played.