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I tried getting help through live chat with this matter but got no luck. My shop's rating has been 4.8 for most of last week - yet the stars on my page and everywhere next to my items on Etsy show barely 4.5 stars right now, and have been switching between 5 full stars and 4.5. Sometimes I log on and it's 5 full stars and sometimes it's 4.5. I would think at 4.8 it should be 5 full stars as that is also the minimum for star sellers. It makes no sense for the stars then suggesting that this shop is 4.5 stars.
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They are 2 different metrics.
The star rating that shows on your shop front page is the average of all reviews you have received for the past 12 months. That rating can change as reviews from over 12 months ago fall off the calculation and new ones are added.
The Star Seller rating is just for the star seller program and only for the current or previous 3 month review period.
Again, 2 different metrics and calculations for 2 different things and time periods.

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Thank you for the helpful answers. It's strange that some Etsy customer service agents don't know this as it's important to explain the discrepancy between what the account holder sees. Now I understand.

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They are 2 different metrics.
The star rating that shows on your shop front page is the average of all reviews you have received for the past 12 months. That rating can change as reviews from over 12 months ago fall off the calculation and new ones are added.
The Star Seller rating is just for the star seller program and only for the current or previous 3 month review period.
Again, 2 different metrics and calculations for 2 different things and time periods.

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Re: Star rating appearance is different from score
Your current Star Seller score is based on May, June & July; your visible review score is based on the last 12 months. As old feedback drops off of the 12 months and new gets added, that score will go up and down. If you lose a 5 star and don't gain a new one, it goes down, for example.
Your source code says that your current score is 4.7487; when it goes to 4.75 it will display 5 stars.

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Re: Star rating appearance is different from score
Ooh, good news! You got a 1-star on Aug 6, 2021, so once that drops off you will go up again. It should be back to 5 tomorrow.

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Thank you for the helpful answers. It's strange that some Etsy customer service agents don't know this as it's important to explain the discrepancy between what the account holder sees. Now I understand.

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Re: Star rating appearance is different from score
And it's an uphill battle for the ratings, there are the customers who get frustrated with the technical difficulties of downloading PDF files to their devices, those whose projects don't end up looking like the photos (mostly beginners) and the occasional "review bomber" targeting my best selling products who never leave comments on what they disliked.