Amazon.com Inc., far from dominating the retail sector, is actually the weakest of the big U.S. players based on operating results, Moody’s Investors Service said Wednesday.

The e-commerce giant is the subject of a number of myths regarding its size and clout that mask the reality of its position compared with rivals like Wal-Mart Stores Inc. WMT, +0.90% and Costco Wholesale Corp. COST, +1.43% , according to Charlie O’Shea, Moody’s vice president and lead retail analyst.

Amazon’s stock AMZN, +5.69% has outperformed rivals, but it’s mostly based on the company’s growth story, and particularly the success of its cloud business, Amazon Web Services, O’Shea wrote in a new report.

“That potential is overshadowing the superior real-time operating performance of Amazon’s key retail competitors,” O’Shea wrote. “The emphasis on stock performance is, in our view, forcing brick-and-mortar competitors toward managing more irrationally for short-term performance just when they’re confronting secular change.”

He cited as an example Staples Inc.’s US:SPLS decision to sell itself to private-equity firm Sycamore Partners as a way to boost shareholder value.

The perception that Amazon is poised to take over the grocery business via its acquisition of Whole Foods, which closed this week, is another myth, said O’Shea.

“Online sales still account for only about 10% of overall U.S. retail sales, with a much lower percentage in the grocery segment, leaving the big brick-and-mortar retailers, led by Walmart, still really formidable competitors in the industry,” he wrote.

Estimates for the Amazon Prime membership base are also wildly inflated, O’Shea said, with some pundits betting the figure is as high as 85 million. Amazon itself has never provided a number, other than to say it is in the tens of millions.

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Moody’s calculations, which are based on demographic information, suggest Prime membership is closer to 50 million, which compares with Costco’s total membership of 86.7 million as of the end of its fiscal year in August 2016, and its paid membership of 47.6 million.

Amazon is also far from controlling U.S. food sales, which come to about $800 billion a year. Wal-Mart Stores Inc. WMT, +0.90% alone sells more than $200 billion in food, or over 25% of the total, according to O’Shea.

Kroger Co. KR, +0.83% sells about $130 billion in food, while Safeway parent Albertson’s sells food worth about $60 billion annually and Costco sells about $50 billion.

“We believe it’s a big stretch to say Amazon will dominate the U.S. food retail business in the next two years,” O’Shea said. “Even with Whole Foods in its basket, its food sales still amount to less than $20 billion annually.”

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The perception that as soon as Amazon enters a product category, it immediately wins is also flawed, said the analyst. While Amazon is clearly disruptive, it does not dominate any category in which it operates. In consumer electronics, for example, Amazon has about a third of the share of Best Buy Co. Inc. BBY, +1.56% .

“When it announced that it would enter services, we think it received way more attention than it deserved,” said O’Shea. “Best Buy has Geek Squad embedded with its customers, and 20,000 employees will be difficult to tackle, especially when considering the added advantage of the store base to support this effort.”

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Amazon is unlikely to become a player in appliances with the addition of the Kenmore brand, despite the excitement that news of its cooperation with Sears Holdings Inc. US:SHLD initially raised. “We think this is largely a non-event and looks like any other third-party relationship,” said the report. “If anything, we think that struggling Sears has entered this agreement to help with its sagging public-relations image.”