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Why do some sellers go for coins for tons of oil, and others go almost for nothing. Is this how the seller's fame, reputation, works ?
Most auctions include a mix of coins: some truly rare, others scarce and still others that are relatively common. Even coins of the same year and denomination can sell for dramatically different prices due to their condition or the mint at which they were struck.
For example, in May 2021, an 1895-S
Morgan dollar in XF-45 sold at auction for $1,260, in April 2021 an example graded MS-63 hammered at $5,760 and one graded MS-66 sold for $75,000 in April 2021. So, a coin from the same year, with the same denomination and same mint mark sold for as low as $1,260 and for as high as $75,000 at essentially the same time point on the calendar. Why the difference? Rarity due to grade. The coin in grades MS-65 and above is truly rare (likely 100 or fewer surviving examples per PCGS), while there are literally thousands available in circulated grades such as XF-45. So, supply and demand rules - if you want a pristine example, it's going to cost you!
An example that looks at the 1883
Morgan dollar across the mints at which is was struck while maintaining the same grade illustrates my other statement. The 1883
Morgan dollar was struck in Philadelphia, Carson City, New Orleans and San Francisco. In May 2021, a Philadelphia strike in MS-65 sold for $180. A like-graded MS-65 coin struck at Carson City (CC) sold for $528 in May, as well. A New Orleans example of the coin graded MS-65 sold in June 2021 for $228 and a San Francisco struck coin in MS-65 sold for $31,800 in September 2020. Again, the selling price differential is based on market availability for the coin from each Mint facility in the given grade.
There are other factors (e.g., eye appeal) that can cause large swings in the price paid for a coin, but most cases boil down to how "common" the coin is in the marketplace.
To your "reputation" question...
While a "no name" auction house might not get the highest premiums on the coins it sells - though I've sometimes seen the exact opposite - it is safe to say that similar results can be had across all of the major numismatic auction companies. Collectors certainly have their individual favorites, but, overall, years of data suggests reasonable parity among the top firms.
Hope that helps answer your question!
Note: All prices quoted are for PCGS-graded coins sold at auction.