This doesn’t apply just to collectors who can afford 1804 dollars and 1913 Liberty Head nickels. It applies to all collectors.
Most collectors are probably familiar with the halo effect at name auctions. Otherwise common coins go for more money than they are worth just because the coins have a famous collection on their pedigree.
At the other end of the spectrum, dealers will look at Lincoln sets or other more commonly collected coins to see if the keys are present. If they aren’t, the set is basically evaluated at face value. This doesn’t mean that some of the other coins might not have a little bit more value, it simply means that the would-be buyer doesn’t have the time or inclination to wade through a set of common coins to wring out the last few dollars.
The most important reason that complete sets do better is that to assemble them, a collector has to be focused and consistent. Sets need to be complete and they need to be comprised of a group of coins that are matched by grade.
To do this, a collector needs to shut out the distractions and focus on his task. Collectors who don’t have the discipline imposed by a set, might make a killing buying the first 2007 First Spouse coins from the Mint, but then they might guess wrong and buy some other item that they thought should have been hot. They waste a great deal of time and money chasing fads.
Think of the fad items you might have in your collection. I have some extra Statue of Liberty uncirculated half dollars. The mintage seemed low at the time. Nobody else in my lifetime will make that assessment. While I have several extra Buffalo commemorative silver dollars, I also have some extra West Points to offset them.
If I were building a complete set of modern commemoratives, there would be a reason to own these. Because I am not, they are simply unfocused, undisciplined purchases that distract me from more constructive buys.
Can I prove any of this with statistics? No. Collectors love their privacy too much to leave statistical evidence for me to look at. I look forward to comments from others on this topic.