The International Olympic Committee likes to puff up its chest about its Games' influence on a host nation. It'll say that thanks to the 2008 Games in Beijing, for example, China was better situated on the path to having a more free society because of all the athletes and Western visitors whom the city hosted.
Except that wasn't always the feeling I got, even during the Games.
The hotel our group stayed in when I covered Beijing was run by the Chinese Army, and soldiers escorted us to the elevator, met us when it reached our floor and led us to our room. There seemed to be no extra freedom.
What will these Sochi Olympics go down in history for? Maybe for the palm trees visitors saw when they got off the plane in Sochi. Really? Should there be palm trees at the Winter Olympics? There were some great photos of cross-country skiers finishing their races in short sleeves. It was hot out!
I suspect the people who had the yellow water coming out of their faucets before the Games started will have in mind a different legacy than, say, the Russians who won the first-ever team figure skating event.
The U.S. hockey team's legacy, and the empty space it reserved for a medal in the luggage, will be different from the legacy Teemu Selanne and the Finnish hockey team will bring back to Finland—or the legacy both Canadian hockey teams will remember decades from now, the paired gold medals.
One suspects another legacy of these Games will be major changes for hockey. NHL general managers weren't happy about injuries and seasons disrupted. ESPN hockey analyst Barry Melrose said on SportsCenter, "I suspect this will be the last time hockey will be in the Olympics."
It's easy to understand why. The NHL teams pay a lot of money for those players. But it will be too bad. Olympic hockey is one of the best parts of the Games.
Russian president Vladimir Putin may have been proud to have spent more money than all the previous Winter Games, yet when athletes and journalists arrived, hotel rooms weren't finished and room occupants were told not to use the water that came out of the faucets.
But leave it to the athletes to leave us with pleasant memories.
Who didn't cry along with Bode Miller when he won his bronze medal, likely his final ever? Who didn't get goosebumps when Meryl Davis and Charlie White skated the long program that earned them an ice dancing gold medal?
Here's what I wish would be the legacy of these Olympics.
First, that there would be a spending cap on each and every Games forever. Whenever NBC showed the brand-new, and empty, $8 billion road climbing up from the Black Sea and Sochi to the mountains, one wondered: Will that road always be empty?
A manufactured ski resort is not what the Olympics should be about.
Once again, peace didn't break out in honor of the Olympics. As the Games progressed, so did violence in nearby Ukraine.
We've seen photos of swim stadiums and gymnastics arenas from the 2004 Athens Games that were in shambles. These sparkling new hotels and sports venues need money for upkeep. Not all the countries have that money.
Here's another legacy that would be nice to have: Let the nations' leaders stay away.
The Games aren't about them or about having them show up and start political discussions. They are about short-track speedskater Victor An and his four medals (three gold) or 18-year-old American Mikaela Shiffrin winning her first-ever skiing gold medal, likely the first of many for her.
Who would want to forget the beaming smile that covered the face of Norway's Marit Bjoergen, who won gold in the 30-kilometer mass-start cross-country event? That was her sixth Olympic gold medal and 10th overall for the 33-year-old.
That's a legacy.
Which will be the biggest part of your memories from the Sochi Games?
So is this, and it highlights how the humanity of these athletes can overcome all: How about American slopestyle skier Gus Kenworthy rescuing a family of dogs, a mother and her pups, who took up residence near the athletes village? That will stay with me.
But finally, let's hope we can forget one thing in future Games: Let's hope that every two years, we don't have to worry about whether there will be some sort of horrific terrorist attack during the two-week Olympiad.
When my Los Angeles Times team was sent off to Athens in 2004, the first Summer Games after 9/11, we had to carry gas masks and take a special class in how to hide from possible terrorist attacks. Yep, nothing happened, and somewhere I may have a gas mask stashed away.
But it always felt as if we were on the edge of something terrible happening, and that's no way to have the Olympics.
In all, these just weren't especially memorable Games.
The Dutch speedskating team will certainly be famous in the Netherlands. The Canadians will never forget their men's or women's hockey teams. It's clear the board and slope sports, the X Games sports, are here to stay.
But if your legacy is yellow water coming out of hotel water faucets, palm trees and athletes coming home with tan lines from the Winter Games, these probably weren't the best ever, no matter what IOC boss Thomas Bach said during the closing ceremony.
Diane Pucin is the Olympics lead writer for Bleacher Report. She covered eight Games for The Philadelphia Inquirer and the Los Angeles Times. You can follow her on Twitter @mepucin.