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Here are the explanations:

Gold Badges are rare. You’ll have to actively work toward these. They’re something of an accomplishment!

Silver badges are awarded for longer term goals. Silver badges are uncommon, but definitely attainable if you’re interested.

Bronze badges are awarded for basic use of Stack Overflow. They are easy to earn.

The statistics don't really agree with that for many of the badges; for example, Booster, Epic, Generalist, and Outspoken are all awarded more rarely than the average gold badges. Booster, in particular, is rarer than all of the gold badges, except for the 'gold' version of essentially the same thing (Publicist). The biggest WTF is the that the rarest badge is a bronze one, Precognitive, that has never been awarded and I guess never will (is there any point in it existing if it can't be awarded?).

So, am I looking too deeply into this? Were they just made up by someone, when the site was being designed?

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I think Precognitive has meaning outside SO. On SO it is basically an easter egg. –  user7116 Jun 4 '11 at 15:02
    
Ah, I get it .. it's to promote Area 51, and possibly to discourage people from trying to 'collect' all the badges :D –  wim Jun 6 '11 at 2:04
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1 Answer 1

Using the Precognitive badge as example of a difficult to obtain bronze badge is not correct; the description for the badge is the following:

Followed the Area 51 proposal for this site before it entered the commitment phase

As Stack Overflow has not been created from a proposal, nobody can have that badge. It is reported for Stack Overflow because, I think, the list of badge cannot be personalized for a specific Q&A site; the only exception is Area 51 for which there are badges specific for that site. That is also the reason why Area 51 didn't have a Super-Collider Drop-down Menu: the site is using custom code, and integrating features that are available in other sites is a little more difficult for the fact there is code that needs not to be changed, on Area 51.

Golden badges are more difficult to obtain that other badges:

  • Legendary requires your reputation increased by 200, 150 times
  • Great Answer requires that your answer has been up-voted from at least 100 users
  • Publicist requires that you shared a link that has been visited from 1000 different IPs in 5 days

The difficulty of obtaining a badge, and the distribution of the badges are not correlated. Golden badges normally require more time, to get them; the distribution of the badges depends from how long the users have been using the SE site.

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"The difficulty of obtaining a badge, and the distribution of the badges are not correlated" <-- I get what you're trying to say (e.g. learning to walk is very "difficult", even though a lot of people have successfully done it), but it's still something that appears to be a statistical impossibility. Gold badges should be rarer than silver badges, and they're not. –  wim Aug 23 '11 at 3:38
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