Mortarboard is a bronze badge that is supposed to be reasonably easy to get if you put in the effort. Earning 200 reputation in a day once is not terribly difficult, and even easier with our upvote-happy community.
Having a single good answer on a question that happens to hit the Network Hot Questions list is often sufficient (and a good way) to hit the daily reputation cap. I have hit the cap several days in a row on other, far more mature sites that way.
Legendary is the corresponding gold badge, which requires hitting the daily reputation cap on 150 separate (UTC) days. That one, like most gold badges, is hard to get. Having earned it on our site would be even more of an achievement given that the site has only been around for about twice that length of time.
- On Worldbuilding, right now among our about 8800 users
- 122 "Mortarboard" badges have been awarded,
- with no awarded Epic (silver, 50 times hitting the cap)
- or Legendary (gold, 150 times
hitting the cap) badges,
- for an overall ratio of about 72 users to 1 Mortarboard.
- On Stack
Overflow, which is arguably
the most active site in the network, right now among its 4.3 million users
- Mortarboard has been awarded 22k times,
- Epic 529 times
- and Legendary 193 times,
- for an overall ratio of about 114 Mortarboard to 1 Legendary
and 22500 users to 1 Legendary; or about 195 users to 1 Mortarboard.
If our Mortarboard-to-Legendary ratio
was the same as that on Stack Overflow, we would have a single Legendary badge awarded by now,
but given that our site is so young, anyone having achieved that this
early is not really reasonable to expect. If our user-to-Legendary
ratio was the same, we'd have 0.4 Legendaries. (The user that had
Legendary would be at about 30k rep minimum, while the users we do
have which have the most reputation have about 23k rep currently.)
In this case, the fact that we are officially awesome does not help much.
Bottom line: Keep working on it! I don't see Mortarboard being converted into a gold badge, and even if it were to get converted into a gold badge, that is not something a site moderator can do.
If you want a gold badge, good badges to aim for would be either Marshal, Steward or Copy Editor (with good edits), as all of these help to directly improve the site experience for everyone. The corresponding bronze and silver badges are also fairly easy to get, and the gold badges aren't terribly hard to get, indicating their perceived value for the community, relative to other gold badges.