I haven't worked out how the Legendary lottery works. You need to get a minimum of merit and activity, and then it appears to go into a predefined calculation, and it seems to be a function of activity, post count, and member name.
...
https://bitcointalksearch.org/topic/special-hero-question-4594234
Or these posts:
Post #1
https://bitcointalksearch.org/topic/m.41521937
Post #2
https://bitcointalksearch.org/topic/m.35423016
Post #3
https://bitcointalksearch.org/topic/m.35865187
I can tell you nearly everything about this 'Legendary Lottery' except the 'salt' Theymos uses in the database...
This predefined calculation is not a difficult thing to understand, but you cannot do anything without the 'salt'...
I was just a few activity periods away from becoming a Legendary, before the Merit system was introduced, this is why I've read everything about it after...
The Hero to Legendary cut off was one of the most brutal to require 500 merits for the next level, so it was good that theymos provided a few more members the extra 500 merits benefit of the doubt so long as they had already reached the minimum legendary activity level by the time of the January 24, 2018 implementation date (even if they were still then hero members). On the other hand, if you were almost to the minimum activity level as a hero member but not quite there, then you did not get the extra 500 merits .. so a bit tougher to build up 500 merits.. could take a couple of years, even if you work hard... even though there are about 23 members who have already earned 500 merits, but most of those members were already well established forum members.
By the way, I think that the merit system presumes an average of about a merit per day for active members, which seems a bit of a high presumption, so maybe 1/4 to 1/2 merit per day on average would be more achievable for regularly active members?