It has taken several weeks of searching, but I think I’ve figured out the mysteries of the Steemit reputation score, that little number that appears next to your username. The objective of this post is to explain how the reputation score system works in plain English.
There are several posts and FAQ pages that explain the math behind converting your raw reputation into the reputation score next to your name. It is a logarithmic formula that converts any positive raw reputation into a score of at least 25 and any negative raw reputation into a score of less than 25. There is no real limit on the maximum or minimum on your reputation, but as your reputation increases it become increasingly difficult to rise to the next level.
That is all just great, but where does the raw reputation score come from?
It took quite a bit of searching to find the answer to this question. My first clue came from a helpful post by 
I’m not much of a programmer, but I was able to figure out how the relevant bit of code works.
When you are the author of a post and someone gives you an upvote, your reputation increases by an amount that is proportional to the voter’s voting percentage times their Steem Power (the product is called rshares). That is it -- in all of the code that makes Steemit work, there appears to be only one line that can increase your reputation score and it just adds the rshares value of an upvote to your raw reputation.
There are a few rules associated with reputation scores that I’ll cover in a moment, but the most important rule is:
The only way to increase your reputation is receiving an upvote on your post or comment!
The number of followers you have and the number of people you follow does not have a direct effect on your reputation. In my searching related to reputation calculations I came across some misinformation about what your reputation means and how to improve it. One common misconception had to do with the number of followers for an account or the ratio of followers to followed accounts. Having few followers or following a lot of accounts will not harm your reputation. Of course, having a large number of followers means that there are more people reading and upvoting your posts, but it is the upvoting that improves your score, not the following. You should follow all of the users who post content that you find interesting. It won't improve your reputation to unfollow a bunch accounts, even if they have low reputations.
Upvoting a user with a low reputation will not lower your own reputation. This is an important point. A low reputation will not spread like cooties. If a new user with a low reputation posts something good, your upvote will boost the author’s reputation right away. They are likely to appreciate the attention and will follow you and upvote your posts, which might have a small benefit for you in the future. There is certainly no harm and in most cases it is a win-win situation.
Upvoting a popular post can earn you curation rewards, but it won’t increase your reputation. (Please check me on this one and let me know if I’m wrong. Follow the Github link above and search for the line “r.reputation += (cv->rshares >> 6).”) The only event that can trigger a change in your reputation is a voting event and the only reputation that changes is the author’s reputation, not the voter’s. This is sort of counterintuitive because most of the time the activities that earn monetary rewards also increase reputation. I guess you could make an new account, load it up with Steem Power, and only use it to vote without ever posting or commenting. Nobody could give you an upvote and your reputation would remain at 25, but you could still earn curation rewards from voting.
Some more rules associated with reputation scores
votes made after the payout deadline have no effect on the author’s reputation
votes from accounts with a reputation less than 25 have no effect, regardless of how much Steem Power they have
upvotes will increase the author’s reputation in proportion to the voter’s Steem Power, not the voter’s reputation
upvotes from accounts with lower reputation will increase your reputation, but only users with a higher reputation can reduce your reputation with a downvote(flag)
These rules were put it place to ensure that flagging another user must always be done with caution. If two users get into a flagging war, the one with the higher reputation is completely immune will be able to downvote his/her opponent into oblivion. The loser of a flagging war can delegate Steem Power to a new account and pick another fight with the victor, but the new account will start with a reputation of 25 and will be just a single downvote away from having no effect.
On the other hand, a wealthy participant can buy a huge amount of Steem Power in a new account and use it to upvote good content with tremendous effect. The voting and flagging system is very asymmetric that way. New users with lots of money can generate bit benefits for other users, but if they get out of line just about anyone can downvote them away.
To put it another way, you can buy as much voting power as you want, but you have to earn your reputation.
Reading the Steemit whitepaper, the Steemit code, and especially the conversations between the programmers who wrote the code has given me a new appreciation for the Steemit project. The people who conceived this idea and brought it to life are tremendously brilliant, skilled, and hard-working. It makes so happy to have found this community in its infancy so that I can watch it grow up.