Understanding reputation

Your reputation score, the number in brackets beside your username is the most visible measure of the value of your account, but it's a little impenetrable to see where that magic number comes from.

Assumption #1:- Steemit users sometimes assume that reputation is directly proportional to Steem Power.
Reputation is unrelated to Steem Power, it is related though to the value of the votes a user receives. The more the $ value of those votes the higher the reputation score.

Assumption #2:- Steemit users also sometimes assume that money invested will increase reputation.
Again this is not the case, only votes count.

Assumption #3:- Reputation progresses linearly with equal weight votes.
Did you think it seemed to be much harder to increase your reputation than it used to be. Well you are right! To increase your reputation from 50 to 51 is significantly harder than to increase your reputation from 30 to 31 as it has a logarithmic relationship. To look at this in a bit more detail, I'm going to show you how to work out how much more effort you need to put in to 'level up'.
Firstly you need to start by going to https://steemd.com/yourusername in my case that is https://steemd.com/@maxbullion

Scroll down until you get to the line that gives your reputation. It'll look something like this.

Hold it, that can't be right, that's a number in the billions? Well spotted, what you are looking at here is the raw reputation value. As this is a bit of a big number what is displayed in the user interface is your simple reputation value. The two are related by this equation:-
Simple Reputation = ((Log10 ( raw reputation) -9) x 9) + 25
The following tables will make that more understandable

Note that to get from 16 to 25 requires 900 million reputation points, but to get from 25 to 34 requires 9 trillion and from 34 to 34 requires 90 trillion reputation points. Of course the higher your reputation, the more people will read and vote on your articles and therefore you are likely to earn more from producing articles, so there isn't perhaps as impossible a climb ahead as it seems.

In summary reputation is all important. You can build your reputation by writing good quality content and commenting and voting on other quality articles. Reputation grows non-linearly, the higher your reputation, the harder it is to grow it. Remember of course it is also possible to damage your reputation too. If you are downvoted(flagged) by a whale, you can fall a long way.