Curation sure is complicated, isn't it? You may have heard something about the square root curation rewards curve, e.g. here.

In this post we will walk through where this is implemented, and look at some scenarios.

This is the part of the code that that assigns the weight of a vote.

uint64_t old_weight = util::evaluate_reward_curve( old_vote_rshares.value, curve, reward_fund.content_constant ).to_uint64();
uint64_t new_weight = util::evaluate_reward_curve( comment.vote_rshares.value, curve, reward_fund.content_constant ).to_uint64();
cv.weight = new_weight - old_weight;

If you look now at evaluate_reward_curve, it simply takes the square root of the value, since curve is set to square root for hardfork 19, which is done here.

Note that this weight gets tallied up into the comment's total vote weight, and the fraction of the curation rewards pool you will get is given by this weight divided by the total vote weight.

If you voted earlier than 30 minutes, then the amount you get is discounted further, as discussed in this post.

Now rshares is simply the number of VESTS assigned to the post. If OV is the old value on the post before your vote, and YV is the value you assign to the post, and TV is the total value assigned at payout, then we have

as the fraction of the curation rewards that goes to you.

But note that as in the last post we can translate from VESTS to STEEM using the steem_per_mvests parameter, and then to the $ amount shown in the UI by multiplying by feed_price everywhere, but these factors cancel out in the numerator and denominator. Thus, the formula above applies to the $ vote value as well!

If that last part didn't make sense to you, just take the last formula to be in terms of the $ value of the post before your vote, the $ value of your vote, and the total $ value of the post.

Full Formula

Now putting it all together, the amount of curation rewards for a given vote is

where OV is the old value of the post before your vote, YV is the value of your vote, TV is the total value of the post at payout, and r is the discount due to voting early (as a reminder, r=0 if you vote at 0 minutes, r=0.5 if you vote at 15 minutes, and r=1 if you vote after 30 minutes).

Sample Scenario #1

Now for some sample scenarios to run through.

Say you cast the first vote after 30 minutes, and your vote is worth 1$, and your vote comes before a 99$ whale vote, and then that's all.

Then OV=0, YV=1, TV=99 and you get 1/10th of the curation rewards, and the whale gets the other 9/10ths, of 25$ in curation rewards. So author gets 75$, you get 2.5$, and the whale gets 22.5$.

(These are again not in SBD or USD, see e.g. how payout works.)

The Square Root Property

Here's an interesting property of the square root function: taking the square root (or any root, really) of a particular value will pull that value towards 1. For instance, the square root of 0.01 is 0.1 and the square root of 100 is 10.

This property actually allows even minnows to get a "good" chunk of the curation for voting first on a post that eventually blows up in value. And if you're lucky while browsing the bot tracker for posts that you might be able to front run, you may be able to find one that can get you a little more curation.

Curation for lower SP folks?

Let's say that your vote is worth 0.005, which would be common when just starting. And let's say you vote on a fresh post with no votes (admittedly rare, because most people self-vote at 0 minutes), and that you get lucky or are stalking a bot-- that post eventually gets 100 total value.

According to the formula, OV=0, YV=0.005, TV=100, and if you voted after 30 minutes, you would get 0.177 of that value in rewards (half of that to SBD, the other half divide by price feed and goes to SP).

It's not much, but not bad considering your stake is very low!

However, if the author self-votes at 1$ worth say (or the post already has 1$ worth of votes), then this quickly disappears. OV=1, and you'd get

(sqrt(1.005) - sqrt(1)) * 10 / 4 = 0.006

in rewards.

Summary

There is no summary, curation rewards are complicated. However, you now have a formula to estimate what you would get in curation rewards if you were to front run a bot vote that you know is coming.

Also, I suspect I may have messed something up, so I will be testing out my computations on real bot votes soon just to see how it goes. Will record any updates I make to this post in an Addendum section, if there are any.

Let me know below if you want to run through some examples perhaps!

Addendum

@yabapmatt has a tool for doing this computation, and you can find out more in his post here. The same tool that lets you stalk upcoming bids let's you find what your curation possibilities are.

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