Today we're going to explore how to compare delegations with self-voting!

We're going to focus specifically on a ROI neutral bot, meaning that incoming bids are controlled in a way that does not allow the round to have too much or too little total bid amounts. Naturally, the higher the total bids, the more delegators get, so adjust this computation accordingly. (It also means, if you are delegating, the best returns possible will be ones that have a max ROI cap for bidders but no min ROI cap).

What we'll see is essentially that for those of you that want to maximize your SP efficiency, self voting gives you better returns than using the same SP to delegate to a bot. Now why, if I'm against this behavior anyway, would I tell you this? Well it certainly doesn't really matter if you have already chosen to self vote, vote sell, or delegate. Abuse is abuse. If you're going to milk it, milk it whole. Actually just kidding... this isn't really a secret, and those with stake that choose to do so are already doing so anyway.

The other interesting question is that well, if self-voting gives better returns, why isn't every abuser just doing that? The real reason is that self-voting invites flags, whereas delegating makes you immune to it*.

(* Sort of. One can always choose to flag whatever else you do. And besides that, the bot itself can be a target and can affect its stability. Though we hardly see that happening, eh?)

The Setup

We'll focus on the model from post-promoter, which is what most of the bots that are out there are based on. But anyway most bots will be set up with the same idea.

How it works is that for a given round, the bot takes in bids for posts, and at the end of the round, splits its 100% VP vote among the bidders, in proportion to the bid amounts. This means that every bidder gets the same % ROI (assuming same post age). Now for the delegators, the bids are then split, with some percentage (usually 5%) going to the bot runner, and the rest going to delegators, in proportion of the SP that they delegate to the bot.

This means simply the following: if the bot has 100 SBD at the end of the day, and you delegated 50 out of the 950SP that let's say the bot has, you will get 5 SBD from that pot. (50/950 of 95% of 100)

With this setup, it appears that there would be no way to predict the income for either the bidders or the delegators, but now there are all sorts of parameters that make the bot quite predictable:

1. Min ROI. The higher the bid amounts in the round, the lower the ROI. In the past there would be cases where a giant last minute bid killed the returns for everyone in the round. This parameter, which is now commonly set at -10%, makes it so that if an incoming bid would make the ROI worse than this parameter, it would reject it for the round.
2. Max ROI. Likewise, the lower the bid amounts, the higher the ROI, but it's worse for the delegators income stream. This parameter, which is commonly set to +10%, makes it so that if there aren't enough bids, the bot will not use its full 100% vote. It will scale down the vote so that the bidders get less. Consequently, the next round becomes shorter.
3. Min post age If set (usually to say 20 minutes), this forces votes cast to ensure the bot receives part of the ~25% curation.

A bot that is fair to bidders and delegators will essentially set these parameters so that the vote given is predictable, centered around an (bidder) ROI of 0%. And that is to say:

• If you're using bid bots as a bidder for rewards purposes, you are going to lose. At this point you are trying to bank on the USD value of STEEM rising before payout time, as the only way it could possibly give you returns. It's like trying to time the market, except you have no control over the trades! (The caveat is finding the bid bots who set parameters favorable to bidders.) And one other thing-- If the value of STEEM goes down before payout, you will have lost big as well. So anyway it is a gamble!

Expected Returns from Delegating

We're going to be shuffling some symbols around now, so feel free to skim. Those more interested in checking my figures can audit this section for you.

Because we'll be comparing this to self voting, we won't need to care about the current state of liquid rewards. This is how we'll represent it:

If x is the vote value of your post at payout time after curation, Let k(x) be the SBD market value of both the liquid and SP components of the reward. If you chase the formulas, you will see that it is a linear function, and so we'll just denote this as kx.

Let v be the $ (STU) value vote per SP at 100% VP.

Let S be the total SP of the bot.

Let M be your delegated SP to the bot.

If you self voted with your M SP at 100% VP instead, and immediately after posting, note that your vote would be worth vM ($, or STU), and kvM is how much you would get at payout time.

Now the bot's vote similarly is worth vS.

For a given round, let b be the sum of the bids, again in terms of SBD.

Neutral ROI is when the market value of what you get in payout is equal to the market value of the input, or when

0.75 * k * v * S = b  

Remember the timing of the vote means that 25% of that vote would go to curators. Also hidden here is the fact that since the vote is split in proportion of bids, everyone gets the same ROI, so we can assume without loss of generality there's just 1 bidder in computing break-even point.

This b is what goes into the liquid pool of the bot to be distributed. Let's assume for simplicity that the bot does not take any cut out of the bid. Because you have M of the S SP of the bot, you will get

(M/S) * .75 * kvS = .75 * kvM

Well, what do you know! You get less than what you would have gotten if you had just self-voted. By exactly the curation factor.

Note this amount is tweaked further by the following factors:

1. Bot % cut (again, usually 5%)
2. Actual bid amount, which at worst, if the max ROI is set to (+10%), and is reached, it would reduce the formula above by about 9% (Use 1.1b instead of b). At best, if the min ROI is set to say (-10%), and is reached, it would increase the formula by about 11% (Use 0.9b instead of b). And if there's no min ROI and the bid fills like crazy, well then. Profit island!

Summary

Here are the take-aways, in my opinion:

1. Don't bid on bid bots if your goal is profits. The only way you're getting anywhere with them is if you bid for exposure (and for that, you're going to need A LOT). Results may be better if you know how to fish out bidder-favorable bots. Even then it's still a gamble if the USD-STEEM price drops.
2. Delegating to the bid bot gives less than self voting. So you exchange flexibility for how you use the stake (since delegated SP is no longer controlled by you) for no fear of flags. And again, results may be better if you know how to fish out delegation-favorable bots.

You may notice I left out vote selling. But it's really not much different. You'll get similar returns as bid bot delegation, except you have flexibility in your stake usage, and you get curation. But... the income may or may not be as steady depending on the supply/demand for votes.

And to be clear, my position is that self-voting, vote selling, and delegating to bid bots is still bad for the platform. The main purpose of this post is to educate both bidders and delegators on what is happening.

(Meta: Does this count in the "M" of steem-stem? Just kidding...)