How Much Do Whales Influences on Rewards? Introducing New Statistics

Summary

This post introduces two new statistics about influences on rewards with the consideration of the leverage of Steem Power (IPR) to provide more through understanding about the whale issue.

Introduction

The whale issue of Steem is one of the most frequently debated topic from its beginning. But we still do not have through understanding regarding the current situations, such as how much whales have influences on rewards, or how unequal the situation is. In this post, I would like to introduce two new statistics, 1) Influences on (author) rewards, 2) Influence to Steem Power Ratio (IPR), to provide more comprehensive knowledge about the whale issue.

Methods

The data is from Steem blockchain from 2016/8/16 (After v0.13.0) to 2016/9/8.
Influences of whales on rewards is calculated based on the following equations.

- Rshares of a post: sum(voters_rshares)
- Vshares of a post: (posts_rshares)^2
- Daily vshares: sum(posts_vshares)
- Voter's vshares on a post: posts_vshares * (voters_rshares / posts_rshares)
- Voter's daily vshares: sum(voters_vshares)
- Voter's influence: voters_daily_vshares / daily_vshares

To get IPR, we just need a simple equation.

- IPR = Influence / (voters_vests / total_vests)

Note: Steemit account's vests are excluded from total_vests

Results

Rank	Account	Influence(%)	Steem Power (%)	IPR
1	smooth	13.34	2.86	4.67
2	blocktrades	11.60	3.71	3.13
3	berniesanders	10.55	2.97	3.55
4	steemed	3.92	1.62	2.42
5	itsascam	3.82	1.53	2.49
6	tombstone	3.62	1.87	1.93
7	dantheman	3.51	2.54	1.38
8	summon	3.11	1.29	2.41
9	jamesc	2.78	3.20	0.87
10	complexring	2.37	0.67	3.52
11	smooth.witness	2.32	0.53	4.37
12	wang	1.97	0.66	2.97
13	nextgencrypto	1.81	0.51	3.53
14	rainman	1.78	1.51	1.18
15	recursive	1.56	0.31	5.11
16	silversteem	1.55	0.46	3.39
17	riverhead	1.53	0.68	2.23
18	pharesim	1.53	0.88	1.74
19	ned	1.52	5.73	0.27
20	steemit200	1.38	0.57	2.42
21	steempty	1.30	0.69	1.87
22	kushed	1.15	0.50	2.29
23	xeldal	1.15	0.64	1.79
24	hr1	1.00	0.21	4.69
25	satoshifund	0.99	0.35	2.85
26	enki	0.91	0.53	1.71
27	val-a	0.91	2.80	0.32
28	silver	0.74	0.19	3.85
29	au1nethyb1	0.72	0.42	1.71
30	badassmother	0.63	0.26	2.44

Surprisingly, top 10 have about 60% (actually over 60% since smooth and smooth.witness is controlled by same person) of author rewards, while they only have 22% of Steem Power. And the top 3 (smooth, blocktrades, berniesanders consist of 35.5% of influences, for instance, if daily author reward is $20,000, about $7,000 is from these three's voting activities. The average IPR of the top 10 is 2.63, but if we do the same calculation with rank 41~50, they only have IPR of 0.75. This means that influences on rewards is unequally distributed, more specifically it is biased to some whales.

Additionally, I calculated some basic statics about top rankers voting patterns.

• Range: Number of unique writers they voted for
• Mean: Average number of votes per writer
• Max: Maximum number of votes on a writer
• Stdev: Standard deviation of votes

Rank	Account	Range	Mean	Max	Stdev
1	smooth	340	2.32	65	7.49
2	blocktrades	480	1.31	22.4	1.51
3	berniesanders	785	1.27	14.5	1.7
4	steemed	80	3.64	44	6.43
5	itsascam	79	3.69	44	6.49
6	tombstone	196	1.64	12.1	2.18
7	dantheman	339	0.66	10.3	1.23
8	summon	220	1.65	14.4	1.99
9	jamesc	135	1.1	12.8	1.81
10	complexring	534	1.75	39	3.04
11	smooth.witness	324	2.4	65	7.61
12	wang	213	8.29	82	10.41
13	nextgencrypto	755	1.4	14	1.51
14	rainman	170	1.18	9.7	1.3
15	recursive	121	9.78	51	11.76
16	silversteem	760	1.82	15	2.08
17	riverhead	334	1.53	12.6	1.4
18	pharesim	404	2.03	54	3.89
19	ned	238	0.18	2.6	0.35
20	steemit200	175	2.41	13	2.29
21	steempty	164	2.89	34	4.84
22	kushed	250	2.61	84	7.36
23	xeldal	204	2.92	48	5.65
24	hr1	104	10.34	52	11.86
25	satoshifund	130	2.51	21	3.61
26	enki	174	3.22	46	5.58
27	val-a	75	0.36	1.5	0.42
28	silver	763	1.83	15	2.13
29	au1nethyb1	205	1.97	11	1.79
30	badassmother	235	2.75	15	2.77

Among these statistics, max and stdev should be highlighted, since higher numbers imply that a whale's voting is very concentrated (possibily due to his/her preferences or favorable connection with authors?), and this can further create perception of inequality. (People recursively see high rewards on same author's posts). For comparison, while blocktrades and berniesanders have similar influences with smooth, they have much lower max and stdev, which implies that their votes are widely dispersed to many writers. But we can see very high max and stdev in hr1, recursive, wang, and smooth. In addition, we can find smooth and smooth.witness, and recursive and hr1 have the similar patterns respectively, probably because each pair of accounts is using the same voting bot.

Wrap-up

The results show that influence is much higher than whales' actual steem power, especially by active whale bots. In my humble opinion, the fundamental cause is the squared rshares, which makes large voting power much greater. We need further discussion about this issue and have to address it for better Steem society.

P.S. Do you think that I have to post these stats everyday, weekly, or monthly? (Everyday data has influence and IPR only because the second table requires more samples)