Correlation Analysis of Reward Rate in a DPoS Blockchain
Hidemasa Tanaka

Shiori Hironaka

Kazuyuki Shudo

Tokyo Institute of Technology
Tokyo, Japanhidemasa.tanaka1116@gmail.com

Kyoto University
Kyoto, Japan
0000-0001-7994-2858
hironaka@media.kyoto-u.ac.jp

Kyoto University
Kyoto, Japan
0000-0002-3939-9800

Abstract—In the blockchain architecture, there are various
consensus methods, such as Proof of Work (PoW), Proof of
Stake (PoS) and Delegated Proof of Stake (DPoS) for validator
selection. A DPoS protocol works similarly to an election,
where token holders vote for validator candidates. Electedvalidators generate blocks and receive block generation rewards. BNB Chain adopting DPoS has implemented a levelingmechanism to prevent the concentration of votes on a small
number of validators. However, voting token holders do notalways act in economically rational ways. This causes disparity
in rewards to votes by token holders. We investigated the BNB
Chain and factors related to the reward rates. We calculated
Spearman’s rank correlation coefficient between reward rates
and several factors: the number of delegate-related transactions, the amount of delegated tokens, the rate of change in
the amount of delegated tokens, and the average number ofvoting validators. As a result, we found that the number ofdelegate-related transactions has the strongest correlation withreward rates, and that there is a non-linear correlation between
the reward rate and the average number of voting validators.
Index Terms—Blockchain, Delegated Proof of Stake, BNB
Chain, Correlation coefficient

1. Introduction
Following the advent of Bitcoin in 2008 [1], the coretechnology, blockchain, has been employed in a variety offields, including finance [2], healthcare [3], and the Internetof Things [4]. One of the basic functions of the blockchain
is the consensus protocol. The consensus protocol defines
the rules for verifying transactions and creating a block.
The first blockchain Bitcoin employs Proof of Work (PoW)
protocol. Subsequently, Proof of Stake (PoS) and Delegated
Proof of Stake (DPoS) protocols were developed for otherblockchains [5]. DPoS is an election-like protocol where
token holders vote for validator candidates, and selectedvalidators generate a block and distribute the rewards earned.
In this paper, token holders who have voted are referred to asdelegators. Compared to the previous consensus protocols
such as PoW, DPoS does not waste energy [6] and improvestransaction throughput [7]. The DPoS was first introduced
in 2014 [8]. Since then, it has been employed by manysuccessful blockchains, including EOSIO [9], Tron [10], andBNB [11].
The BNB Chain employs a mechanism to balance thenumber of votes for each validator in order to control theconcentration of votes on some validators. This mechanism
is called a leveling mechanism. The leveling mechanism
provides economic incentives to vote for validators withfewer votes. In theory, if delegators act with complete
economic rationality, they receive the same rate of reward.
In practice, delegators do not act with economic rationality,
which results in a disparity in the reward rates they receive.
This disparity is caused by the election-like process in
DPoS, while no such disparity occurs in PoS. Tanaka etal. [12] analyzed the relationship between the reward rate
and the number of deletage-related transactions. However,other factors related to reward rates are not clear.
This paper examines the relationship between the reward rate and four attributes of a delegator: the numberof delegate-related transactions, the amount of delegatedtokens, the rate of change in the amount of delegated tokens,and the average number of voting validators. The results
show that the number of delegate-related transactions has
the strongest correlation with the reward rate. In addition,
the results show that delegators with an average number ofvoting validators between two and three showed a higher
reward rate than those with other average numbers.

2. BNB Chain
2.1. Overview
The BNB Chain is one of the most popular blockchainsin the world and its market cap is reaching 90 billion dollars1 . BNB plays a significant role in the field of decentralized finance, with the second highest volume of transactions
on decentralized exchanges after Ethereum.
The BNB Chain is composed of two blockchains: the
BNB Beacon Chain (BC) and the BNB Smart Chain (BSC)2 .
1. https://coinmarketcap.com/ (accessed 2024-04-24)
2. https://docs.bnbchain.org/docs/overview/ (accessed 2024-04-24)

Proc. 7th IEEE Int'l Conf. on Blockchain(IEEE Blockchain 2024), August 2024

The BC is the blockchain component responsible for thegovernance of the BNB Chain and manages voting on the
BNB Chain. In contrast, the BSC is a blockchain componentof that is Ethereum Virtual Machine compatible, consensus
layers, and with hubs to multi-chains.

2.2. Delegated Proof of StakeIn the BNB Chain, validators are selected according to
the DPoS protocol. First, BNB token holders vote for validator candidates. The elected validators then generate blocks
and subsequently receive rewards. Finally, the delegators
who have voted for the elected validators are then distributed
rewards by the validator.
Token holders can vote for any number of validator
candidates with any amount of tokens. The total amountof tokens voted is counted daily at 00:00 UTC, and the
top 21 validator candidates are selected as the cabinet,
while the top 22–29 validator candidates are selected as thecandidate [13]3 . Subsequently, in each epoch, the probabilityof a cabinet being selected as a validator is higher thanthat of a candidate. This results in cabinets receiving more
rewards and candidates receiving relatively fewer rewards.
Blocks are generated every three seconds. Validators
receive a block generation reward from the gas fees of thetransactions included in the generated block. Each validator
sets its own commission rate, and the validator distributes
the block reward minus the commission to the delegators
who voted. The reward received by delegator 𝑖 from validator 𝑣 on day 𝑑 is calculated using the following equation:



𝑉𝑖,𝑑
,
(1)
𝑅𝑖,𝑑 = 𝑅 𝑣,𝑑 × (1 − 𝐶 𝑣,𝑑 ) ×
𝑉𝑣,𝑑where 𝑅 𝑣 ,𝑑 is the block generation reward of validator 𝑣
earned on day 𝑑, 𝐶 𝑣,𝑑 is the commission rate of validator 𝑣
on day 𝑑, 𝑉𝑖,𝑑 is the amount of tokens delegator 𝑖 voted forvalidator 𝑣 on day 𝑑, and 𝑉𝑣,𝑑 is the total amount of tokens
voted for validator 𝑣 on day 𝑑.
Assuming that all delegators act economically rationally,
the average reward rate should be the same regardless ofwhich validator they vote for. Validators generate blocks
with the same probability regardless of the number of votes
they receive, which means that all validators earn the same
average reward. Since every cabinet is selected as a validator
with the same probability, the expected rewards earned by
the cabinet are equal. The same can be said for candidates.
This leveling mechanism creates an economic incentive tovote for the validator candidates with the low number ofvotes. This is because, assuming that 𝑅 𝑣,𝑑 is constant and𝐶 𝑣,𝑑 is equal across validators, the validator with fewer 𝑉𝑣 ,𝑑has a larger 𝑅𝑖,𝑑 . This leveling mechanism equalizes thenumber of validators’ votes and also avoids the concentration of votes on a small number of validators and prevents
delegators with a large number of tokens from having an
excessive impact on the election.
3. These numbers are current at the time of data collection.

However, the number of delegators who act in an economically rational manner is unclear. Furthermore, changes
in the number of validators or alterations to the election
process would result in disparities in the number of votes
received. It is important that the delegators exist who maximize their rewards by acting economically rational. Suchdelegators contribute to maintaining a balance in the numberof votes between validators.

3. Related Work
Since the development of DPoS, numerous studies
have been conducted regarding attacks specific to DPoS.
Hasanova et al. [14] highlighted the risks of a large token
holder taking over the election under low voter participation
rates and collusion among validators as vulnerabilities specific to DPoS blockchains. In this context, Liu et al. [15]investigated EOS, one of the DPoS blockchains, and revealed that influence is concentrated on some delegators andthere are suspicions of collusion among some validators.
Furthermore, Wang et al. [16] proposed a method to give
more rewards to nodes that actively participate in voting,by classifying voting nodes using a clustering algorithm
to mitigate such risks. This method intentionally created adifference in rewards and encouraged nodes to participate
in voting. However, in the BNB Chain, not only the voting
participation rate but also the imbalance in the number ofvotes for validators can lead to vulnerabilities.
There is a study by Tanaka et al. [12] that examined theimbalance in the number of votes as other than attacks in
DPoS. They examined the relationship between reward rates
and voting behavior and showed that delegators who frequently generate delegate-related transactions receive more
rewards. However, the relationship between reward rates andattributes other than the number of delegate-related transactions is unclear. In this paper, we examine the relationshipbetween reward rate and four delegator attributes.

4. Data
4.1. Delegated Token AmountIn order to analyze the disparity in reward rates, we collect delegate-related transactions. From these transactions,
we calculate the amount of delegated tokens and rewards
for each delegator.
We collected delegate-related transactions from BNB
Chain Explorer4 . The three types of delegate-related transactions are as follows:
Delegate Smart Chain Validator
Vote for delegator candidates using BNB tokens.
Redelegate Smart Chain Validator
Change the vote from one delegator candidate
to another.
4. https://explorer.bnbchain.org/ (accessed 2024-04-15)

Proc. 7th IEEE Int'l Conf. on Blockchain(IEEE Blockchain 2024), August 2024

Undelegate Smart Chain Validator
Cancel the current vote.
Finally, we collected 709,133 delegate-related transactions
generated between August 16, 2020 and May 31, 2023.
The amount of delegated tokens is calculated using timestamp, delegator_address, validator_address, delegation_amount in the Delegate Smart Chain Validator andUndelegate Smart Chain Validator transactions. The Redelegate Smart Chain Validator transaction does not affect the
total amount of delegated tokens, and thus it is not includedin the calculation.
The amount of delegated tokens of delegator 𝑖 on day 𝑑is calculated using the following equation:
𝑉𝑖,𝑑 = 𝐴delegate,𝑖,𝑑 − 𝐴undelegate,𝑖,𝑑 ,(2)where 𝐴delegate,𝑖,𝑑 is the sum of the tokens in the Delegate
Smart Chain Validator transactions generated by delegator 𝑖
before day 𝑑, and 𝐴undelegate,𝑖,𝑑 is the sum of the tokens in
the Undelegate Smart Chain Validator transactions generated
by delegator 𝑖 before day 𝑑. In addition, the amount ofdelegated tokens of delegator 𝑖 in month 𝑚, denoted by 𝑉𝑖,𝑚 ,is calculated as the sum of 𝑉𝑖,𝑑 .

delegated tokens, the rate of change in the amount of delegated tokens, and the average number of voting validators.
The number of delegate-related transactions is defined as
the total number of delegate-related transactions generated
by the delegator in a given month. The existence of theleveling mechanism in the BNB Chain implies that the
reward rate may be reduced if the delegator fails to appropriately change a validator with a low reward rate to anotherwhen the amount of delegated tokens of the validator ischanged. To change the delegating validator, it is necessary
to generate a delegate-related transaction. Consequently, it isexpected that delegators who generate more delegate-relatedtransactions will have a higher reward rate.
The amount of delegated tokens, denoted by 𝑉𝑖,𝑚 , isdefined in Section 4.1. The phenomenon of the rich getting
richer has been a topic of discussion in PoS blockchainsfor some time [17]. Our hypothesis was that a similar phenomenon might occur in DPoS-based BNB Chains, where
delegators with larger amounts of delegated tokens may havehigher reward rates.
The rate of change in the amount of delegated tokens ofdelegator 𝑖 in month 𝑚 is defined as follows:
CR𝑖,𝑚 =

4.2. Reward Rate
In order to calculate the reward received by each delegator, we collect reward transactions. First, we calculated
the total amount of delegated tokens for each delegator as of
May 31, 2023. Then, we determined the top 1,000 delegators
as the collection target. Finally, we collected the reward
transactions for the top 1,000 delegators. This resulted in
1,616,939 reward transactions.
Next, we calculate the monthly reward rate for eachdelegator. The total reward received by delegator 𝑖 in month𝑚 is calculated as the sum of tokens in reward transactions
generated in month 𝑚. The monthly reward rate was calculated by excluding delegators who had a monthly delegatedtoken volume of zero.
The monthly reward rate of delegator 𝑖 in month 𝑚 is
calculated as follows:


𝑅𝑖,𝑚
365
×
× 100,(3)
𝑟 𝑖,𝑚 =
𝑉𝑖,𝑚𝑁𝑚
where 𝑅𝑖,𝑚 is the sum of rewards received by delegator 𝑖,
𝑉𝑖,𝑚 is the total amount of delegated tokens of delegator𝑖 in month 𝑚, and 𝑁 𝑚 is the number of days in month𝑚. The value of 𝑟 𝑖,𝑚 is calculated on the assumption thatthe reward and the amount of delegated tokens of delegator
𝑖 will continue for one year. Consequently, the formula ismultiplied by 365
𝑁𝑚 . The monthly reward rate was calculated
between January 2022 and May 2023.

𝑉end,𝑖,𝑚 − 𝑉start,𝑖,𝑚,𝑉start,𝑖,𝑚(4)

where 𝑉start,𝑖,𝑚 is the amount of delegated tokens of delegator 𝑖 at the beginning of month 𝑚 and 𝑉end,𝑖,𝑚 is the amountof delegated tokens of delegator 𝑖 at the end of month 𝑚.
In the BNB Chain, delegators must cast as many tokens
as possible in order to maximize the rewards they receive.
We hypothesized that delegators who increase the amountof delegated tokens may be more conscious of profitability,
and therefore select the most suitable validator candidates,
resulting in a higher reward rate.
The average number of voting validators is the average
number of daily voting validators whose votes were castby delegator 𝑖 in month 𝑚. This value must be at least
one. Voting for validator candidates has an investment-like
aspect, where the reward rate is determined by the validators
they vote for. In general, investment diversification tends toreduce the standard deviation of total returns. Thus, if adelegator votes for a large number of validator candidates,
there is a high probability of convergence to the averagereward rate. Furthermore, since the expected reward canbe calculated by the amount of delegated tokens cast fora validator, it is expected that the average reward will be
improved by concentrating votes on a small number ofvalidators with high expected rewards. Consequently, thereward rate is expected to decrease as the number of voting
validators increases.

5. Correlation Analysis

4.3. Delegator Attributes

5.1. Linear Correlation

Four attributes of delegators were selected for analysis:
the number of delegate-related transactions, the amount ofIn the first analysis, Spearman’s rank correlation coefficients are calculated between the reward rates and the four

Proc. 7th IEEE Int'l Conf. on Blockchain(IEEE Blockchain 2024), August 2024

p 0.05
p < 0.05

0.4
0.3
0.2
0.1
0.0Jan 2022

Apr 2022

Jul 2022

Oct 2022

Month-YearJan 2023

0.15

Correlation Coefficient

Correlation Coefficient0.5

p 0.05p < 0.05

0.10
0.05
0.00
0.05
0.10Jan 2022

Apr 2023

0.10

0.20

0.05

0.15

0.00
0.05
0.10
0.15

p 0.05p < 0.05

0.20Jan 2022

Apr 2022

Jul 2022

Oct 2022

Month-YearJan 2023

Jul 2022

Oct 2022

Month-YearJan 2023

Apr 2023(b) The amount of delegated tokens.

Correlation Coefficient

Correlation Coefficient(a) The number of delegate-related transactions.

Apr 2022

Apr 2023(c) The rate of change in the amount of delegated tokens.

p 0.05p < 0.05

0.10
0.05
0.00
0.05
0.10
Jan 2022

Apr 2022

Jul 2022

Oct 2022

Month-YearJan 2023

Apr 2023(d) The average number of voting validators.

Figure 1. The Spearman’s rank correlation coefficients between reward rates and the four attributes of the delegators from January 2022 to May 2023.
Correlation coefficients with p-values less than 0.05 are indicated by cross dots. The number of delegate-related transactions and the rate of change in theamount of delegated tokens were correlated with reward rates in most months.

attributes for each month, covering the period from January2022 to May 2023. Since the four attributes are highlyvariable across the delegators and do not follow a normal
distribution, we decided to use Spearman’s rank correlation
coefficients. In addition, 𝑝-values were also calculated under
the null hypothesis that there is no correlation between
the two variables. A 𝑝-value less than 0.05 indicates thepresence of a statistically significant correlation. When calculating the correlation coefficient for the rate of change in
the amount of delegated tokens, delegators with a zero rateof change in the amount of delegated tokens were excluded.
For reference, a scatter plot of the May 2023 reward rate
and the four indicators is included in the Appendix A.
The results are shown in Figure 1. Correlation coefficients with 𝑝-values less than 0.05 are indicated by crossdots in the graph. The correlation coefficients for the reward rate and the number of delegate-related transactions(Figure 1a) range from +0.15 to +0.34, indicating a significant correlation across all months. Given the consistently
certain absolute values of the correlation coefficients, there
is a weak positive correlation between the reward rate andthe number of delegate-related transactions. For the reward
rate and the amount of delegated tokens (Figure 1b), thecorrelation coefficients range from −0.07 to +0.07, with only

two months showing a significant correlation. The small
absolute correlation coefficients and the lack of significancein most months suggest a very weak to no correlation. The
correlation coefficients for the reward rate and the rate ofchange in the amount of delegated tokens (Figure 1c) range
from −0.19 to +0.09, with only two months showing asignificant correlation. Similar to the result for the amountof delegated tokens, the small absolute coefficients and lackof broad significance suggest a very weak to no correlation.
As for the reward rate and the average number of voting
validators (Figure 1d), the values range from −0.09 to +0.12,
with a significant correlation in half of the months. However,the small absolute coefficients and the lack of consistentsignificance suggest no linear correlation, or at best a very
weak one.

5.2. Non-linear Correlation
To observe relationships that could not be distinguishedby the correlation coefficient alone, delegators were classified into five groups based on attribute values, and theaverage reward rate ratio was calculated for each group.
The delegator classification criteria were as follows: For
the number of delegate-related transactions, the groups were

Proc. 7th IEEE Int'l Conf. on Blockchain(IEEE Blockchain 2024), August 2024

1.20

x=0
x=1
x=2
x=3
x>4

Reward Rate Ratio

Reward Rate Ratio

1.25

1.15
1.10
1.05
1.00
Jan 2022

Apr 2022

Jul 2022

Oct 2022

Month-YearJan 2023

Apr 2023

1.02
1.00
0.98
0.96

x < 10k
10k x < 15k
15k x < 25k
25k x < 100k
x 100kJan 2022(a) The number of delegate-related transactions.

1.10

x< 4
4 x<0
x=0
0<x 4
x>4

1.05
1.00
0.95
Jan 2022

Apr 2022

Jul 2022

Oct 2022

Month-YearJan 2023

Jul 2022

Oct 2022

Month-YearJan 2023

Apr 2023(b) The amount of delegated tokens.

Reward Rate Ratio

Reward Rate Ratio

1.15

Apr 2022

Apr 2023(c) The rate of change in the amount of delegated tokens.

1.15
1.10

x=1
1<x 2
2<x 3
3<x 4
x>4

1.05
1.00
Jan 2022

Apr 2022

Jul 2022

Oct 2022

Month-YearJan 2023

Apr 2023(d) The average number of voting validators.

Figure 2. The average reward rates grouped by the four attribute values. The reward rates are normalized. A non-linear correlation was observed, with theaverage reward rate showing a peak in the group with the average number of voting validators between 2 and 3.

0, 1, 2, 3, and 4 or more transactions. For the amount ofdelegated tokens, the groups were less 10,000, 10,000 toless than 15,000, 15,000 to less than 25,000, 25,000 to lessthan 100,000, and 100,000 or more. Because the rate ofchange in the amount of delegated tokens included negativevalues, we calculated the logarithm of the absolute values tocreate an index for the grouping. For the rate of change in
the amount of delegated tokens, the groups were an index
value of less than −4, −4 to less than 0, 0, greater than 0
to 4, and greater than 4. For the average number of voting
validators, the groups were 1, greater than 1 to 2, greaterthan 2 to 3, greater than 3 to 4, and 4 or more. Next, one
group was selected as the baseline, and its average reward
rate ratio was set to 1. The average reward rate ratios of theother groups were calculated relative to the baseline. These
calculations were performed for each month from January2022 to May 2023.
Figure 2 shows the average reward rates for each groupon a monthly basis. Consistent with the analysis in Section 5.1, there is a positive correlation between the reward
rate and the number of delegate-related transactions. No
correlations were observed between the reward rate andthe amount of delegated tokens or the rate of change in
the amount of delegated tokens. For the average number ofvoting validators, the highest reward rate was observed in the

2 < 𝑥 ≤ 3 group, with a gradual decrease observed aroundthis group, indicating a non-linear correlation. Because it
was a non-linear correlation, it was not captured by theSpearman’s correlation coefficient.

6. Discussion
When examining the relationship between the reward
rate and the number of delegate-related transactions, Figure 1a shows a weak correlation. This finding is consistent
with the expectation that the existence of the leveling mechanism requires the generation of delegate-related transactions
to maintain a certain minimum reward rate. The results
obtained are also consistent with those reported by Tanaka
et al. [12].
We could not observe a correlation between the reward
rate and the amount of delegated tokens from Figures 1band 2b. Contrary to expectations, this suggests that thephenomenon of the rich getting richer, often discussed in
PoS blockchains, has not occurred in the BNB Chain.
However, delegators were identified based on their delegatoraddresses, which do not necessarily correspond to actual
individuals or organizations. If an individual has more than
one address, they are recognized as multiple delegators in
our analysis. In addition, while the amount of delegatedProc. 7th IEEE Int'l Conf. on Blockchain(IEEE Blockchain 2024), August 2024

tokens did not correlate with the reward rate for the top
1,000 delegators, the results may be different for the top
10,000 delegators.
A correlation between the reward rate and the rate ofchange in the amount of delegated tokens was not observedin Figures 1c and 2c. Increasing the amount of delegated tokens would increase the reward, but in calculating the reward
rate, the denominator also increases, so simply increasing
the amount of delegated tokens does not improve the reward
rate. In other words, if delegators increase the amount ofdelegated tokens, they must vote for validators who canearn more rewards with the increased tokens. Otherwise,
the reward rate will not improve. Since it was found from
Figure 1b that increasing the amount of delegated tokens
does not increase the reward rate, it is assumed that the rateof change in that amount did not increase the reward rateeither.
We could not observe a correlation between the reward
rate and the average number of voting validators in Figure 1d. However, in Figure 2d, we observed a non-linear
correlation, with the highest reward rates for the group with
2 < 𝑥 ≤ 3, and a gradual decrease around that group. Sincedelegators can calculate expected rewards by checking theamount of delegated tokens on a validator when voting,concentrating votes on a small number of validators withhigh expected rewards improves the average reward rate.
However, changing where votes are cast is not always free
due to cost and frequency constraints. When voting for alarge number of validators, a delegator’s average reward
rate converges to the global average reward rate withoutchanging the voting target, which is why the reward rate
gradually decreases when the average number of voting
validators is greater than 3. The reward rate also decreases
when the average number of voting validators is less than2, possibly because when the number of voting validators is
too small, the reward rate is more likely to decrease withoutchanging the voting target.

tween the reward rate and the average number of voting
validators.

7. Conclusion[12] H. Tanaka, S. Hironaka, and K. Shudo, “Quantitative Analysis of the
Reward Rate Disparity Among Delegators in a DPoS Blockchain,” inProceedings of the 2024 IEEE International Conference on Big Dataand Smart Computing, 2024, pp. 136–142.

The BNB Chain using DPoS has a leveling mechanism
to prevent the concentration of votes on a small number ofvalidators, but the voting behavior of token holders is not
economically rational, resulting in different reward rates. We
investigated the factors that affect the delegator’s reward ratein the BNB Chain.
We calculated the Spearman’s correlation coefficient every month from January 2022 to May 2023 to investigate therelationship between the reward rate and the four delegator
attributes: the number of delegate-related transactions, theamount of delegated tokens, the rate of change in the amountof delegated tokens, and the average number of voting
validators. We also examined by plotting the average reward
rates of delegators grouped by their attributes. As a result,
we found that there is a weak positive linear correlation
between the reward rate and the number of delegate-relatedtransactions, and that there is a non-linear correlation be-

Acknowledgment
This work was supported by JSPS KAKENHI Grant
Number JP21H04872 and JP24H00691.

References[1]

S. Nakamoto, “Bitcoin: A peer-to-peer electronic cash system,” 2008.

[2]

L. Zhang, Y. Xie, Y. Zheng, W. Xue, X. Zheng, and X. Xu, “Thechallenges and countermeasures of blockchain in finance and economics,” Systems Research and Behavioral Science, vol. 37, no. 4,
pp. 691–698, 2020.

[3]

M. Attaran, “Blockchain technology in healthcare: Challenges andopportunities,” International Journal of Healthcare Management,
vol. 15, no. 1, pp. 70–83, 2022.

[4]

Q. Wang, X. Zhu, Y. Ni, L. Gu, and H. Zhu, “Blockchain for the IoT
and industrial IoT: A review,” Internet of Things, vol. 10, p. 100081,
2020.

[5]

S. M. H. Bamakan, A. Motavali, and A. Babaei Bondarti, “A surveyof blockchain consensus algorithms performance evaluation criteria,”
Expert Systems with Applications, vol. 154, p. 113385, 2020.

[6]

J. Sedlmeir, H. Buhl, G. Fridgen et al., “The energy consumptionof blockchain technology: Beyond myth,” Business & Information
Systems Engineering, vol. 62, pp. 599–608, 2020.

[7]

Q. Hu, B. Yan, Y. Han, and J. Yu, “An improved delegated proofof stake consensus algorithm,” Procedia Computer Science, vol. 187,
pp. 341–346, 2021.

[8]

D. Larimer, “Delegated proof of stake (DPoS) white paper by daniel
larimer,” 2014, https://example.com/whitepaper.pdf.

[9]Block.one, “EOS.IO technical white paper v2,” 2018, https://github.
com/EOSIO/Documentation/blob/master/TechnicalWhitePaper.md.

[10] T. Foundation, “Tron: Advanced decentralized blockchain platform,”
2018, https://tron.network/static/doc/white_paper_v_2_0.pdf.
[11] Binance, “Binancebinance-chain/bsc.

Smart

Chain,”

2020,

https://github.com/[13] “BEP-131: Introduce candidate validators onto BNB Smart Chain,”https://github.com/bnb-chain/BEPs/blob/master/BEPs/BEP131.md.
[14] H. Hasanova, U.-j. Baek, M.-g. Shin, K. Cho, and M.-S. Kim,
“A survey on blockchain cybersecurity vulnerabilities and possible
countermeasures,” International Journal of Network Management,
vol. 29, no. 2, p. e2060, 2019.
[15] J. Liu, W. Zheng, D. Lu, J. Wu, and Z. Zheng, “Understanding thedecentralization of DPoS: Perspectives from data-driven analysis on
EOSIO,” CoRR, vol. abs/2201.06187, 2022.
[16] L. Wang, P. Xu, W. Su, Y. Li, and X. Chen, “Research on improvement of blockchain DPOS consensus mechanism based on HK
clustering,” in 2021 China Automation Congress (CAC), 2021, pp.
1167–1172.
[17] Y. Huang, J. Tang, Q. Cong, A. Lim, and J. Xu, “Do the rich getricher? Fairness analysis for blockchain incentives,” in Proceedingsof the 2021 International Conference on Management of Data, 2021,
pp. 790–803.

Proc. 7th IEEE Int'l Conf. on Blockchain(IEEE Blockchain 2024), August 2024

x=0
x=1
x=2
x=3
x>4

100

Reward Rate

Reward Rate

4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0

102

101

4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0

x < 10k
10k x < 15k
15k x < 25k
25k x < 100k
x 100k1012

The number of delegate-related transactions +1

4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0

x< 4
4 x<0
x=0
0<x 4
x>4

10

5

0

5

log(the rate of change in the amount of delegated tokens)(c) The rate of change in the amount of delegated tokens.

1014

1016

1015

The amount of delegated tokens(b) The amount of delegated tokens.

Reward Rate

Reward Rate(a) The number of delegate-related transactions.

1013

4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0

x=1
1<x 2
2<x 3
3<x 4
x>4

0

5

10

15

20

The average number of voting validators(d) The average number of voting validators.

Figure 3. Scatter plot between reward rates and the four attributes on May 2023.

Appendix A.
Scatter Plot between Reward Rates and FourAttributes
Scatter plots were generated for each month from January 2022 to May 2023, showing the relationship between
reward rates and the four attributes of delegators. The
delegators were classified into five distinct groups basedon their attribute values and plotted using different colors.
The number of delegate-related transactions was grouped
as follows: 0, 1, 2, 3, and 4 or more. With the amountof delegated tokens, the groups were as follows: 10,000,
10,000 to 15,000, 15,000 to 25,000, 25,000 to 100,000, and100,000 or more. Because the rate of change in the amountof delegated tokens included negative values, we calculated
the logarithm of the absolute values to create an index forthe scatter plot. The delegators were subsequently classified
into five groups based on this index: those with an index
value of less than −4, greater than or equal to −4 and lessthan 0, 0, greater than 0 and less than or equal to 4, andgreater than 4. The average number of voting validators wasused to categorize the groups as follows: 1, greater than 1
and less than or equal to 2, greater than 2 and less than orequal to 3, greater than 3 and less than or equal to 4, greaterthan or equal to 4, and 4 or more. The 𝑥 axis is plotted ona logarithmic scale for the scatter plot of the number ofdelegate-related transactions and the amount of delegatedtokens. Log-transformed values are also plotted for the rateof change in the amount of delegated tokens.
Due to space limitasions, a scatter plot for May 2023, thelatest month in the data, is shown in Figure 3. The numberof delegators for each group in Figure 3a was 609 for 𝑥 = 0,
195 for 𝑥 = 1, 67 for 𝑥 = 2, 32 for 𝑥 = 3, and 78 for 𝑥 > 4.
The number of delegators for each group in Figure 3b was
140 for 𝑥 < 10, 000, 212 for 10, 000 ≤ 𝑥 < 15, 000, 197 for
15, 000 ≤ 𝑥 < 25, 000, 100 for 25, 000 ≤ 𝑥 < 100, 000, and237 for 𝑥 ≥ 100, 000. The number of delegators for eachgroup in Figure 3c was 198 for 𝑥 < −4, 44 for −4 < 𝑥 < 0,676 for 𝑥 = 0, 45 for 𝑥 ≤ 4, and 8 for 𝑥 > 4. The number ofdelegators for each group in Figure 3d was 403 for 𝑥 = 1,
184 for 1 < 𝑥 ≤ 2, 141 for 2 < 𝑥 ≤ 3, 79 for 3 < 𝑥 ≤ 4,
and 164 for 𝑥 > 4.
In Figure 3b, all the delegators with a reward rate below
1.0% were included in the 10, 000 ≤ 𝑥 < 15, 000 group.
In Figure 3c, all the delegators with a reward rate below
1.0% were included in the 𝑥 = 0 group. In Figure 3d, therelationship between the reward rate and the average numberof voting validators for the delegators in the 𝑥 > 4 group isobserved to converge around 2.5% as the average numberof voting validators increases.

Proc. 7th IEEE Int'l Conf. on Blockchain(IEEE Blockchain 2024), August 2024