When Staking Rewards Compound: Measuring the impact of Ethereum’s Pectra Upgrade Mohammed Benseddik
Benjamin Kraner
Claudio J. Tessone
University of Zurich Zurich, Switzerland [email protected]
University of Zurich Zurich, Switzerland [email protected]
University of Zurich Zurich, Switzerland [email protected]
arXiv:2606.23337v1 [cs.DC] 22 Jun 2026
Abstract Ethereum’s beacon chain hosts over 920,000 active validators, a number inflated by the legacy 32 ETH stake cap. The Pectra upgrade (May 2025) addresses this by introducing 0x02 compounding validators, raising the maximum stake per validator from 32 to 2,048 ETH and enabling automatic reward reinvestment. This paper examines how compounding affects consensus-layer rewards, whether higher balances provide execution-layer advantages, and whether the APR uplift justifies migration for different staker types. We analyse adoption patterns across solo stakers and staking providers, investigate the role of consolidation (merging multiple 32 ETH validators into one) in early migration, and identify barriers slowing the transition. Through simulation, we find that compounding provides roughly +5% relative consensus-layer APR uplift for small balances, diminishing to under 1% for large staking providers. Empirical analysis of all active beacon chain validators shows 0x02 validators achieving modestly higher median CL APR. Solo stakers show higher relative adoption but face operational barriers, whilst providers cite infrastructure costs and protocol constraints. The results suggest that without improved reward accessibility and stronger economic incentives, 0x02 migration will remain gradual despite its network efficiency benefits.
Keywords Ethereum, Pectra, proof-of-stake, staking rewards, compounding, validator consolidation, EIP-7251, beacon chain § Replication package [3] (data, figures, and analysis code).
1
Introduction
Ethereum operates under a Proof-of-Stake (PoS) consensus mechanism that is widely regarded as more energy-efficient and accessible than Proof-of-Work (PoW). These advantages come with a more complex system of economic incentives designed to ensure correct and honest validator behaviour. In PoW systems such as Bitcoin, incentive-related concerns are largely limited to reward schedules [15, 19] or strategic attacks like block withholding [22], with centralization emerging as the dominant long-term issue. The transition to PoS introduced a fundamentally different incentive landscape. At the micro level, protocol parameters govern validator behaviour on a per-block basis, including mechanisms related to Maximal Extractable Value (MEV) and proposer-builder separation. At the macro level, the protocol shapes the network’s monetary policy, staking rewards, and the structure of the staking ecosystem. Empirical studies suggest that participation is broadly fair at the address level [28], though individual actors may still extract
disproportionate value by exploiting MEV or protocol edge cases [20, 23, 24]. At the macro level, more fundamental challenges arise, including sustainable inflation management, fairness across heterogeneous stakers, and effective risk management under fluctuating capital flows. The resulting techno-economic system is difficult to model [18], and ongoing innovation such as liquid staking and restaking further complicates its dynamics [25]. Ethereum’s beacon chain currently hosts over 920,000 active validators, a number inflated by the legacy 32 ETH stake cap. Following the introduction of proof-of-stake, The Merge, and ShanghaiCapella withdrawals [12], the Prague-Electra (Pectra) upgrade (EIP7251 [7]) addresses validator proliferation by raising the maximum effective balance to 2,048 ETH through new 0x02 withdrawal credentials. This enables reward compounding and validator consolidation [7, 13]. For solo stakers, legacy 0x01 credentials sweep rewards above 32 ETH to the withdrawal address rather than compounding, requiring over 11 years at current returns to accumulate enough stake for a new validator [14]. With 0x02, rewards compound directly in the beacon balance, reducing entry frictions [13]. For large operators managing hundreds of thousands of validators, consolidation reduces key management overhead while preserving total stake [4, 14]. Eleven months post-upgrade (Apr. 2026), adoption has reached 25% of staked ETH (9.7M ETH, Fig. 1), with new deposits dominating over consolidation. This raises three related research questions: (i) to what extent do 0x02 compounding validators improve staking returns in practice, and how does this effect vary by stake size; (ii) why has adoption remained limited despite the theoretical benefits; and (iii) which classes of stakers benefit most from 0x02, and which face structural or operational disadvantages. We address these questions through a combination of simulations and empirical analysis. The remainder of the paper is structured as follows: Sections 2–3 cover reward mechanics and simulations; Section 4 presents the empirical analysis; and Sections 5–6 discuss limitations and conclusions.
1.1
Methodology & Data
This study combines simulation-based analysis with empirical investigation. For the theoretical component, we employ Monte Carlo simulations to model validator balance evolution under various staking configurations, comparing 0x01 and 0x02 credential types across different stake sizes and time horizons. The empirical analysis draws on multiple data sources: Dune Analytics for on-chain staking metrics and validator entity classification, Beaconcha.in for
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Mohammed Benseddik, Benjamin Kraner, and Claudio J. Tessone Effective Balance Hysteresis Behavior
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consensus-layer performance data, and Etherscan for executionlayer reward attribution. Statistical comparisons of validator performance use annualised APR metrics with IQR-based outlier removal to ensure robustness.
Overview of Ethereum Staking Rewards
This section introduces the core notation used in the analysis. We decompose epoch-level validator rewards into consensus-layer (CL) and execution-layer (EL) components, specify the EIP-7251 effectivebalance update rule, and summarise how effective balance determines proposer selection. These preliminaries form the baseline for the theoretical and empirical comparisons in subsequent sections. In particular, this section summarises the core mathematical expressions used throughout the analysis, defining i. total validator rewards, ii. effective balance updates under EIP-7251, and iii. proposer-selection probabilities.
2.1
33.5 33 32.5 32 31.5
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Balance Types
Each validator maintains two balance quantities on the beacon chain. The actual balance 𝐵 act represents the validator’s true holdings in Gwei, fluctuating continuously as rewards accumulate and penalties are incurred. The effective balance 𝐵 eff is a smoothed, discretised proxy used by the protocol to compute rewards, penalties, and proposer selection probabilities. This separation prevents minor balance fluctuations from causing constant recalculations of validator weights. A validator becomes active and eligible for staking duties only when its actual balance reaches the MIN_ACTIVATION_BALANCE of 32 ETH, at which point the effective balance is initialised. The effective balance is bounded by a credential-dependent cap 𝐵 cap (discussed later) and updated each epoch using a hysteresis mechanism1 . The effective balance 𝐵 eff is updated only when the 1 In Ethereum, hysteresis refers to the protocol mechanism by which a validator’s
effective balance is updated only when its actual balance crosses predefined upward or downward thresholds, thereby preventing frequent oscillations in effective balance and stabilising reward calculations.
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Figure 1: ETH staking since Shapella (Apr 2023). As of Apr 2026: 38.8M ETH staked (32% of 121.6M supply); 9.7M ETH (25%) on 0x02. Source: Dune.
Effective Balance Beff
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Figure 2: Hysteresis behaviour of effective balance 𝐵 eff (orange) vs. actual balance 𝐵 act (blue). The effective balance remains constant until 𝐵 act crosses the downward threshold (𝐵 eff − 0.25 ETH, red) or upward threshold (𝐵 eff + 1.25 ETH, green), preventing frequent oscillations from small balance fluctuations. actual balance 𝐵 act exits the hysteresis band: min ⌊𝐵 act ⌋, 𝐵 cap , if 𝐵 act ∉ 𝐵 eff − Δ↓ , 𝐵 eff + Δ↑ 𝐵 eff ← (1) 𝐵 eff, otherwise where Δ↓ = 0.25 ETH and Δ↑ = 1.25 ETH are the downward and upward hysteresis thresholds, respectively2 . Fig 2 illustrates the resulting staircase behaviour of 𝐵 eff as 𝐵 act grows.
2.2
Reward Structure
A validator’s reward in a given epoch is the sum of CL and EL components: 𝑅𝑣,epoch = 𝑅CL,𝑣,epoch + 𝑅EL,𝑣,epoch
(2)
Here, 𝑅𝑣,epoch denotes the reward earned by validator 𝑣 in a given epoch, 𝑅CL,𝑣,epoch is the sum of all CL rewards and penalties accrued by 𝑣 during that epoch, and 𝑅EL,𝑣,epoch represents the total execution-layer rewards (priority fees and MEV) earned by 𝑣 in the same epoch. Unless stated otherwise, any use of the term “reward” in the remainder of this paper refers to validator-level, epoch-level quantities of the form 𝑅𝑣,epoch and its CL/EL components. 2.2.1 Consensus-layer Rewards. CL rewards 𝑅CL are the sum of all CL rewards and penalties in a given epoch: 𝑅CL = 𝑅source + 𝑅target + 𝑅head + 𝑅sync + 𝑅proposer − 𝑃source + 𝑃 target
(3)
Here, 𝑅source , 𝑅target , and 𝑅head denote attestation rewards for correct source, target, and head votes, respectively; 𝑅sync represents the sync committee reward; 𝑅proposer is the proposer reward for including attestations and sync committee messages; and 𝑃source 2 EIP-8068 proposes revising these thresholds to address yield disparities [10].
When Staking Rewards Compound: Measuring the impact of Ethereum’s Pectra Upgrade
and 𝑃target denote penalties incurred for missed or incorrect source and target votes. Each CL reward component earned by validator 𝑣 in a given epoch scales with a common base reward that depends on the validator’s effective balance and the total active stake. Specifically, the reward for a given CL component can be written as 𝑅component,𝑣,epoch = 𝐵 eff,𝑣,epoch ×
𝑤 component 𝐹 , × √ 64 𝐷 𝑆 total
2.2.2 Execution-layer Rewards. Execution-layer rewards 𝑅EL are the sum of all execution-layer rewards (priority fees and MEV) in a given epoch. Unlike CL rewards, these are realised per slot where the validator is selected as block proposer in the proof-ofstake protocol [8]; in other epochs, the expected execution income is zero. (5)
Here, 𝑅priority_fees denotes priority fees from included transactions and 𝑅MEV additional MEV revenue; execution-layer rewards are not analysed explicitly, as they are driven by proposer selection (i.e. they are proportional to the stake). We neglect any compounding associated with EL rewards.
2.3
EL-only rewards), we obtain the corresponding component-specific APRs. APR denotes a simple annual rate: it linearises the observed growth of a validator’s balance over the measurement window to a one-year horizon using (6).4
2.4 (4)
where 𝐵 eff,𝑣,epoch denotes the effective balance of validator 𝑣 in that epoch, 𝑆 total is the total active stake on the network, and 𝐹 and 𝐷 are protocol constants defined in the Ethereum CL specifications [2, 27]. The factor 𝑤 component represents the fixed weighting associated with each CL reward type.3 Since all other protocol parameters are validator-independent, a validator’s total CL rewards in a given epoch satisfy 𝑅CL,𝑣,epoch ∝ 𝐵 eff,𝑣,epoch , i.e., they scale proportionally with the validator’s effective balance.
𝑅EL = 𝑅priority_fees + 𝑅MEV
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Performance Metrics
The Annual Percentage Rate (APR) measures a validator’s annualized yield based on the growth of its staking balance over a selected measurement window, using epoch-level granularity. APR is widely used as a standard metric in the industry to evaluate a validator’s performance and capacity to generate rewards and return on investment (ROI). The APR is defined as the period growth rate scaled to one year:
𝐸 year 𝑅𝑣,window × × 100 (6) 𝐵 act,start,𝑣 𝐸 window Here, 𝐵 act,start,𝑣 denotes the actual staking balance of validator 𝑣 at the beginning of the measurement window, 𝑅𝑣,window is the total rewards accrued by validator 𝑣 during the window, 𝐸 window is the number of epochs in the measurement window, and 𝐸 year ≈ 51,480 denotes the number of epochs per year (with one epoch lasting approximately 6.4 minutes). This quantity measures the annualized return on the validator’s initial staking balance over the selected window. By restricting 𝑅𝑣,window in (6) to particular reward components (e.g., CL-only or APR𝑣 =
3 The weighting factors 𝑤 component correspond to individual CL reward components (e.g., source, target, head, proposer, and sync committee rewards) and are fixed by protocol parameters.
Withdrawal Credentials
Each validator has a 32-byte withdrawal credential; the first byte (0x00, 0x01, or 0x02) indicates the credential type. Validators are distinguished by this prefix: “0x01” validators pay rewards to an execution-layer address, while “0x02” validators pay rewards to an internal beacon-chain balance that can auto-compound. Both credential types existed before Pectra, but 0x02 validators only became relevant once EIP-7251 increased the maximum effective balance [7]. Throughout this paper, we refer to “0x01 validators” and “0x02 validators” as shorthand for validators with the corresponding withdrawal credential type. 0x00 are legacy BLS credentials (Dec 2020) requiring conversion to 0x01 before withdrawals [6]; fewer than 1% of validators remain on 0x00 as of April 2026. A future 0x03 type is proposed in EIP-7804 [21]. We exclude both 0x00 and 0x03 from this analysis.
3
Proof-of-Stake (PoS) Related Changes Post-Pectra
The Pectra upgrade introduces a fundamental change to how validator rewards can grow over time. Building on the general framework for validator balances and rewards established earlier, this section examines how 0x02 validators enable automatic compounding of consensus-layer rewards, a mechanism previously unavailable to individual validators. Post-Pectra, validators with 0x02 withdrawal credentials automatically compound their CL rewards: income remains in the beacon-chain balance until the effective balance cap is reached. In contrast, 0x01 validators have their effective balance capped at 32 ETH. While the actual balance can temporarily exceed this cap (e.g., 32.23 ETH), the excess does not contribute to staking rewards since only the effective balance determines reward calculations. This surplus is periodically swept to the withdrawal address via automatic partial withdrawals, meaning 0x01 rewards do not compound on-chain. We analyse the balance changes, compounding dynamics, the role of hysteresis in determining when effective balance increases, and the practical implications for validator profitability.
3.1
Balance Changes
EIP-7251 increased the MAX_EFFECTIVE_BALANCE while introducing a MIN_ACTIVATION_BALANCE of 32 ETH to preserve the lower bound for solo-stakers [7]. The post-Pectra caps on effective balance are: ( 𝐵 cap =
32 ETH, 2048 ETH,
0x01 validators 0x02 validators
4 As a concrete example, if a validator starts a 90-day window with 𝐵
(7)
act,start,𝑣 = 100 ETH and earns 𝑅𝑣,window = 1 ETH over that window (so 𝐸 window /𝐸 year ≈ 1/4), then APR𝑣 ≈ (1/100) × 4 × 100 = 4% (e.g., APRCL,𝑣 = 3.5% and APREL,𝑣 = 0.5%).
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Effective Balance Growth (64.5 ETH, 164,250 epochs = 2y 0m 0d)
0x02 Compounding Mechanism
The two reward layers differ not only in calculation but also in whether they compound (Table 1). EL rewards are paid directly to the withdrawal address and do not compound. The impact of effective balance on block proposer probability is discussed later. CL rewards drive compounding by increasing the validator’s actual balance 𝐵 act . However, compounding only takes effect when 𝐵 act crosses the hysteresis threshold and 𝐵 eff increases by 1 ETH. Listing 1 summarises this process.
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Effective Balance (ETH)
3.2
Mohammed Benseddik, Benjamin Kraner, and Claudio J. Tessone
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0x02 Effective Balance 0x01 Effective Balance
66 65.5 65 64.5 64
Listing 1 0x02 CL Rewards Compounding Mechanism
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1: while 𝐵 min ≤ 𝐵 eff < 𝐵 cap do ⇒ Validator active, balance below
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cap CL rewards (𝑅CL ) accumulate in 𝐵 act 𝐵 act grows until it exceeds 𝐵 eff + 1.25 ETH 4: 𝐵 eff ← 𝐵 eff + 1 ETH ⇒ higher 𝑅CL (𝑅CL ∝ 𝐵 eff ) 5: end while 6: Exit: 𝐵 eff hits 𝐵 cap ⇒ 𝑅CL still accrues in 𝐵 act but no longer boosts future rewards
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Figure 3: Effective balance evolution over 2 years: 0x02 grows via compounding whilst 0x01 validators remain at their 32 ETH caps.
2.22
Here 𝐵 min = 32 ETH for all validators; 𝐵 cap = 32 ETH (0x01) or 2048 ETH (0x02). When 𝐵 eff reaches 𝐵 cap , CL rewards continue to accumulate in 𝐵 act , not the withdrawal address.
Simulating the Compounding Advantage
We compare a single 0x02 compounding validator against two 0x01 validators (2 × 32 ETH, rewards unstaked) over 730 days, starting at 64.5 ETH total stake with 99% participation rate. Swept 0x01 rewards are not restaked, as the validator would need to accumulate at least 32 ETH to activate a new validator. We also do not model 𝐵 eff gaming strategies; see EIP-8068 [10] for discussion of hysteresis optimisation. The simulation models all CL reward components under fixed network conditions, with total active stake held constant at 38.8M ETH (as of April 2026). In practice, staked ETH fluctuates (∼34M to ∼38.8M ETH during 2025–2026, representing ∼14% variation [1]), but this simplification does not materially affect relative comparisons. We exclude execution layer priority fees from block proposals to provide a conservative baseline; inclusion would improve absolute returns but depends heavily on proposal frequency, which is probabilistic and validator-count dependent. Fig 3 illustrates the key difference: 0x02 effective balance grows from 64 to 67 ETH through discrete hysteresis-driven increments, whilst 0x01 remains capped at 32 ETH per validator. Each 1 ETH increment in 𝐵 eff increases future attestation rewards proportionally, creating a positive feedback loop. Fig 4 quantifies the APR impact. We calculate APR using total portfolio ETH (staked balance plus swept rewards), so 0x01 APR
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Figure 4: Rolling APR (top) and ΔAPR (bottom) over 164,250 epochs. The APR gap widens initially as 0x02 𝐵 eff grows, then stabilises around 2 bps.
decreases over time as idle ETH accumulates whilst waiting to reach 32 ETH for a new validator. In Year 1, 0x02 achieves 2.21% APR versus 2.20% for 0x01 (∼2 bps difference, ∼1.9% relative CL reward uplift). By Year 2, the gap widens as 𝐵 eff continues growing for 0x02. Table 2 summarises the full 2-year results. The compounding advantage is bounded by two factors: (1) the slow rate of 𝐵 eff growth due to hysteresis thresholds, and (2) the diminishing marginal impact of each additional ETH on percentage returns. The next section examines how this advantage scales across different stake sizes.
Table 1: 0x02 validator rewards.
3.4 Type
Compounding
Destination
𝑅CL 𝑅EL
Yes (cap: 𝐵 cap = 2048 ETH) No
𝐵 act (beacon) Withdrawal address
Scaling Effects Across Balance Ranges
To analyse how compounding scales with stake size, we simulate validator behaviour over a 1-year horizon for balances ranging from 32 ETH to 10,240 ETH using Monte Carlo simulation (200 runs per balance point, 96–99% participation rate). Fig 5 shows APR as a
When Staking Rewards Compound: Measuring the impact of Ethereum’s Pectra Upgrade
Metric
Value
Unit
Initial Balance Simulation Period Participation Rate
64.5 730 99.0
ETH days %
0x02 Compounding Validators (initial) Validators (final) Final Balance Final Effective Balance Total Rewards Balance Growth APR (Year 1)
1 1 67.3848 67 2.8848 4.47 2.2134
ETH ETH ETH % %
0x01 Non-Compounding Validators (initial) Validators (final) Final Balance Final Effective Balance Total Rewards Balance Growth APR (Year 1)
2 2 67.3314 64 2.8314 4.39 2.1950
ETH ETH ETH % %
Difference (0x02 - 0x01) Extra Rewards Reward Advantage APR Difference
0.0534 1.89 0.0184
ETH % %
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The compounding advantage is most pronounced for smaller balances typical of solo stakers, where 0x01 suffers from idle ETH sitting below the 32 ETH activation threshold. As stake size increases, APR converges between both setups: large staking providers can allocate capital more efficiently across multiple validators, reducing the impact of remainder ETH.5 Based on these simulations, the CL APR uplift from compounding should range from +4.7% for solo stakers (32–2,048 ETH) to +0.3% for large providers (8,192–10,240 ETH). This suggests that 0x02 credentials should offer the greatest benefit to solo stakers and smaller operators, whilst large staking providers would gain only marginal improvement relative to their existing infrastructure.6
3.5
Table 2: Simulation results comparison: 0x02 compounding vs. 0x01 non-compounding validators (64.5 ETH initial balance, 730 days).
Practical Implications
Our simulations support the expected benefits: 0x02 compounding democratises returns for solo stakers (+4.7% CL APR uplift for 32– 2,048 ETH) whilst offering marginal gains for large providers (+0.3% for 8,192–10,240 ETH). These assume idealised conditions: fixed network stake, high participation rates, no queue delays, and zero gas fees. Long-term holders benefit most from 0x02. Rewards compound automatically without gas fees, and the advantage grows over time. Staking-as-a-Service operators face a nuanced trade-off. With 0x01, excess balance above 32 ETH is automatically swept at no cost. With 0x02, accessing compounded rewards requires explicit partial withdrawal requests, incurring gas fees and queue delays. Operational costs may erode the theoretical APR advantage for providers needing frequent distributions. Queue dynamics further complicate this trade-off (Fig 6). For 0x01, entry queues delay activation of new validators funded by
CL Rewards - 0x02 Compounding vs 0x01 Validator APR Simulation 1Y
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5 In practice, validator entry and exit queues also affect performance (Fig 6); new validators may wait days or weeks to activate, making 0x02 compounding additionally attractive by avoiding queue delays. 6 Regarding Execution-layer rewards (priority fees and MEV): They are earned when selected as block proposer. Per EIP-7251 [7], the probability of validator 𝑣 being selected
APR (%)
𝐵
1.8
is proportional to its effective balance:Pr𝑣 ( proposer ) = 𝐵 eff,𝑣 For equivalent total total stake, aggregate proposer probability is identical regardless of credential type: a single 0x02 validator with 2,048 ETH has the same expected proposals as 64 0x01 validators at 32 ETH each. However, as 0x02 effective balance grows through compounding, proposer probability increases proportionally, whilst 0x01 setups require activating new validators subject to entry queue delays (Fig 6).
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Figure 5: APR vs initial balance: 0x02 compounding validators maintain a consistent APR around 2.25%, whilst 0x01 non-compounding validators show lower APR at smaller balances, gradually converging as balance increases.
function of initial balance for both 0x02 and 0x01 setups, whilst Table 3 summarises the results by balance interval.
Table 3: Monte Carlo simulation results (200 runs per balance point, 1-year horizon): Mean APR (%) ± std and ETH rewards by balance bucket. 𝑅CL (ETH)
APRCL (%)
Uplift
Balance (ETH)
0x01
0x02
0x01
0x02
(%)
32–2,048 2,048–4,096 4,096–6,144 6,144–8,192 8,192–10,240
22.7 69.2 115.0 160.8 203.8
23.8 69.8 115.6 161.4 204.4
2.17±.12 2.23±.01 2.23±.00 2.23±.00 2.23±.00
2.26±.01 2.25±.00 2.24±.00 2.24±.00 2.24±.00
+4.7 +0.9 +0.5 +0.4 +0.3
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100
% of ETH Staked
60 50 40 30
Figure 6: Validator entry and exit queue wait times since Shapella (Apr 2023). Peak entry wait reached 45 days (June 2023); exit queue peaked at 46 days (September 2025). Data: validatorqueue.com [16].
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O Ja A Ja O Ju A Ja O Ju 20 ct 20 n 20 pr 20 l 20 ct 20 n 20 pr 20 l 20 ct 20 n 20 23 23 24 24 25 25 26 24 24 25 25
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7 Small numerical differences across figures (e.g., 911,146 vs 901,650 for 0x01) reflect whether 0x00 validators are grouped with 0x01 (as non-compounding) or excluded entirely. The total staked ETH is unaffected.
Figure 7: Validator adoption since Pectra launch: 0x01 validators (top) showing approximately 911,000 validators with 75% stake share, and 0x02 validators (bottom) showing growth to 11,573 validators with 25% stake share as of April 2026. Data source: Dune Analytics [17].
Jun 2025
As of the data collection period (April 7, 2026), the beacon chain hosts approximately 38.8 million staked ETH across 922,721 active validators [1, 17]. This total comprises 9,496 legacy 0x00 validators (1.0%), 901,650 0x01 validators (97.7%), and 11,575 0x02 validators (1.3%). Following our convention (Section 2.4), we exclude 0x00 credentials from the analysis, yielding a 0x01/0x02 subset of 913,225 validators used in all subsequent figures and statistics.7 Fig 1 illustrates the broader staking landscape since Shapella, showing that 9.7M ETH (25% of total stake) has migrated to 0x02 credentials in the eleven months following Pectra. Fig 7 provides a detailed view of this adoption trajectory. The top panel tracks total ETH staked in 0x02 validators, whilst the bottom panel shows the number of 0x02 validators and their share of total staked effective balance. Adoption grew steadily, reaching
Sep 2025
0x02 Validator Adoption
Aug 2025
4.1
Jul 2025
Post-Pectra Empirical Analysis
Having established the theoretical framework and simulation results, we now turn to on-chain data from the Ethereum beacon chain to examine the realised performance and adoption patterns of 0x02 validators since the Pectra upgrade went live.
0 Jun 2025
4
0 May 2025
accumulated rewards; exit queues exceeded 45 days during September 2025 when Kiln withdrew 1.6M ETH [26]. For 0x02, partial withdrawal requests face similar constraints. In summary, the simulated APR uplift represents a lower bound for long-term holders. For operators requiring recurring distributions, the advantage may be smaller after accounting for gas costs and withdrawal delays. The following section examines these findings using on-chain data.
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Mohammed Benseddik, Benjamin Kraner, and Claudio J. Tessone
Figure 8: Consolidation requests since Pectra: daily volume (bars), cumulative total (solid line), and cumulative breakdown by type, multi-validator (blue) and self-consolidation (red). Data source: Dune Analytics [5].
When Staking Rewards Compound: Measuring the impact of Ethereum’s Pectra Upgrade
Self-Cons. 0.20M ETH (6,165 validators)
Multi-Val. 1.71M ETH (53,561->2,150 validators) 0x02 9.67M ETH (11,575 validators)
Solo Stakers
16 14 Pectra
Staked ETH (M)
0x01 1.91M ETH (59,726 validators)
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0x02
0x01
0x02
0x01
12 10 8 6 4 2 0
New Validators 7.76M ETH (~3,260 validators)
11,575 validators and approximately 25% of total effective balance by April 2026. This adoption pace, whilst accelerating, remains incomplete relative to the network’s scale. With 75% of staked ETH still on 0x01 credentials eleven months post-Pectra, the transition continues gradually. The following subsections examine who is adopting and through which mechanisms.
4.2
Validator Consolidation
EIP-7251 enables operators to merge multiple validators into a single 0x02 credential with effective balance up to 2,048 ETH [7]. Unlike new deposits, consolidation represents existing stake reorganisation, providing insight into how operators restructure fleets post-Pectra. Consolidation requests are 96-byte transactions sent to a predeploy contract at 0x00..7251, processed via a dedicated queue with source validators exiting through standard churn limits [11]. Fig 8 presents consolidation activity since Pectra launch. Daily volume averaged 186 requests per day across the observation period, but the cumulative curve reveals a clearly non-uniform pattern: activity remained low through the first ten months, then accelerated sharply in March 2026. Daily requests peaked at 3,343 in mid-March, and the three busiest days (3,343, 3,062 and 2,971 requests) all fell within that same month. Roughly half of the total 60,405 consolidation requests occurred in this final one-month window, more than doubling the 28,195 cumulative total observed through December
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Figure 9: ETH flow to 0x02 validators (Apr 7, 2026). Consolidation contributes 1.91M ETH (197k ETH from 6,165 self-consolidations, 1.71M ETH from 53,561 multi-validator merges into 2,150 targets), whilst new direct deposits contribute 7.76M ETH across 3,260 validators. Total 0x02 stake: 9.67M ETH across 11,575 validators. Data: Dune Analytics [5], beaconcha.in [1].
Staking Providers 35
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Figure 10: Staked ETH distribution by credential type for solo stakers (top) and staking providers (bottom) since Pectra launch. Solo stakers show higher 0x02 adoption relative to their stake, while staking providers remain predominantly on 0x01. Data source: Dune Analytics [17].
2025. Two modes emerge across the full period: multi-validator consolidation (merging multiple validators) dominates at 89.5% (54,049 requests), whilst self-consolidation (upgrading credentials without merging) accounts for 10.5% (6,356 requests). Fig 9 illustrates ETH flow to 0x02 validators. Consolidation contributes 1.91M ETH (20% of total 0x02 stake), whilst new deposits contribute 7.76M ETH (80%). With consolidation accounting for only 20% of the 9.67M ETH on 0x02, new deposits continue to dominate adoption. This suggests most 0x02 adoption comes from fresh capital rather than existing validators migrating. The dominance of multivalidator consolidation (89.5% of requests, 1.71M ETH) indicates that operators who migrate prioritise reducing management overhead by aggregating stake, whilst self-consolidation (10.5%, 197k ETH) captures the smaller share of pure credential upgrades.
4.3
Solo Stakers vs Staking Providers Adoption
The beacon-chain protocol does not record who operates each validator, so the “Solo Stakers” / “Staking Providers” split relies on an external attribution. We use the community-maintained Dune Analytics validator labels [17], which map individual validator indices
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Figure 11: Cumulative 0x02 ETH per staker category, decomposed into new deposits (green) and 0x01→0x02 migration (orange). Left y-axis: absolute ETH (M); right y-axis: same series as a share of total beacon-chain stake (%). Solo and Providers 0x02 reach 16.4% and 8.5% of the 38.8M ETH beacon stake respectively (25% total). Cut-off: 7 Apr 2026.
to known staking entities (Lido, Coinbase, Binance, Kraken, Rocket Pool, EigenLayer operators, exchange platforms, LSTs, and so on). A validator that appears in any labelled entity set is counted as a Staking Provider; any validator that does not appear in any labelled set is counted as a Solo Staker. This is a conservative solo-staker definition: it catches genuine home stakers but also absorbs any professional operator whose validators have not yet been tagged by the community, so the Solo count is a slight upper bound. We apply the same mapping throughout the paper, including in Fig 10, Fig 11, and the Mann-Whitney cohorts of Section 4.5. We then split 0x02 adoption by staker category (Fig 10, Fig 11) and decompose each category’s cumulative 0x02 stake into two components: new deposits (validators entering the beacon chain post-Pectra and defaulting to 0x02) and migration (pre-existing 0x01 stake converted via consolidation). The migration component is anchored to the 1.91M ETH Sankey total of Fig 9 (59,726 unique source validators × 32 ETH), so that the aggregate migrated ETH in Fig 11 exactly matches the real consolidation flow. Migration therefore accounts for only 1.91M ETH (19.8%) of the 9.67M ETH cumulative 0x02 stake, with the remaining 7.76M ETH (80.2%) coming from new direct deposits. New capital entering 0x02 dominates over conversion of existing 0x01 stake by a factor of four. At the category level, solo stakers hold 6.37M ETH of 0x02 (16.4% of the 38.8M ETH beacon stake) and staking providers hold 3.29M ETH (8.5%), summing to the 25% figure cited above. The two components follow very different trajectories in Fig 11. New deposits (green) grow steadily for both categories throughout the
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Mohammed Benseddik, Benjamin Kraner, and Claudio J. Tessone
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Figure 12: Effective balance distribution for 0x02 validators (left) and 0x01 validators (right), shown for all beacon chain validators (top), solo stakers (middle), and staking providers (bottom). Cut-off: 7 Apr 2026. Data sources: beaconcha.in [1] and Dune Analytics [17]. 333-day window, with a mild acceleration towards the cut-off but no sharp inflection. Migration (orange) instead plateaus for most of the observation window (the cumulative line is nearly flat from mid-2025 through February 2026) before a late uptick in March 2026 that is visible in both subplots and coincides with the consolidationevent burst already noted in Fig 9.
4.4
Effective Balance Distribution
Beyond adoption rates, understanding how stake concentrates within 0x02 validators reveals distinct consolidation behaviours. Fig 12 presents effective balance distributions for 0x02 validators (left) and 0x01 validators (right), segmented by validator type. The 0x02 distribution exhibits a bimodal pattern: approximately 30% cluster at low balances (32–64 ETH), representing recently migrated validators, whilst 40% concentrate above 1,024 ETH, reflecting aggressive consolidation. Solo stakers show a broader spread (mean 842 ETH), consistent with organic accumulation over time. Staking providers display a similar mean balance (815 ETH), with validators concentrated either at entry-level or near the 2,048 ETH cap. This bimodal pattern suggests two distinct migration strategies: some operators upgrade credentials without consolidating, whilst others aggressively merge validators to reduce operational overhead.
When Staking Rewards Compound: Measuring the impact of Ethereum’s Pectra Upgrade
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Table 4: CL APR medians by credential type. Δ is the relative median difference. The 30-day row uses the cl_31d accumulator (raw, covers 89% of 0x02 stake); the 335-day row covers the full post-Pectra era (7 May 2025 → 7 Apr 2026) via the timeadjusted 365-day accumulator, 5/95 winsorised to remove lower-tail annualisation noise from recent-deposit validators (same cohort as the Mann-Whitney test in Table 5).
2.25 ± 1.09 2.52 ± 0.92 +12.3% 10,763 8.65M ETH 2.61 ± 0.27 2.65 ± 0.22 +1.5% 11,395 9.37M ETH
Empirical Validator Performance
We analyse APR data from 913,225 active validators (901,650 0x01 and 11,575 0x02) ending 7 April 2026 [1], matching the 0x01/0x02 subset introduced in Section 4. beaconcha.in exposes per-validator reward accumulators for four fixed rolling windows (1, 7, 31 and 365 days). To assess whether the compounding advantage is sustained over longer horizons (R2.5), we use the two that map cleanly onto these accumulators: a 30-day window (from the 31-day accumulator) and a 335-day window corresponding to the exact postPectra era (7 May 2025 → 7 Apr 2026). For the 335-day window we use a time-adjusted annualisation of the 365-day accumulator, APR = (cl365𝑑 /𝐵 eff ) × 365/min(𝑑, 365), where 𝑑 is the validator’s days of active history; we require 𝑑 ≥ 7 to avoid extreme extrapolation. Fig 13 presents the APR distributions for both windows and Table 4 summarises medians. CL APR here sums the attestation baseline (≈ 2.24%/yr at 38.8M ETH staked) with proposer and sync-committee rewards, so the pervalidator distribution has a long right tail driven by proposer luck and sync-committee selection; an “average” 0x01 validator earns approximately 2.61% once annualised over 365 days.8 Our simulations predicted a +4.7% relative CL APR uplift for small balances (32–2,048 ETH), decreasing to +0.3% for large operators (Table 3). We now compare these predictions against the empirical record, first descriptively at the two time horizons and then via a formal hypothesis test on the long-horizon window. 30-day window. Over the most recent 30-day window, 0x02 validators show an aggregate CL APR advantage of +12.3% relative to 0x01 (median 2.525% vs 2.249%), but this advantage is highly uneven across staker types: solo stakers show a +13.9% uplift (median 2.561% vs 2.248%), whilst staking providers are essentially at parity with the attestation baseline (+1.1%; 2.274% vs 2.249%). The 30-day cohort covers 10,763 of the 11,575 active 0x02 validators and represents 8.65M ETH out of the 9.67M ETH total 0x02 stake, so these statistics reflect essentially the full 0x02 population. The 0x02 distribution is notably wider than 0x01 (std 0.92% vs 1.09%) because 8 Full component breakdown: (i) attestation rewards each epoch for voting on source,
target and head, providing the ≈ 2.24% baseline; (ii) proposer rewards, equal to 1/8 of the attestation rewards in the block, earned roughly ∼ 2.85 times per year per validator at 921k active validators; (iii) sync-committee rewards, earned during a ∼27-hour slot every 256 epochs by 512 randomly-chosen validators (roughly once every six years per validator in expectation).
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Figure 13: CL, EL, and Total APR distributions for 0x01 (red) and 0x02 (blue) validators, broken down by validator type. “30d” uses the 31-day reward accumulator (raw); “335d” (the full post-Pectra era, 7 May 2025 → 7 Apr 2026) uses the 365day accumulator time-adjusted to each validator’s observed history (≥7 days) and 5/95 winsorised within each group, matching Table 4 and the Mann-Whitney test cohort. Cut-off: 7 Apr 2026 [1].
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Mohammed Benseddik, Benjamin Kraner, and Claudio J. Tessone
Table 5: Mann-Whitney 𝑈 test of 335-day CL APR, 0x02 vs 0x01, by cohort. Δmed is the raw median difference (0x02−0x01) in percentage points; 𝑝 is the two-sided MannWhitney 𝑈 𝑝-value. All three cohorts reject 𝐻 0 at 𝛼 = 0.05. Cut-off: 7 Apr 2026.
med 0x02 = 2.651% med 0x01 = 2.611%
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Figure 14: Overlaid histograms of 335-day CL APR for 0x01 (red) and 0x02 (blue), both winsorised at the 5/95 percentiles; dashed vertical lines mark the per-group medians. The 0x02 distribution is slightly right-shifted of the 0x01 baseline. Both distributions are markedly non-Gaussian and carry heavy right tails driven by proposer-reward and sync-committee excursions (the raw 0x01 distribution has excess kurtosis of +10.9, an order of magnitude above a Normal).
proposer-reward luck over a 31-day window produces large pervalidator variance. The observed solo uplift (+13.9%) exceeds the simulated prediction (+4.7% for 32–2,048 ETH). The mechanism is proposer-reward variance, not compounding: solo 0x02 validators are disproportionately consolidated to higher effective balances (𝐵 eff median 480 ETH in the 30-day cohort), so their proposer selection probability (which is proportional to effective balance) is roughly 15× that of a 32 ETH validator, and a lucky month of block proposals lands them on the right tail of an already heavy-tailed rewards distribution. The direct proof of this interpretation is the convergence at longer horizons: the +13.9% solo lead collapses to +1.5% at 335 days (Table 4). A genuine compounding gap would persist or grow with time; a proposer-variance gap averages out, which is exactly what the data show. 335-day (full post-Pectra era) window. A naive “last 365 days” filter would only cover the ≈20% of 0x02 stake that belongs to validators activated before Pectra, because Pectra is only ≈11 months old and fresh-deposit 0x02 validators do not yet have a full year of history. To avoid that bias, we use the longest window the data actually spans (335 days, the exact gap between Pectra activation and the snapshot cut-off) and annualise each validator’s own observed history by scaling the 365-day accumulator by 365/min(𝑑, 365) (with 𝑑 the days of active history and 𝑑 ≥ 7). For a validator active only a few days, 𝑑 is tiny and the scaling factor 365/𝑑 is correspondingly large (e.g., 𝑑 = 10 gives a factor of 36.5): tiny fluctuations in the raw reward accumulator are amplified into large per-validator APR swings, and a disproportionate share of recent 0x02 deposits end up in the left tail of the empirical distribution. To keep these scaling artefacts from dominating the per-cohort medians, we apply
2.611 2.611 2.612
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a 5/95 winsorisation within each group before reporting any statistics (Table 4, 335d row). Once we average over each validator’s full observed history and winsorise, the 30-day advantage shrinks dramatically: 0x01 median CL APR settles at 2.61% (vs. 2.25% at 30 days) as proposer-reward luck averages out, and 0x02 settles at 2.65%, a small +1.5% relative gap rather than the inflated +12.3% 30-day lead. The 30-day figure was a short-window variance artefact: high-𝐵 eff validators (disproportionately 0x02) have a higher proposer-selection probability, and in a 31-day window the proposer-reward component dominates any compounding-related signal. Over longer horizons the proposer component averages toward its expectation for every validator, and the distributions converge onto a small residual 0x02 advantage. We formalise the 335-day comparison with a rank-based hypothesis test on three cohorts 𝑐 ∈ {All, Solo, Providers}: 𝐻 0(𝑐 ) states that the 335-day CL APR distributions of 0x02 and 0x01 validators are identical, and 𝐻 1(𝑐 ) (two-sided) that they differ, tested at 𝛼 = 0.05. Picking the right test comes down to the shape of the two underlying samples. A Student 𝑡-test assumes approximately Normal samples and a common variance, and its Welch variant relaxes the common-variance assumption but still relies on near-Normal distributions. Neither holds here: the raw 0x01 distribution carries a long right tail from the lumpy proposer-reward and synccommittee components of CL APR, and even after 5/95 winsorisation it retains a positive skew of +0.50 (Fig 14). A Shapiro-Wilk normality test on the winsorised 0x01 sample rejects the Normal null decisively (𝑊 = 0.957, 𝑝 ≈ 3.8 × 10−36 ). On top of that, the 335-day 0x02 sample has a much larger spread than 0x01 before winsorisation, as the time-adjusted annualisation factor amplifies reward-accumulator noise on recent deposits. We therefore use the two-sided Mann-Whitney 𝑈 (Wilcoxon rank-sum), a nonparametric test that operates on the joint ranks of the two samples and tests the null hypothesis Pr(𝑋 0x02 > 𝑋 0x01 ) = Pr(𝑋 0x01 > 𝑋 0x02 ) without any distributional assumption. With 𝑛 0x01 in the 105 –106 range the test has enormous statistical power, which is exactly the regime in which one needs to separate the two questions a hypothesis test mixes together: is there a real difference and how large is it. We rely on the 𝑝-value for the first question, as a binary rejector-accept flag on the null, and on the per-cohort median difference Δmed = med0x02 − med0x01 (in percentage points) as the effect-size statistic that quantifies the magnitude of the shift, since with samples this large the 𝑝-value alone saturates for any non-negligible effect. Table 5 and Fig 15 report the results. At 𝛼 = 0.05, 𝐻 0 is rejected in all three cohorts:
When Staking Rewards Compound: Measuring the impact of Ethereum’s Pectra Upgrade
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Δmed = +0.039 pp p = 1.8×10-12 n02 = 11,395
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Figure 15: 335-day CL APR distributions for 0x01 (red) and 0x02 (blue) by cohort. Box statistics are winsorised at the 5/95 percentiles; each panel reports the median difference Δmed = med0x02 − med0x01 , the Mann-Whitney 𝑈 𝑝-value, and 𝑛 02 . • All Validators: Δmed = +0.039 pp, 𝑝 = 1.8×10−12 ≪ 0.05 ⇒ reject 𝐻 0 . • Solo Stakers: Δmed = +0.039 pp, 𝑝 = 2.0×10−3 < 0.05 ⇒ reject 𝐻 0 . • Staking Providers: Δmed = +0.040 pp, 𝑝 = 8.8×10−6 ≪ 0.05 ⇒ reject 𝐻 0 . The direction is positive in every cohort: the 335-day CL APR of 0x02 is stochastically higher than 0x01 by +0.04 pp in absolute terms (about +1.5% relative), so 𝐻 1 is supported throughout. This gap is about one-third of the +0.13 pp uplift (+4.7% relative) our simulation predicts for a 32–2,048 ETH validator in Section 3.4. The remaining two-thirds are consistent with a compounding mechanism operating on a multi-year horizon that 11 months of post-Pectra data have only begun to sample: at current ∼2.25% yield, a 32 ETH validator needs ∼193 days to trigger its first effectivebalance increment, and most 0x02 validators have not yet crossed this threshold naturally. A reassessment after 2–3 years, or under the accelerated hysteresis proposed in EIP-8068 [10], would better capture organic compounding. Putting everything together, the empirical record directionally confirms the simulation’s prediction that 0x02 compounding validators outperform 0x01 on CL APR: we observe a small but statistically significant positive shift in every cohort we tested, matching the sign and qualitative behaviour of Section 3.4. Quantitatively, however, the empirical uplift is only about a third of the simulated multi-year steady-state: +0.04 pp (+1.5%) in the 335-day window against the simulation’s +0.13 pp (+4.7%). This is a partial match rather than a full one, and the size of the gap is exactly what the hysteresis-dominated compounding mechanism predicts for an 11-month observation window. The simulation and the data are therefore not in tension; they describe the same effect at different points in its accrual trajectory, and the residual two-thirds are a prediction about the next two to three years rather than a missing effect in our measurement.
Limitations
Our findings are subject to several limitations. The simulation assumes a fixed total network stake of 38.8M ETH and a participation rate of 96–99%, and excludes proposer rewards, which may affect the absolute APR levels. The empirical analysis uses two observation windows: a 30-day window (from the cl_31d reward accumulator) and a 335-day window corresponding to the full post-Pectra era (Pectra: 7 May 2025 → cut-off: 7 April 2026 = 335 days), time-adjusted via the 365-day accumulator. The 335-day window is already the longest observation period the data permit, but 335 days is still a short horizon for a compounding mechanism whose first effective-balance increment under current hysteresis rules takes ∼193 days at 2.25% yield. A reassessment after 2–3 full years post-Pectra would be needed to observe the full simulated uplift directly; however, the mechanism itself is likely to change before then (Section 6), so any follow-up will need to rebaseline against the new rules. Additionally, early adopters of 0x02 withdrawal credentials may represent more sophisticated operators, introducing potential selection bias; this concern is mitigated but not eliminated by the growing sample (11,575 0x02 validators versus 901,650 0x01, total 913,225 in the analysis subset). Validator classification further relies on heuristic tagging from the Dune validator tags dataset, and misclassification, particularly of solo stakers, cannot be ruled out. Finally, 0x02 validators received a higher number of block proposals during the 30-day measurement window, inflating the short-horizon CL APR gap with proposer rewards that are independent of compounding; this is the reason we restrict the formal hypothesis test in Section 4.5 to the 335-day window.
6
Conclusion
This paper quantified the performance implications of 0x02 compounding validators introduced by EIP-7251. Simulations show +4.7% relative CL APR uplift for small balances (32–2,048 ETH), diminishing to +0.3% for large providers. The formal 335-day hypothesis test over the full post-Pectra era confirms a small but statistically significant 0x02 advantage across all three cohorts (All, Solo, Providers), with median CL APR differences of +0.04 pp (≈ +1.5% relative). The observed magnitude is about one-third of the simulated multi-year prediction, consistent with the hysteresisdominated compounding mechanism being truncated by the 11month observational window. Despite theoretical benefits, adoption has reached 25% of staked ETH (9.7M ETH) eleven months post-Pectra, with new deposits flowing into 0x02 and 0x01→0x02 migration plateauing for most of the observation window before a late uptick in March 2026: both cumulative new 0x02 deposits and consolidation requests accelerate in the final month of our data, visible in Fig 11 and Fig 8. 0x02 validators must explicitly request partial withdrawals (inducing gas fees) to access accumulated rewards, whilst 0x01 validators receive automatic sweeps of excess balance to their withdrawal address, using it as liquid cashflow. Staking providers designed their systems for fixed 32ETH balances with automatic reward sweeps, and adapting to compounding yet locked rewards requires significant software changes. The small observed differences are not surprising: over short time horizons, compounding has little effect
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as balance hysteresis delays when rewards increase a validator’s effective balance, only taking effect once the 33.25 ETH threshold is crossed. This reduces the immediate benefit of switching to 0x02, making the change less urgent for most solo stakers. Faster balance updates, for example through adjustments to the hysteresis mechanism, could encourage earlier adoption. Even so, we observe some solo stakers switching to 0x02 early, effectively taking a long-term view on compounding rewards. In contrast, large institutional stakers are less inclined to switch to 0x02 credentials under the current rules, where compounding is effectively the only incentive on offer. As shown in our simulations, the depth of their staking pools already lets them capture a compounding-like effect by activating new validators with earned rewards, which largely offsets the marginal benefit Pectra’s in-place compounding would add. On top of that, 0x02 introduces operational drawbacks for large operators: rewards are no longer swept automatically, so partial withdrawals become a recurring software and cost item, and the locked-balance regime limits their ability to reallocate capital under the current hysteresis rules [10]. Section 6 discusses the draft EIPs (EIP-8068, EIP-8062, EIP-7804) that would address each of these frictions in turn and tilt the cost-benefit calculation towards migration for this cohort. Ethereum’s motivation for 0x02 is reducing validator count to improve network efficiency, as the legacy 32 ETH cap creates congestion disproportionate to actual staked ETH. The approach favours organic migration by making 0x02 attractive rather than penalising 0x01. However, without significant APR uplift and consistent reward withdrawals, the economic case remains weak for both solo stakers and providers. Ongoing discussions between core developers and staking providers [9] continue to explore solutions balancing network efficiency goals with staker economics.
Upcoming Protocol Changes. Several draft EIPs under active discussion by Ethereum core developers would materially alter the 0x02 incentive structure analysed in this paper, and can be read as a direct response to the slow adoption pace documented here. EIP-8068 [10] addresses the hysteresis inefficiency at the core of our findings: it reduces the upward threshold from +1.25 ETH to +0.5 ETH and rounds the effective balance to the nearest integer, cutting the time to the first effective-balance increment from ∼193 days (our simulation) to ∼80 days. This would significantly strengthen the compounding advantage and accelerate the timeline for observing it empirically. EIP-8062 introduces a 0.05% fee on automatic reward sweeps for 0x01 validators, adding a cost to remaining on legacy credentials that would directly shift the cost-benefit equation for migration. EIP-7804 defines a new 0x03 request type enabling validators to update their withdrawal credentials without exiting and re-entering the validator set, removing a key friction point for migration. Together, these proposals signal a deliberate shift toward making 0x02 more attractive (EIP-8068), making 0x01 less attractive (EIP-8062), and reducing migration friction (EIP-7804). If adopted, these changes would likely accelerate 0x02 adoption beyond the current 25% share. Additionally, EIP-8071 addresses an exploit where the consolidation queue was used to bypass exit queues, which may explain some of the consolidation spikes in our
Mohammed Benseddik, Benjamin Kraner, and Claudio J. Tessone
data. Future research could reassess adoption dynamics and measure the realised compounding benefit after these protocol changes take effect.
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NBC 2026, August 21–22, 2026, Zurich, Switzerland
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