Source-linked AI summary
Quantifying Price Improvement in Order Flow Auctions
Brad Bachu, Xin Wan, Ciamac C. Moallemi
TL;DR
Empirical validation of order flow auction benefits has remained limited because blockchain technology and financial-market dynamics are difficult to integrate analytically. The paper develops an open-source framework for defining price improvement, generating counterfactual prices, internalizing gas costs, and attributing outcomes to controllable OFA inputs. Dutch auction-based OFAs yield an average price improvement of 4 to 5 basis points for users.
Problem
Empirical validation of order flow auction benefits has remained limited because blockchain technology and financial-market dynamics are difficult to integrate analytically.
Source: §1 · p. 1Method
Results
Dutch auction-based OFAs yield an average price improvement of 4 to 5 basis points for users.
Source: §1 · p. 3Takeaways & Limitations
The framework provides granular evidence about OFA execution quality and identifies increased liquidity and optimized routing as key contributors for larger trades.
Source: §1 · p. 3The analysis’s major systematic uncertainty comes from estimating gas costs.
Source: §4.6 · p. 13
Abstract
from arXiv · showhide
This work introduces a framework for evaluating onchain order flow auctions (OFAs), emphasizing the metric of price improvement. Utilizing a set of open-source tools, our methodology systematically attributes price improvements to specific modifiable inputs of the system such as routing efficiency, gas optimization, and priority fee settings. When applied to leading Ethereum-based trading interfaces such as 1Inch and Uniswap, the results reveal that auction-enhanced interfaces can provide statistically significant improvements in trading outcomes, averaging 4-5 basis points in our sample. We further identify the sources of such price improvements to be added liquidity for large swaps. This research lays a foundation for future innovations in blockchain based trading platforms.
1. Introduction
The paper introduces an open-source framework for measuring and attributing price improvement in order flow auctions, addressing limited empirical validation of their benefits. Applied to 1Inch and Uniswap, it finds positive execution effects and identifies liquidity, routing, and gas-related contributors.
Empirical Application
- The study evaluates 1Inch and Uniswap on Ethereum mainnet, establishing an initial comparison of interfaces that use similar price-improvement mechanisms.Other batch-auction and rebate interfaces require special treatment for a consistent baseline and are left for future work.Source: §1 · p. 2
Price Improvement Definition And Computational Framework
- The paper introduces a generalizable price-improvement framework based on the difference between realized and counterfactual swap prices, with open-source procedures for generating counterfactuals.The framework is designed to compare different OFA implementations consistently.Source: §1 · p. 2
Methodology For Gas Cost Internalization
- Gas internalization incorporates gas costs into execution prices and addresses bias in simulated same-block transactions while exposing more granular trade-off variation than average or median benchmarks.The method targets a literature gap in statistically precise treatment of gas costs in execution-quality assessments.Source: §1 · p. 2
Price Improvement Attribution Model
- A Taylor Series attribution model maps price improvements to controllable inputs, and empirical results show minimal non-attributable differences for the studied interfaces.The model is intended to give OFA implementers direct optimization insights.Source: §1 · p. 2
Empirical Application
- 4–5 basis points: Dutch auction-based OFAs yield average price improvement across trade sizes, although smaller trades can be statistically indistinguishable from zero.The empirical application evaluates leading Ethereum OFA interfaces and finds statistically precise execution-quality differences.Source: §1 · p. 3
- Price improvement increases for larger trades primarily through added liquidity and optimized routing, while smaller trades benefit mainly from efficient gas usage and lower-gas-cost pools.The attribution differs by trade size, linking large-trade gains to liquidity access and routing and small-trade gains to gas efficiency.Source: §1 · p. 3
2. Literature Review
Prior literature studies execution quality through costs, speed, market structure, routing, and liquidity, but lacks a framework and empirical comparison for onchain trading platforms. This paper addresses that gap by comparing economically consistent outcomes across OFA implementations while incorporating transaction gas costs.
Market structure and routing
- Empirical work links execution quality to market structure changes, investor trading skills, order handling rules, tick sizes, and brokerage routing decisions.The cited literature includes evidence from NYSE and NASDAQ markets before and after decimal pricing and related regulatory changes.Source: §2 · p. 3
Execution quality
- Existing research treats execution quality as multidimensional, covering execution costs, speed, and trade-offs between them.Studies also examine quoted, effective, and realized spreads, whose reported values can depend on measurement techniques.Source: §2 · p. 3
Price improvement
- Price improvement is used to assess execution by comparing executed prices with quoted prices, including effects associated with payment for order flow, negotiations, dealer reputation, and market power.Related models also consider consequences for liquidity, trader welfare, and broker-dealer price competition.Source: §2 · p. 4
Onchain markets
- Cryptocurrency execution-cost research examines Uniswap spreads, just-in-time liquidity, and trade-offs in OFA design.These studies connect liquidity provision with individual-trade execution quality, displayed liquidity, and overall execution costs.Source: §2 · p. 4
Research gap
- The literature does not provide a theoretical framework or empirical comparison of execution quality across onchain trading platforms and interfaces.Such comparisons must remain economically consistent across order-flow auction implementations and include all factors affecting net trading outcomes, especially transaction gas costs.Source: §2 · p. 4
Contribution
- This paper aims to bridge that gap through a framework and empirical analysis for comparing onchain trading outcomes while accounting for transaction costs.The contribution is positioned as a response to the need for economically consistent comparisons across OFA implementations.Source: §2 · p. 4
3. Theoretical Framework
This section presents a framework for standardizing and decomposing price improvement across OFAs, accounting for gas costs, counterfactual baselines, settlement-time offsets, routing, and priority fees. It also addresses tradeoffs among added liquidity, transaction costs, and execution speed under stated Ethereum trading assumptions.
3. Theoretical Framework
- The framework standardizes OFA price comparisons by accounting for differing gas-payment arrangements and restricting transactions to those involving ETH or WETH.This enables uniform price definitions whether users or fillers/solvers bear gas costs, covering approximately 90% of Ethereum mainnet DEX trades.Source: §3 · pp. 4–5
3.1. Price
- Price incorporates output and input amounts, and for non-internalized gas also gas used, base fee, and priority fee.Under fixed input, block, and base-fee conditions, the OFA-manipulable variables are output amount o, gas used g, and priority fee f, collected as x = (o, g, f).Source: §3.1 · p. 5
3.1.1. Example - Price In Transactions With Gas Cost
- When users pay gas in ETH, price is based on net balance changes, so gas is added to ETH input or subtracted from ETH output.If ETH output is smaller than gas cost, the resulting price can be negative because both token balances decrease.Source: §3.1.1 · p. 6
3.1.2. Example - Price In “Gas-free” Transactions
- In gas-free Permit2 transactions, a filler pays gas, receives the input tokens as compensation, and the user’s price uses only net output and input balance changes.The user’s wallet shows no gas-token balance change, making price the negated ratio of output increase to input decrease.Source: §3.1.2 · p. 6
3.1.3. Example - Price In Transactions With Potential MEV Rebate
- With potential MEV rebates, the effective gas cost is reduced by the rebate and may become negative, so pricing adjusts traditional gas-cost calculations accordingly.MEV Share and MEV Blocker return potential rebates through ETH transfers.Source: §3.1.3 · p. 6
3.2. Price Improvement
- Price improvement π is the relative difference between realized price p and a baseline price p′ generated from a counterfactual vector x′.The primary baseline uses Uniswap Classic’s routing API with historical state data to approximate what a typical user could achieve without the OFA.Source: §3.2 · pp. 6–7
3.3. Price Improvements Across Time
- The framework evaluates price improvement at settlement and across offsets Δt from settlement to assess execution speed, selection bias, transient blockchain effects, and transaction-ordering sensitivity.Setting Δt = 0 recovers settlement-time improvement, while multiple offsets compare alternative arrival, execution, and ordering counterfactuals.Source: §3.3 · pp. 7–8
3.4. PI Attribution
- Price improvement is decomposed into πrouting, πgas, and πfee, representing gains from liquidity access, reduced gas usage, and lower priority fees.This decomposition makes the aggregate metric more interpretable across systems.Source: §3.4 · p. 8
- Route selection balances added liquidity against gas costs, because each additional liquidity source can increase transaction expenses and offset routing gains.πrouting captures improvement from using more liquidity than the baseline.Source: §3.4 · p. 8
- Priority-fee recommendations can reduce price improvement when higher fees offset gains from efficient trading and routing, while πfee measures improvement from paying less than baseline.Under EIP-1559, interfaces may recommend fees above zero to pursue faster execution despite the potential cost.Source: §3.4 · p. 9
- The attribution method Taylor-expands p(x) to estimate leading-order contributions, while retaining a remainder term that may not always be small.For gas-internalizing OFAs, onchain data can recover pre-transaction-fee output and support attribution.Source: §3.4 · p. 9
4. Methodology
This methodology evaluates leading OFA interfaces and their conventional and auction-based settlement paths using counterfactual simulations, historical trade data, gas calibration, and uncertainty analysis. It quantifies statistical and systematic uncertainty while documenting limitations related to gas-estimation accuracy and simulation assumptions.
4.1. Sample Interfaces
- The study evaluates the 1Inch and Uniswap interfaces, each of which separates conventional aggregation from auction-based settlement paths.Uniswap uses Uniswap Classic and UniswapX, while 1inch uses 1inch Aggregator and 1inch Fusion.Source: §4 · p. 9, §4.1 · p. 10
4.2. Selection of Baseline
- The empirical baseline simulates the same swap through the Uniswap open-source routing API at the end of the settlement block using Tenderly.This baseline preserves onchain execution conditions and supports comparisons involving routing, gas, and priority fees.Source: §4.2 · pp. 10–11
4.3. Data Collection
- The dataset collects input amount, output amount, gas used, base fee per gas, and priority fee per gas for WETH-USDC trades in November and December 2023 using Dune Analytics.Source: §4.3 · p. 11
- Fusion and UniswapX are the dominant settlement paths for 1Inch and Uniswap, respectively, with concentration more pronounced by USD volume.The passages attribute this pattern to OFA systems integrating more liquidity sources and providers, particularly for large trades.Source: §4.3 · p. 12, Table 1 · p. 12
4.4. Baseline Gas Corrections
- Baseline gas estimates can differ systematically from actual gas use, so the method regresses estimated gas on actual gas and corrects counterfactual estimates by g′ ←g′/β1.The analysis parameterizes uncertainty because bottom-of-block simulation and intra-block execution prevent exact alignment.Source: §4.4 · p. 12
4.5. Uncertainty Analysis
- The uncertainty analysis distinguishes statistical σstat and systematic σsys contributions for the evaluated metrics.The supplied passage states that these are the two significant uncertainty contributions.Source: §4.5 · p. 13
- Statistical uncertainty is computed as the weighted standard error of the weighted mean, while gas-estimation uncertainty is propagated asymmetrically from the Figure 1 fit parameter δβ1.The systematic uncertainty on the gas estimate derives entirely from gas estimation and is evaluated by varying gas by δβ1.Source: §4.5 · p. 13
4.6. Uncertainty and Limitations
- The major uncertainty source is gas estimation because observed points do not consistently follow gas estimate = gas used, partly after changes to the simulation algorithm.This systematic uncertainty comes entirely from gas estimation.Source: §4.6 · pp. 13–14
- The simulation omits intra-block dynamics and can include transaction-induced front-running when replaying Uniswap pools, motivating consistent routing, intra-block simulation, and transaction removal before simulation.These are identified as planned approaches for addressing the methodology’s limitations.Source: §4.6 · p. 14
5. Results
Across interface-level comparisons, Uniswap and 1Inch deliver significantly positive price improvement, with gains increasing for larger trades and arising mainly from added liquidity through better routing.
Interpretation and scope
- Settlement-path comparisons are affected by selection bias and offset sensitivity, so users cannot directly expect path-level sample performance without changing interface defaults.The authors select offset 0 for further analysis because it is the most optimistic choice.Source: §5 · p. 15
Interface-level results
- 4.6 basis points for Uniswap and 4.3 basis points for 1Inch measure significantly positive interface-level price improvement at offset zero.The result remains robust across settlement-block offsets and exceeds the common baseline.Source: §5 · p. 15
- Uniswap and 1Inch interfaces significantly outperform the common baseline across all eight offsets, with Uniswap generally higher except from offsets -4 to -1.Interface-level aggregation addresses selection bias from settlement-path recommendations.Source: §5 · p. 15
Trade-size analysis
- For median trade sizes below $25k, price improvement is noisy; as size rises, it stabilizes positively, reaching almost 4 basis points for Uniswap near $200k.1Inch stabilizes around 2 basis points over the larger-size range.Source: §5 · p. 15
Attribution analysis
- Most price improvement for both interfaces comes from better routing, interpreted as access to additional liquidity sources and providers.Corrections are small for 1Inch Aggregator and Uniswap Classic, supporting the attribution approximation in those paths.Source: §5 · p. 16
- Relative to Uniswap Classic, 1Inch Aggregator incurs small but non-zero gas overhead, translating to roughly 0.5-1 basis points of degradation in execution quality.For OFAs, correction terms are economically interpretable as interactions between gas efficiency and priority fee.Source: §5 · p. 16
Trade-size attribution
- For large trades, routing contributes consistently 3-4 bps of price improvement, while nonlinear gas-priority-fee interactions contribute materially for UniswapX and 1Inch Fusion.The nonlinear corrections are higher for these OFA paths than for Uniswap Classic and 1Inch Aggregator.Source: §5 · p. 17
6. Outlook
The framework is presented as a proof of concept for analyzing and optimizing onchain order flow auctions by attributing gains to modifiable components. Future work targets broader mechanisms, nonlinear corrections, and larger empirical coverage.
Contribution
- The framework attributes performance gains to routing efficiency, gas optimization, and priority-fee adjustments, enabling analysis and optimization of OFA systems.Its stated contribution is a model focused on price improvement.Source: §6 · p. 17
Scope
- The methodology is particularly suited to OFAs that internalize gas costs, including 1Inch Fusion and UniswapX.Refining nonlinear corrections is intended to deepen analysis of transaction-cost management.Source: §6 · p. 17
Extensions
- The framework could extend to batched auctions such as COW Swap and rebate systems such as MEV Share.Future analyses would internalize batch gas costs or examine price improvement from mechanisms such as back-running.Source: §6 · p. 18
Future evaluation
- Extending empirical analysis to more OFA systems would help guide users toward efficient platforms.The paper frames this as a direction for future community research rather than a completed evaluation.Source: §6 · p. 18
A. Price Details
The price construction distinguishes realized and counterfactual prices according to whether gas is internalized, while routing and gas-adjustment calculations produce comparable swap outputs.
Price construction
- The framework defines price and price improvement consistently across OFAs and evaluates improvement at settlement time as well as across offsets.This supports comparisons under different gas-internalization configurations.Source: A. Price Details · p. 20
- Realized-price computation differs between systems without gas internalization—Uniswap Classic and 1Inch Aggregator—and systems with internalization—UniswapX and 1Inch Fusion.The corresponding counterfactual calculations likewise use gas-adjusted treatment when gas is internalized.Source: A. Price Details · p. 20
- The routing process estimates available input after gas payment and uses it to generate a token-out estimate.The calculation accounts for gas g′(b + f′) before estimating output.Source: A. Price Details · p. 20
B. Simulation Process
The simulation pipeline builds reproducible counterfactual baselines by routing each realized swap across nearby blockchain states, formatting calldata, and executing it in Tenderly with fixed priority fees.
Route calculation
- For each completed swap, the routing API seeks the best exact-input route using blockchain states from several blocks before and after settlement.This offset range provides a robustness check against nearby state variation.Source: B. Simulation Process · p. 21
Route identification
- The API evaluates available liquidity and TVL, selects an output-maximizing route net of gas, and formats it as executable calldata.It also supplies an estimate of transaction gas costs.Source: B. Simulation Process · p. 21
Simulation
- Tenderly simulates the generated calldata at the specified block with a fixed 0.1 Gwei priority fee.The simulator returns token output, gas consumed, and related execution metadata.Source: B. Simulation Process · p. 21
- The resulting baseline is intended to represent optimal outcomes under varying blockchain states while remaining robust and reproducible for OFA comparisons.This baseline supports evaluation of different order flow auction implementations.Source: B. Simulation Process · p. 21