From AMM to Order Book: Interpreting the Shift in Polymarket's Pricing Mechanism and the Possibility of Integration with DEX

Author: @BlazingKevin_, the Researcher at Movemaker

In Polymarket, each prediction market is essentially a "probability exchange for future events," where users can express their judgment on an event by buying a certain option (such as "Trump will win the 2024 U.S. presidential election").

The buying of probabilistic events is different from common trading, so the pricing and liquidity mechanisms initially used by Polymarket are also different from the common AMM algorithms. The pricing mechanism of Polymarket has undergone significant changes from its initial version to the present, initially adopting an AMM mechanism to provide liquidity and pricing in real-time, called the logarithmic market scoring rule, abbreviated as LMSR. This algorithm is currently also used by some other crypto protocols, such as Ethos.

Understanding the characteristics of LMSR allows one to comprehend Polymarket's pricing mechanism during most periods, as well as the reasons other protocols choose LMSR, and also understand why Polymarket upgraded from LMSR to an off-chain order book.

Characteristics, Advantages, and Disadvantages of LMSR

What is LMSR?

LMSR is a pricing mechanism specifically designed for prediction markets, allowing users to buy "shares" of a particular option based on their judgment, while the market automatically adjusts prices according to total demand. The most notable feature of LMSR is that it allows transactions to be completed without reliance on a counterparty; even if you are the first trader, the system can price and execute the trade for you. This gives prediction markets a similar "perpetual liquidity" to Uniswap.

In simple terms, LMSR is a cost function model that calculates prices based on the "shares" of various options currently held by users. This mechanism ensures that prices always reflect the expected probabilities of different event outcomes in the current market.

The core formula of LMSR

The cost function C of LMSR is calculated based on the number of shares sold for all possible outcomes in a market. The formula is:

The symbols here represent:

C(…): Cost function, representing the total cost incurred by the market maker to maintain the distribution of shares for all current outcomes.

n: The total number of possible outcomes in the market (for example, for a "yes/no" market, n=2).

qi: Indicates the current purchased share of the i-th option (which can be understood as "voting power" or "betting amount")

b: is a liquidity parameter, the larger it is, the more "stable" the market is, and the less sensitive the price is to new trades.

C(q): Represents the cost to change the market from its current state to q.

The most important feature of this formula is that the sum of the prices of all outcomes is always equal to 1(∑Pi=1). When a user purchases a "YES" share, $q(YES) increases, leading to P(YES) rising, while P(NO) decreases, thereby maintaining the total price sum at 1.

How is the pricing generated?

Another key point of LMSR is that the price is the marginal derivative of the cost function. That is, the price pi of the i-th option is the marginal cost you must pay to buy one more unit of that option:

This means:

If the purchase volume of a certain option increases (that is, more people bet that it will happen), its price will gradually rise;

The final price will tend to reflect the market's subjective probability of each option occurring.

For example, in a "yes/no" prediction market, if most people buy "yes," then the price of "yes" may rise to 0.80, while "no" drops to 0.20, which is like saying "the market believes the probability of the event occurring is 80%."

In addition, regardless of the type of liquidity, the curve of the cost function extends upward. This means that the more shares purchased, the higher the total cost that needs to be paid.

The role of the liquidity parameter b: The size of the b value directly determines the "smoothness" of the curve, which is the liquidity or "thickness" of the market.

High liquidity ( The left image, b=100): The curve is relatively flat. This means that even if you purchase a large number of shares, the speed of price increase is relatively slow. Such a market can "absorb" large transactions without causing significant price fluctuations.

Low liquidity ( In the right diagram, b=20): The curve is very steep. This means that even a small purchase can lead to a sharp increase in price. Such a market is very sensitive and has poor liquidity.

High liquidity (large b value) acts like a "buffer" that allows the market to absorb greater purchasing power without significant price fluctuations (gentle curve); low liquidity, on the other hand, is very sensitive (steep curve).

The mechanism trade-offs of LMSR and the paradigm shift of Polymarket

Before discussing the evolution of Polymarket to an order book model, it is necessary to first analyze the LMSR mechanism it adopted in its early stages. LMSR is not a simple technical option, but rather a set of underlying protocols with a clear design philosophy and inherent trade-offs, the characteristics of which determine its historical positioning at different stages of development in prediction markets.

The core mechanism and design trade-offs of LMSR

The fundamental design goal of LMSR is information aggregation, rather than market maker profit. It solves the most challenging "cold start" problem for prediction markets through an automated mathematical model, which provides liquidity when there is a lack of counterparties in the early stages.

1. Advantage Analysis: Unconditional liquidity supply and controllable market-making risk. The core contribution of LMSR is that it ensures there are counterparties in the market at any given point in time. Regardless of how unpopular or extreme the market sentiment may be, market makers can always provide a buy or sell quote. This fundamentally addresses the problem of traditional order books being unable to execute trades due to thin liquidity in early markets.

Correspondingly, the market makers providing guarantees for this "infinite" liquidity have a potential maximum loss that is predictable and bounded. The maximum loss is determined by the liquidity parameter "b" and the number of market outcomes "n", with the formula being "maximum loss = b⋅ln(n)". The certainty of this risk makes the cost of sponsoring a prediction market manageable, eliminating the risk of infinite losses, which is crucial for parties or organizations looking to launch new markets.

2. Intrinsic Flaws: Static Liquidity and Non-Profit Orientation However, the advantages of LMSR also bring about its insurmountable structural flaws.

The b-parameter dilemma and static liquidity: This is the core constraint of LMSR. The liquidity parameter "b" is set when the market is created and usually remains unchanged throughout the market's lifecycle. A large "b" value means deep liquidity and stable prices, but a slow reaction to new information; a small "b" value means price sensitivity and rapid aggregation of opinions, but a fragile market with severe volatility. This static setting prevents the market from adaptively adjusting its depth and sensitivity based on the actual increase and decrease of liquidity and the changes in information flow.

The role of market makers in subsidies: The theoretical mathematical expectation of the LMSR model is a loss. The losses of market makers are seen as the "information cost" they pay to acquire the collective wisdom of the market (i.e., the final accurate price formed by all transactions). This positioning determines that it is essentially a system subsidized by the initiators for trading, which is not suitable for profit-seeking market maker models, and it is also difficult to construct a profitable ecosystem involving a large number of decentralized LPs.

In addition, when LMSR is implemented on-chain, the logarithmic and exponential operations involved consume more Gas compared to the common arithmetic operations in DEX, which further increases trading friction in a decentralized environment.

Paradigm Shift: Polymarket Abandons the Logical Necessity of LMSR

In summary, LMSR is an efficient and practical tool during the early stage of the platform when liquidity is scarce. However, once the user and capital volume of Polymarket surpasses a critical point, its design, which sacrifices efficiency for liquidity, turns from an advantage into a constraint on development. Its migration to an order book model is based on the following strategic considerations:

The fundamental demand for capital efficiency: LMSR requires market makers to provide liquidity across the entire price range from 0% to 100%, which leads to a large amount of capital being tied up at price points with extremely low transaction probabilities, resulting in low capital efficiency. Order books allow market makers and users to precisely concentrate liquidity in the most active price ranges of the market, which aligns closely with professional market making strategies.

Optimization of Trading Experience: The algorithmic characteristics of LMSR inevitably lead to slippage for trades of any scale. In markets with increasingly thick liquidity, this inherent trading friction can hinder the entry of large funds. Mature order book markets can absorb large orders through dense counterparty depth, providing lower slippage and a better trading execution experience.

Strategies to attract professional liquidity require: The order book is the most common and familiar market model for professional traders and market-making institutions. Shifting to an order book means that Polymarket has sent a clear invitation signal to professional liquidity providers in both the crypto world and traditional finance. This is a key step for the platform in moving from attracting retail participation to building professional-level market depth.

The current pricing and liquidity mechanism of Polymarket

The upgrade of Polymarket is an inevitable choice after reaching a critical point in user scale and platform maturity. Behind this change is a systematic consideration of three goals: trading experience, Gas costs, and market depth. Its current architecture can be analyzed from two perspectives: liquidity mechanisms and price anchoring logic.

Hybrid model of on-chain settlement and off-chain order book

Polymarket's liquidity mechanism employs a hybrid architecture that combines on-chain and off-chain elements, aiming to balance the security of decentralized settlement with the smooth experience of centralized trading.

Off-chain order book: Users' limit orders are submitted and matched on an off-chain server, providing instantaneous operations with no Gas costs. This aligns the trading experience of Polymarket with that of centralized exchanges, allowing users to intuitively see the market depth composed of all limit orders (buy and sell orders). Liquidity thus directly comes from all trading participants themselves, rather than from passive liquidity pools.

On-chain settlement: When buy and sell orders in the off-chain order book are successfully matched, the final asset delivery step will be executed on the Polygon chain through a smart contract. This model of "off-chain matching and on-chain settlement" retains the flexibility of the order book while ensuring the finality of transaction results and the immutability of asset ownership. The displayed "price" is the midpoint between the best bid and the best ask in the off-chain order book.

The underlying logic of price anchoring - the cycle of share issuance and arbitrage

For prediction markets, the core mechanism is how to ensure that the sum of probabilities for the two outcomes "Yes" and "No" always equals 100% (i.e., "$1"). The order book model itself does not enforce limit order prices through code but rather relies on a sophisticated underlying asset design and arbitrage mechanism, utilizing the self-correcting power of the market to ensure that the total price always converges towards "$1".

1. Core Foundation: Minting and Redeeming Complete Share Pairs The cornerstone of this mechanism is an unshakeable value equation established by the Polymarket contract layer.

Minting: Any participant can deposit "$1" USDC into the contract and simultaneously receive 1 YES share and 1 NO share. This operation establishes the underlying value peg of "1 YES share + 1 NO share = $1".

Redemption: Similarly, any participant holding 1 YES share and 1 NO share can combine them and return them to the contract at any time to redeem "$1" USDC.

This bidirectional channel ensures that the total value of a complete set of results is firmly anchored at "$1".

2. Price Discovery: Independent Order Book Trading Based on the above foundation, YES shares and NO shares act as two independent assets, trading with USDC on their respective order books. Participants can freely place limit orders at any price, and there are no restrictions imposed by the protocol layer. This free pricing mechanism will inevitably lead to price deviations, thereby creating opportunities for arbitrageurs.

3. Price Constraints: Market-based Arbitrage Correction The profit-seeking behavior of arbitrageurs (typically automated bots) is key to ensuring price returns. Once the sum of the trading prices of YES and NO shares deviates from "$1", a risk-free arbitrage window will open.

When "P(YES) + P(NO) > $1" (, for example, "$0.70 + $0.40 = $1.10"): Arbitrageurs will execute the "mint-sell" operation: deposit "$1" into the contract, mint 1 YES and 1 NO share, and then immediately sell them at "$0.70" and "$0.40" respectively on the order book, gaining a risk-free profit of "$0.10". This behavior occurs frequently, increasing the selling pressure in the market, driving the prices of YES and NO downwards simultaneously until their total returns to "$1".

When "P(YES) + P(NO) < $1" ( For example, "$0.60 + $0.30 = $0.90" ): Arbitrageurs will execute a "buy-redeem" operation: buying 1 YES and 1 NO share at " $0.60" and "$0.30" respectively on the order book, then combining them to redeem the contract for "$1", obtaining a risk-free profit of "$0.10". This behavior will increase the market's buying demand, driving the prices of the two shares to rise in sync until the total returns to "$1".

The essence of the design of this mechanism lies in the fact that the protocol itself does not play the role of an arbiter, but rather establishes a robust set of value anchors and open arbitrage channels, allowing the profit-seeking behavior of market participants to become the decisive force in maintaining the stability of the system's price.

The possibility of combining Polymarket with DEX

Polymarket chose to upgrade from the AMM model to an order book model. On one hand, the platform has experienced explosive growth in user numbers and has ample liquidity, ensuring that the order book experience is not poor; on the other hand, the upgraded pricing mechanism is more suitable for professional market makers to participate.

With X officially announcing its partnership with Polymarket, Polymarket has also become X's official prediction market. The asymmetrical user base between Polymarket and X will undoubtedly bring new users to the former. In this process, Polymarket will also create an asymmetry in the user base with crypto protocols, and user traffic will flow into the crypto industry through X via Polymarket.

Under this premise, what we need to consider is the new possibilities between Polymarket and crypto protocols; further speaking, the possibility of Polymarket's integration with DEX.

First, Polymarket provides native and efficient risk hedging tools for DEX ecosystem participants. Asset holders and LPs in DEX generally face exposure to impermanent loss, protocol risk, or macro volatility. Traditional hedging tools feel disconnected in DeFi, while Polymarket's event contracts can serve as a "mirror layer" for risk pricing. For example, prediction contracts regarding "whether a certain stablecoin will de-peg" or "whether a certain protocol upgrade will succeed" can be directly used by DEX users to hedge potential losses on their on-chain positions. This model transforms risk management from passive absorption to active allocation, becoming a composable financial "building block" in the DeFi ecosystem.

Secondly, the price data from prediction markets can serve as a high-value leading indicator for centralized liquidity management in DEXs. In concentrated liquidity models like Uniswap V3, the capital efficiency of LPs is positively correlated with risk, and the speed of response to market changes determines their profitability. The real-time odds on Polymarket for key events essentially represent the market's collective consensus on future probabilities, and their fluctuations often precede the price movements of on-chain assets. Automated strategies can capture this leading signal to dynamically adjust LP position ranges—widening the range or withdrawing when risk probabilities increase, and narrowing the range when certainty strengthens. This will transform LPs from passive liquidity "sandbags" into active, probability-based risk managers.

Furthermore, by linking the core metrics of DEX to the event outcomes of Polymarket, entirely new structured financial products can be spawned. The growth of the protocol needs to be deeply tied to community interests, and Polymarket provides a transparent and fair external verification mechanism for this purpose. The protocol can design a "conditional" profit distribution model: for example, tying the distribution of most trading fees to the event outcome of whether "this quarter's trading volume can exceed N hundred million USD" on Polymarket. If the result is "yes," then stakers share the excess profits; if "no," then the profits are used for buyback and burn. This design transforms the protocol's KPIs into financial products that the community can directly participate in, creating a more direct community of shared interests and a value capture closed loop.

In summary, the combination of Polymarket and DEX is not merely a simple functional overlay, but a deep integration at the infrastructure level. Polymarket is evolving into a "risk pricing layer" and "information oracle" for the entire crypto industry. As the traffic brought by X gradually penetrates, its integration with foundational protocols like DEX will no longer be optional but will become a key variable determining whether the future DeFi ecosystem can move towards greater efficiency, maturity, and resilience.

About Movemaker

Movemaker is the first official community organization authorized by the Aptos Foundation, jointly initiated by Ankaa and BlockBooster, focused on promoting the construction and development of the Aptos ecosystem in the Chinese-speaking region. As the official representative of Aptos in the Chinese-speaking area, Movemaker is committed to building a diverse, open, and prosperous Aptos ecosystem by connecting developers, users, capital, and numerous ecological partners.

Disclaimer:

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