How Polymarket Casts "Probability" with "Mechanisms"

Classifying Polymarket as a speculative platform is a serious misunderstanding. Its core function is to compress and securitize the collective human judgment on future events into a tradable financial asset in real-time. Therefore, to truly understand its pricing system, we must go beyond the superficial intuition of "0.9 dollars represents a 90% probability."

This article will start from a simple question that you will definitely ask while trading, revealing the rigorous pricing logic behind Polymarket and why this logic is unbreakable.

1. The Two Pillars of Polymarket: "Mathematics" and "Money" as Hard Constraints

To understand Polymarket, you don't need to delve into complex models from the start; you just need to understand two "hard rules" that make it operate.

Pillar One: The Hard Constraint of Mathematics (Probabilities Must = 100%)

First, every market on Polymarket is mathematically a "complete and mutually exclusive" event.

• Complete: This means all possible outcomes are listed.
• Mutually Exclusive: This means two outcomes cannot happen at the same time.

In the simplest binary market (for example: "Will event A happen?"), there are only two outcomes: {Yes} or {No}.

According to basic probability axioms, the probabilities of all possible outcomes must sum to 1 (i.e., 100%). Therefore, we have our first inviolable mathematical constraint: P(Yes) + P(No) = 1

This equation is the mathematical anchor for all subsequent analyses.

Pillar Two: The Hard Constraint of Money (Prices Must ≈ 1 Dollar)

Mathematical axioms are just theoretical; Polymarket's advantage lies in its enforcement of this constraint in reality through financial engineering.

This mechanism is the "1 Dollar Redemption Guarantee."

1. Creating a "Complete Share" You cannot just buy "Yes" or just buy "No." To participate in a market, you must:

1. Deposit Collateral: You deposit 1 USDC into the smart contract.
2. Receive a "Set": The contract will immediately mint and issue a complete set of outcome tokens to you, namely: 1 USDC → 1 A-Token (Yes) + 1 B-Token (No)

2. "Winner Takes All" Settlement At the time of contract settlement, since the events are mutually exclusive (only one of "Yes" or "No" can win), the value of this set of shares is strictly locked:

• When the oracle determines the result as "A":
• Your A-Token (Yes) is now worth 1 dollar, redeemable for 1 USDC.
• Your B-Token (No) is worth zero.
• (If the result is B, then vice versa).

3. "No-Arbitrage" Price Anchoring The most crucial impact of this mechanism is that at the moment of final settlement, the total value of a complete {A-Token, B-Token} share combination is undoubtedly equal to 1 dollar.

Since we know this set of shares is guaranteed to be worth 1 dollar in the future, its market price today must be very close to 1 dollar. If the price deviates, arbitrageurs will immediately appear to force the price back:

• Scenario 1: The total price is below 1 (e.g., $0.95) If A-Token sells for $0.60 and B-Token sells for $0.35, the total price is $0.95. Arbitrageurs will immediately buy a complete set of shares in the market for $0.95 and hold it until maturity. At maturity, this set of shares can be redeemed for $1. Arbitrageurs have purchased a $1 "safe bond" for 95 cents, locking in a (1−0.95)/0.95≈5.26% risk-free return (assuming the platform and USDC are risk-free). This buying pressure will push the price back up to $1.
• Scenario 2: The total price is above 1 (e.g., $1.05) If A-Token sells for $0.70 and B-Token sells for $0.35, the total price is $1.05. Arbitrageurs will immediately deposit 1 USDC, mint a new {A, B} share set, and then sell it in the market for $1.05. They instantaneously cash out $1.05 at a cost of $1, making a profit of $0.05. This selling pressure will push the price back down to $1.

This two-way arbitrage pressure forces the market price to form a strong equilibrium, which we call the financial anchoring relationship: V(A) + V(B)≈$1

Now we have two "hard constraints" from different domains:

1. Mathematical Constraint: P(A)+P(B)=1
2. Financial Constraint: V(A)+V(B)≈$1

Polymarket's pricing system is built upon these two pillars. Next, we will explore how these two constraints combine and ultimately derive the core logic of "price equals probability."

2. Why Does a 90% Probability Sell for $0.9?

In the previous chapter, we established two "hard constraints":

1. Mathematical Constraint: The probabilities of "Yes" and "No" for an event must sum to 1.
2. P(A) + P(B) = 1
3. Financial Constraint: The prices of "Yes" and "No" tokens for an event must sum to approximately 1 dollar.
4. V(A) + V(B)≈$1

2.1 Price Equals Probability: An Intuitive Derivation

When you place these two constraints side by side, the core logic of Polymarket becomes evident: the structure of the two formulas corresponds perfectly.

This strongly suggests that: the price of a token V(A) is the market's best estimate of the probability P(A) of that event occurring.

Why must this equation hold? We can understand it from the perspective of "fair value."

What is "Fair Value"? Suppose an event (A) has a 90% probability of occurring and a 10% probability of not occurring. The future cash flow of the A-Token (Yes) you hold is:

• There is a 90% chance it is worth 1 dollar.
• There is a 10% chance it is worth 0 dollars.

So, what is the reasonable "fair value" (or "expected value" EV) of this "lottery ticket" today?

EV(A) = (90% * $1) + (10% * $0) = $0.9

• *The fair value is $0.9. In a rational market, prices will always tend to approach their fair value.
• If the price < Fair Value: Suppose the market price V(A) is only 0.8. Professional traders will see this as a "discounted probability" and will buy in large quantities until the price is pushed up to 0.9.
• If the price > Fair Value: Suppose the market price V(A) is selling for 0.95. Traders will see this as a "premium probability" and will sell in large quantities until the price is pushed down to 0.9.

Thus, the continuous arbitrage pressure in the market will force the price V(A) to always anchor near its expected value P(A). V(A) ≈ P(A)

2.2 An Important Correction: Price = Probability - "Risk Premium"

Now, we must introduce a professional correction. You will often find that a poll shows a 95% probability of an event occurring, but the price on Polymarket may stabilize at only 0.9 dollars.

Does this mean the market is "wrong"? No. This is precisely the market being "correct" because it is pricing in risk.

In financial engineering, we must distinguish between two concepts:

1. True Probability (P): The objective likelihood of occurrence from an "God's-eye view" (e.g., the 95% from polls).
2. Risk-Neutral Probability (Q): The price actually traded in financial markets (like Polymarket).

In the real world, investors are risk-averse. They hold a token and must bear not only the risk of the event itself but also a series of structural risks associated with the platform:

• Will the oracle make a mistake?
• Will the smart contract be hacked?
• Will USDC depeg?
• Will the platform face regulatory crackdowns?

To bear these additional, unhedgeable risks, investors will demand a "discount" as compensation, which is financially referred to as "risk premium."

Therefore, a more precise pricing formula is: V(A) = Q(A) - λ

Where Q(A) is the risk-neutral probability of the event, and λ (Lambda) is a composite risk discount (or "risk fee") that represents the market's compensation requirement for all the aforementioned structural risks.

When you see a price of 0.9 dollars on Polymarket, the professional information it conveys is: "Market participants are willing to bet real money on the risk-neutral probability of this event occurring, and this price has already been adjusted downward (deducted) for all perceivable platform and event risks."

This is the fundamental difference between Polymarket and polls: polls reflect "opinions," while Polymarket prices reflect "risks."

3. How is Price Formed?

In the previous sections, we established two pillars:

1. Mathematically, the probabilities must sum to 1.
2. Financially, the prices must sum to approximately 1 dollar.

Now, we enter the practical aspect. How is the price of $0.9 that you see on your screen formed? And what prevents it from deviating?

3.1 Formation of Price

The most common mistake beginners make is to imagine Polymarket as an AMM like Uniswap, thinking that prices are calculated by a fixed mathematical formula (like X*Y = K).

This is incorrect.

The core of Polymarket is a "Central Limit Order Book" (CLOB), which operates exactly like Binance, Nasdaq, or any stock exchange.

• The $0.9 you see is the real-time transaction price formed by the "highest bidder" and the "lowest ask" meeting in the market.
• Prices are "discovered" by all participants, not "calculated" by the platform.

Polymarket's system combines "speed" and "security":

1. Lightning Fast (Off-chain Matching): You submit orders, modify prices, cancel orders… all of this is done on a centralized server instantly and for free.
2. Absolutely Secure (On-chain Settlement): Only after your order is executed will the final settlement information be sent to the blockchain, ensuring the safety of your assets.

What does this mean for market makers?

It means "no slippage." They place a buy order at $0.8, and the transaction price is $0.8. This allows them to earn a stable $0.01 spread by placing a buy order at $0.8 and a sell order at $0.81, just like in a real stock market.

3.2 Why Can Prices Always Be "Good" and "Stable"?

You might ask: If it all relies on everyone freely placing orders, what if no one places orders? Wouldn't the price get chaotic?

This is where Polymarket's ingenious incentive design comes into play, which has two layers:

Incentive One: Return "Profit Fees" to "Market Makers"

Polymarket does not charge trading fees, but it will take a percentage (e.g., k%) of your net profit as a "performance fee" after the market settles.

• Key Point: This money does not go to Polymarket!
• The platform returns the vast majority of this fee directly to those who provide liquidity (i.e., place orders) in this market. This incentivizes professional players to flock in and provide you with stable and deep quotes.

Incentive Two: "Quadratic Scoring" (Forcing You to Offer the Best Price)

The way the platform returns rewards is not through "equal distribution," but by using a "quadratic scoring" mechanism.

In simple terms: the better the price you provide (the smaller the bid-ask spread), the more rewards you will receive exponentially.

• For example: In a market with a qualified spread of 4 cents.
• Player A provides a 2-cent spread and scores 0.25.
• Player B provides a 1-cent spread (only twice as good as A), but scores 0.5625 (2.25 times A's score!).
• (This is a simplified formula: Score ∝ (…)\^2)

This nonlinear incentive forces all market makers to "strive to push prices toward the most reasonable midpoint."

What does this mean for beginners?

It means that as an ordinary user, you can always enjoy the extremely narrow bid-ask spreads and very low trading costs brought about by the competition among professional players.

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Disclaimer:

This article/blog is for reference only, representing the author's personal views and does not represent the position of Movemaker. This article does not intend to provide: (i) investment advice or recommendations; (ii) offers or solicitations to buy, sell, or hold digital assets; or (iii) financial, accounting, legal, or tax advice. Holding digital assets, including stablecoins and NFTs, carries high risks, significant price volatility, and may even become worthless. You should carefully consider whether trading or holding digital assets is suitable for you based on your financial situation. For specific issues, please consult your legal, tax, or investment advisor. The information provided in this article (including market data and statistics, if any) is for general reference only. Reasonable care has been taken in compiling this data and charts, but no responsibility is accepted for any factual errors or omissions expressed therein.