Scalar Markets

Taxonomy Note: Scalar markets are similar to range options in finance. They are used to predict specific numbers or ranges (e.g., "30-40"). A notable example platform exploring this space is Trepa.

#Definition

A scalar market (also called a range market or continuous outcome market) is a prediction market where the outcome is a specific number within a defined range. Unlike binary markets with Yes/No outcomes, scalar markets pay based on where the actual value falls between a minimum and maximum bound.

In prediction markets, scalar markets capture granular predictions about numerical quantities: GDP growth rates, election margins, temperature readings, or price levels. The market price represents the crowd's expected value, while trading reveals the probability distribution across possible outcomes.

#Why It Matters in Prediction Markets

Scalar markets extract more information than binary alternatives.

Precision over binary: A binary market asking "Will GDP exceed 3%?" loses information about how much above or below 3% participants expect. A scalar market from 0% to 5% captures the full distribution.

Expected value revelation: The market price in a well-functioning scalar market approximates the probability-weighted average outcome, the crowd's best guess of the expected value.

Natural for continuous variables: Many real-world quantities are inherently numerical: temperatures, vote shares, economic indicators, sports scores. Scalar markets match this reality.

Hedging flexibility: Businesses and traders can hedge specific numerical exposures rather than just directional bets.

#Scalar vs. Binary Markets

#How It Works

#Basic Structure

A scalar market defines:

• Lower bound: Minimum possible value (pays $0)
• Upper bound: Maximum possible value (pays $1)
• Settlement formula: How outcomes map to payouts

#Linear Payout Formula

Payout = (Actual Value - Lower Bound) / (Upper Bound - Lower Bound)

Example: Unemployment rate market with range 3.0% to 7.0%

If actual unemployment = 5.0%:

Payout = (5.0 - 3.0) / (7.0 - 3.0) = 2.0 / 4.0 = $0.50 per share

If actual unemployment = 3.5%:

Payout = (3.5 - 3.0) / (7.0 - 3.0) = 0.5 / 4.0 = $0.125 per share

/**
 * Calculates the payout per share for a scalar market.
 * 
 * @param actualValue - The final resolved value (e.g., 5.0%)
 * @param lowerBound - The minimum value of the range (e.g., 3.0%)
 * @param upperBound - The maximum value of the range (e.g., 7.0%)
 * @returns Payout between 0.0 and 1.0
 */
function calculateScalarPayout(actualValue, lowerBound, upperBound) {
  // Clamp value within bounds
  if (actualValue <= lowerBound) return 0.0;
  if (actualValue >= upperBound) return 1.0;

  // Linear interpolation
  return (actualValue - lowerBound) / (upperBound - lowerBound);
}

// Example: Unemployment at 5.0% in 3.0%-7.0% range
const payout = calculateScalarPayout(5.0, 3.0, 7.0);
// Result: 0.5 (Pays $0.50 per share)

#Payout Visualization

#Boundary Conditions

What happens outside the range:

• Below minimum: Pays $0 (as if at minimum)
• Above maximum: Pays $1 (as if at maximum)

This capping prevents unbounded payouts but creates asymmetric risk at the boundaries.

#Numerical Example: GDP Growth Market

Market: "What will Q4 GDP growth be?"

• Range: -2% to +5%
• Current price: $0.57

Interpreting the price:

Expected value = Lower + (Price × Range)
               = -2% + (0.57 × 7%) = -2% + 4.0% = +2.0%

The market implies expected GDP growth of approximately 2.0%.

Your analysis: You expect +3.0% growth

Implied fair price for +3.0%:

Fair price = (3.0 - (-2.0)) / (5.0 - (-2.0)) = 5.0 / 7.0 = $0.714

If you're right, buying at $0.57 yields ~$0.14 profit per share.

#Examples

#Example 1: Election Margin

Market: "What percentage of the vote will the winning candidate receive?"

• Range: 45% to 60%
• Current price: $0.47

Implied expectation: 45% + (0.47 × 15%) = 52.0%

A trader expecting a landslide at 57% calculates:

Fair price = (57 - 45) / (60 - 45) = $0.80
Value = $0.80 - $0.47 = $0.33 per share

#Example 2: Temperature Forecast

Market: "What will the high temperature be in NYC on July 4?"

• Range: 70°F to 100°F
• Current price: $0.50

Implied expectation: 85°F (midpoint)

If a heat wave makes 95°F likely:

Fair price = (95 - 70) / (100 - 70) = $0.83
Buy opportunity at $0.50

#Example 3: Economic Data

Market: "What will the initial CPI report show for monthly inflation?"

• Range: -0.5% to +1.0%
• Current price: $0.60

Implied expectation: -0.5% + (0.60 × 1.5%) = +0.40% monthly inflation

A trader expecting hot inflation at +0.7%:

Fair price = (0.7 - (-0.5)) / (1.0 - (-0.5)) = 1.2 / 1.5 = $0.80

#Example 4: Sports Total

Market: "What will the combined score be in the championship game?"

• Range: 30 to 70 points
• Current price: $0.45

Implied expectation: 30 + (0.45 × 40) = 48 points

A defense-oriented matchup might warrant betting the under (selling the market).

#Risks and Common Mistakes

Boundary risk

If the outcome exceeds the upper bound, the payout caps at $1.00. A trader who correctly predicted "higher than expected" receives no extra payout above the boundary. Similarly, outcomes below the lower bound pay$0 regardless of how far below.

Misinterpreting price as probability

In binary markets, price directly equals probability. In scalar markets, price represents normalized position along a range, not a probability. A $0.60 price doesn't mean 60% chance of anything specific.

Ignoring distribution shape

The market price reflects expected value but obscures the probability distribution. Two distributions with the same mean but different spreads trade at the same price despite very different risk profiles.

Range selection matters

A poorly chosen range distorts incentives. If the upper bound is set too low, outcomes frequently hit the cap, eliminating price sensitivity for high-side movements.

Lower liquidity than binary

Scalar markets often attract fewer traders who understand the mechanics, resulting in wider spreads and shallower depth.

#Practical Tips for Traders

• Understand the range before trading: Know the minimum and maximum bounds and consider whether they're appropriately set for likely outcomes

• Calculate your expected value explicitly: Convert your probability distribution into an expected payout, then compare to market price

• Consider tail scenarios: If your thesis involves extreme outcomes, check whether they hit the range boundaries (limiting your upside)

• Use scalar markets for relative value: If multiple scalar markets exist on related metrics, compare implied expectations for consistency

• Factor in time value: Scalar markets may trade at slight discounts before resolution due to capital opportunity costs

• Check for correlated binary markets: Sometimes binary markets (e.g., "Will X exceed 50?") offer better liquidity for similar directional exposure

• Mind the settlement source: Scalar markets are sensitive to exact reported values; ensure you understand which source and measurement determines the outcome

#Related Terms

• Binary Market
• Categorical Market
• Expected Value (EV)
• Implied Probability
• Resolution Source
• Order Book

#FAQ

#How is a scalar market different from a binary market?

A binary market has exactly two outcomes: Yes (pays $1) or No (pays$0). A scalar market has infinite possible outcomes along a numerical range, with payouts interpolating between $0 and$1 based on where the actual value falls. Binary markets answer "Will X happen?" while scalar markets answer "What will the value of X be?"

#What does the price mean in a scalar market?

The price represents the market's estimate of where the outcome will fall within the range, normalized to a 0-1 scale. If the price is $0.60 in a market ranging from 0% to 10%, the implied expected value is 6%. It's the probability-weighted average payout, not a probability of any specific outcome.

#What happens if the actual outcome is outside the range?

Outcomes below the lower bound pay $0 as if they were at the minimum. Outcomes above the upper bound pay$1 as if they were at the maximum. This "capping" means extreme outcomes don't provide proportionally higher payouts, a limitation traders should consider when analyzing risk.

#Are scalar markets more profitable than binary markets?

Neither is inherently more profitable. Scalar markets may offer opportunities when you have precise numerical views that binary markets can't express. However, they're often less liquid and more complex to analyze. Profitability depends on finding mispriced expectations relative to your edge, not on market type.

#Can I lose more than my investment in a scalar market?

No. Like binary markets, your maximum loss is your initial investment. If you buy at $0.70 and the market settles at$0, you lose $0.70 per share. The scalar payout structure doesn't introduce leverage or unlimited downside.