Binary vs Scalar Markets: When to Use Each

Learning Objectives

By the end of this module, you will:

Why Market Type Matters

The same real-world event can be expressed as different market types, each with distinct risk/reward profiles:

Event: Port of Los Angeles December 2024 throughput

Binary Market: "Will LA Port exceed 1.0M TEUs in December 2024?"

Scalar Market: "LA Port December 2024 TEU Volume (range: 900k-1.1M)"

Your Edge Determines Optimal Market:

Key Principle: Your analytical advantage should match the market type. Don't trade scalar markets if your edge is directional-only.

Binary Markets: Mechanics and Math

How Binary Markets Work

Structure: Two outcomes (YES or NO), each pays $1 if it occurs, $0 otherwise.

Pricing: YES price + NO price always = $1.00 (ignoring small spreads)

Example Market: "Will Suez Canal December 2024 transits exceed 1,800 vessels?"

| Outcome | Current Price | Implied Probability | Payout if Occurs | Payout if Doesn't | |---------|---------------|---------------------|------------------|-------------------| | YES | $0.58 | 58% | $1.00 | $0.00 | | NO | $0.42 | 42% | $1.00 | $0.00 |

Buying YES at $0.58:

Buying NO at $0.42:

Binary Payoff Curves

Asymmetric Risk/Reward:

When you buy YES at $0.58:

This is ASYMMETRIC. Your downside (100% of capital) exceeds your upside (72% of capital) in absolute terms.

When to Buy Expensive YES (>$0.60):

Only when your estimated probability significantly exceeds market price.

Example:

Even though max profit is only $0.25 (33% ROI), if you're correct 85% of the time over many trades, you have positive expected value.

When to Buy Cheap NO (<$0.40):

When you believe market is overestimating YES probability.

Example:

Quotable Framework: "In binary markets, you're not betting on outcomes—you're betting on probabilities being mispriced. A 10-percentage-point edge on a 50% probability market is worth more than a 5-point edge on a 90% market."

Worked Example: Binary Strategy

Market: "Will Panama Canal December 2024 transits exceed 950 vessels?"

Current Prices:

Your Analysis:

Step 1: Gather Data

Step 2: Forecast Outcome

Step 3: Calculate Probabilities

Your forecast: 837 vessels (well below 950 threshold)

Uncertainty range:

Your estimated probability of exceeding 950: 5% (only if restrictions lifted unexpectedly)

Step 4: Compare to Market

Step 5: Trade Setup

Action: Buy NO at $0.56

Position Sizing: Risk $1,000 → buy 1,786 NO shares at $0.56 each

Payoff:

Expected Value: (0.95 × $1,786) - $1,000 = +$697 (+69.7% expected return)

Step 6: Risk Management

Even with 95% confidence, allocate only 10-15% of trading capital to single position. If wrong 1 in 20 times, diversified portfolio absorbs losses.

Outcome (Jan 8, 2025 resolution):

Panama Canal Authority reports December 2024 transits: 862 vessels (below 950 threshold)

Try binary strategies on Ballast → Panama Canal Markets

Scalar Markets: Mechanics and Math

How Scalar Markets Work

Structure: Continuous range divided into buckets. Each bucket pays $1 if outcome falls within that range.

Example Market: "Port of Long Beach December 2024 TEU Volume"

Range: 700,000 - 900,000 TEUs (divided into buckets)

Bucket System:

| Bucket Range | Bucket Label | Current Price | Implied Probability | |--------------|--------------|---------------|---------------------| | 700k-750k | Very Low | $0.08 | 8% | | 750k-800k | Low | $0.22 | 22% | | 800k-850k | Medium | $0.45 | 45% | | 850k-900k | High | $0.25 | 25% |

Note: Prices sum to $1.00 (representing 100% probability distributed across outcomes)

Buying Medium Bucket (800k-850k) at $0.45:

Scalar Advantages Over Binary

1. Precision: Express views on magnitude, not just threshold crossing

Binary: "Will Long Beach exceed 850k TEUs?" (yes/no) Scalar: "Long Beach will be 800k-850k" (specific range)

If you forecast 825k, binary market offers no advantage over someone forecasting 870k (both bet YES). Scalar market rewards your precision.

2. Multiple Shots: Can buy multiple buckets to express uncertainty

Example: You forecast 810k-840k range (uncertain exact value)

3. Volatility Trading: Bet on distribution width, not just mean

Scenario: Market prices suggest narrow distribution (90% probability in two middle buckets). You believe outcome is uncertain (wider distribution).

Action: Buy tails (Very Low + High buckets) cheaply

Scalar Payoff Curves

Unlike binary (step function at threshold), scalar has multiple thresholds:

Example: "LA Port TEU Index (range 0-150, baseline=100)"

Buckets: 0-50, 50-75, 75-100, 100-125, 125-150

If you buy 100-125 bucket at $0.50:

| Actual Outcome | Payout | Profit/Loss | |----------------|--------|-------------| | 110 (in range) | $1.00 | +$0.50 (+100%) | | 99 (just below) | $0.00 | -$0.50 (-100%) | | 126 (just above) | $0.00 | -$0.50 (-100%) |

Key Insight: You have TWO cliffs (lower and upper bucket boundaries). This is riskier than binary (one threshold) if you're wrong about magnitude.

Quotable Framework: "Scalar markets punish overconfidence about precision. If you know direction but not magnitude, stick to binary. If you have high-resolution forecasts, scalar markets reward that edge."

Worked Example: Scalar Strategy

Market: "Suez Canal Monthly Transits Index — January 2025 (range 0-150, baseline=100)"

Baseline: 1,800 monthly transits (12-month average)

Index Calculation: (Actual January transits / 1,800) × 100

Bucket Structure:

| Bucket | Range | Transits | Price | Implied Prob | |--------|-------|----------|-------|--------------| | A | 0-75 | 0-1,350 | $0.05 | 5% | | B | 75-100| 1,350-1,800 | $0.32 | 32% | | C | 100-125| 1,800-2,250 | $0.48 | 48% | | D | 125-150| 2,250-2,700 | $0.15 | 15% |

Your Analysis:

Step 1: Context

Step 2: Forecast

Step 3: Bucket Selection

Your forecast of 108 falls in Bucket C (100-125), currently priced at $0.48

Uncertainty Analysis:

Your probability distribution:

Step 4: Compare to Market

Market implies:

Your estimate:

Mispricing: Market underprices Bucket C by 22 percentage points

Step 5: Trade Setup

Action: Buy Bucket C at $0.48

Position Sizing: Risk $1,000 → buy 2,083 shares of Bucket C at $0.48

Payoff:

Expected Value: (0.70 × $2,083) - $1,000 = +$458 (+45.8% expected return)

Step 6: Alternative Strategy (Lower Risk)

If you're less confident in precision, buy multiple buckets:

Hybrid Position:

Payoff if index is 103 (your conservative scenario):

Payoff if index is 108 (base case):

Why lower return? You're paying $0.32 + $0.48 = $0.80 per "unit" of protection across two buckets. This reduces upside but increases win probability (now correct if outcome is anywhere in B or C).

Outcome (Feb 10, 2025 resolution):

Suez Canal Authority reports January 2025 transits: 1,985 vessels (index = 110.3)

Try scalar strategies on Ballast → Suez Canal Index Markets

Binary vs Scalar: Direct Comparison

Let's analyze the SAME underlying forecast using both market types:

Scenario: You forecast Port of Oakland December 2024 will handle 225,000 TEUs (historical December average: 210,000).

Option 1: Binary Market

Market: "Will Oakland exceed 220k TEUs in December 2024?"

Your Forecast: 225k TEUs (above 220k threshold)

Trade: Buy YES at $0.52

Payoff:

Win Probability: High (your forecast is 5k TEUs above threshold, ~5% margin of safety)

Expected Value (assuming 80% probability you're right): (0.80 × $1.00) - $0.52 = +$0.28 per share (+53.8% expected return)

Option 2: Scalar Market

Market: "Oakland December 2024 TEU Index (0-150, baseline=100)"

Your Forecast: 225k TEUs = Index 107

Buckets:

| Bucket | Index Range | TEU Range | Price | |--------|-------------|-----------|-------| | Low | 75-100 | 157.5k-210k | $0.28 | | Medium | 100-125 | 210k-262.5k | $0.55 | | High | 125-150 | 262.5k-315k | $0.17 |

Your forecast (107) falls in Medium bucket

Trade: Buy Medium bucket at $0.55

Payoff:

Win Probability: High (your 225k forecast is within bucket, 15k TEU margin on lower boundary, 37.5k margin on upper boundary)

Expected Value (assuming 75% probability of falling in Medium bucket): (0.75 × $1.00) - $0.55 = +$0.20 per share (+36.4% expected return)

Comparison Summary

| Factor | Binary Market | Scalar Market | |--------|---------------|---------------| | Cost | $0.52 | $0.55 | | Max Profit | $0.48 (92% ROI) | $0.45 (82% ROI) | | Win Threshold | over 220k TEUs (single threshold) | 210k-262.5k TEUs (range) | | Precision Required | Low (just need to exceed 220k) | Medium (need to land in 52.5k range) | | Expected Return | +53.8% (if 80% probability) | +36.4% (if 75% probability) |

When to Choose Binary: Your edge is directional confidence (you're sure Oakland will be strong, but uncertain if 215k, 225k, or 240k). Binary's single threshold is easier to clear.

When to Choose Scalar: You have precise forecast (specifically 225k ±10k) and want to exploit market underpricing of that specific range. Higher risk (two boundaries) but rewards precision.

Decision: If win probabilities are 80% (binary) vs 75% (scalar), choose binary (higher expected value).

Try comparative analysis on Ballast → Port of Oakland Markets

Advanced Strategy: Spread Trades in Scalar Markets

Concept: Buy underpriced bucket, sell overpriced bucket. Profit from relative mispricing without taking directional risk.

Example Market: "Port of Houston January 2025 TEU Index (0-150)"

Market Prices:

| Bucket | Price | Your Probability Estimate | |--------|-------|---------------------------| | 75-100 | $0.40 | 30% | | 100-125 | $0.35 | 50% | | 125-150 | $0.25 | 20% |

Analysis:

Spread Trade:

Net Cost: $0.35 - $0.40 = -$0.05 (you receive $0.05 credit upfront)

Payoff Scenarios:

If outcome is 75-100 (30% probability):

If outcome is 100-125 (50% probability):

If outcome is 125-150 (20% probability):

Expected Value: (0.30 × -$0.95) + (0.50 × $1.05) + (0.20 × $0.05) = -$0.285 + $0.525 + $0.01 = +$0.25 per spread unit

You have positive expected value AND received upfront credit. This is a high-conviction relative value trade.

Risk: If outcome surprises to 75-100 bucket (worse than your 30% estimate), you lose $0.95. But if your probability estimates are accurate, you profit 70% of the time.

Risk/Reward Optimization

Binary Markets: Optimal Entry Points

Framework: Only trade binary markets when estimated probability differs from market price by over 10 percentage points.

Example Scenarios:

Marginal Edge (Don't Trade):

Strong Edge (Trade):

Quotable Framework: "In binary markets, edge is everything. A 5-point edge at 50% probability (where max profit is 50%) yields only 10% expected return. A 15-point edge at the same price yields 30% expected return. Triple the edge, triple the expected profit."

Scalar Markets: Optimal Bucket Selection

Framework: Choose buckets where your estimated probability exceeds market by over 20 percentage points.

Why Higher Threshold? Scalar markets have two failure modes (miss on lower or upper boundary) vs binary's one (threshold). Need larger edge to compensate for precision risk.

Example:

Your Probability Estimates:

Market Prices:

Edge Calculation:

Decision: Trade Bucket B (18-point edge, meets minimum threshold). Buckets A and C are mispriced against you.

Common Pitfalls

Pitfall 1: Overtrading Low-Edge Binaries

Problem: Buying YES at $0.80 because you think probability is 83% (only 3-point edge).

Why It Fails: Max profit is $0.20 (25% ROI). If you're wrong 1 in 4 times (actual probability is 75%, not 83%), you break even due to losses.

Solution: Require over 10-point edge on binary markets. At $0.80 price, your estimate should be over 90% probability.

Pitfall 2: Buying Multiple Scalar Buckets at Premium Prices

Problem: Buying three buckets at $0.40 + $0.35 + $0.25 = $1.00 total.

Why It Fails: You've paid $1.00 to guarantee $1.00 payout (zero profit). You're buying the entire probability distribution at market prices—no edge.

Solution: Only buy buckets trading BELOW your estimated probability. If you buy multiple buckets, total cost should be below $0.70 (leaving room for profit).

Pitfall 3: Ignoring Boundary Risk in Scalar Markets

Problem: Forecasting 125k TEUs. Buying 100k-150k bucket at $0.50. Outcome is 152k TEUs (just outside upper boundary).

Why It Fails: You were directionally correct (strong volume) but missed by 2k TEUs on precision. Binary market with 150k threshold would've paid off.

Solution: For high-uncertainty forecasts, use binary markets (directional edge) rather than scalar (precision edge).

Pitfall 4: Confusing Bucket Width with Probability

Problem: Assuming wider bucket = higher probability (e.g., 100k-200k bucket vs 100k-150k bucket).

Why It Fails: Bucket width is arbitrary (set by market creator). A wide bucket can still be low probability if outcome distribution is skewed elsewhere.

Solution: Focus on price (implied probability), not bucket width. A 50k-wide bucket at $0.20 and a 100k-wide bucket at $0.20 both imply 20% probability, but the wider bucket has lower probability density.

Frequently Asked Questions

1. Can I short sell in binary markets (sell YES without owning it)?

Most prediction market platforms (including Ballast) allow selling. If you sell YES at $0.60, you receive $0.60 upfront and owe $1 if YES occurs. This is functionally identical to buying NO at $0.40 (prices sum to $1).

2. What happens if scalar outcome falls outside all buckets?

Rare, but if market defines range 0-150 and outcome is 160, typically the highest bucket (125-150) pays out OR market voids and refunds. Check market rules before trading.

3. Can I buy fractional shares?

Depends on platform. Ballast allows fractional shares (e.g., 1.5 shares of YES at $0.60 = $0.90 cost). Payout is proportional (1.5 shares × $1 = $1.50).

4. How do spreads (bid-ask) differ between binary and scalar?

Spreads are typically wider on scalar buckets (more granular liquidity fragmentation). Binary markets have tighter spreads due to concentrated liquidity on YES/NO. Factor spread costs into expected value calculations.

5. Can I change my position after buying?

Yes, you can sell shares before market resolves (at current market price). If you bought YES at $0.50 and price moves to $0.70, you can sell at $0.70 for $0.20 profit (40% return) without waiting for resolution.

6. What if I'm equally confident about two scalar buckets?

Buy both proportionally. If you think 40% probability in Bucket A and 40% in Bucket B, buy both. Total cost should still leave room for profit (e.g., buy both for $0.70 total, not $0.80+).

7. How do index-based scalar markets work?

Index scales raw outcome to 0-150 range (baseline=100). This normalizes different ports' sizes. Index 110 means 10% above baseline, whether that's LA (1M TEUs) or Oakland (200k TEUs).

8. Can I trade options or derivatives on prediction market positions?

Not directly on most platforms. You hold shares until resolution. No options chains or futures. But you can SELL shares early (see #5) as a form of "closing position."

9. What's the optimal position size?

Kelly Criterion: Bet (Edge × Probability) / (Edge). For 60% probability and 10-point edge, bet 6% of capital. Most traders use fractional Kelly (1/4 or 1/2 Kelly) for safety.

10. How do I backtest binary vs scalar strategies?

Download historical data for a port (monthly TEUs past 5 years). Simulate binary markets at various thresholds (median, 75th percentile, etc.) and scalar buckets. Calculate which market type would've been more profitable given your forecasting errors.

Ready to Apply What You've Learned?

Turn knowledge into action.

Start Trading on Ballast Markets →

Use prediction markets to apply the concepts from this learning module. Trade real contracts based on port volumes, shipping delays, chokepoint transits, and tariff impacts.

Next Steps

Practice Exercises:

  1. Binary Valuation Drill: Market shows YES at $0.67. Calculate break-even probability, max profit, max loss, and expected value if your estimate is 75% probability.

  2. Scalar Bucket Selection: Given four buckets priced at $0.15, $0.35, $0.40, $0.10, and your probability distribution is 10%, 45%, 35%, 10%, which bucket(s) should you trade?

  3. Market Type Decision: You forecast port throughput will be "significantly above average" but uncertain by how much. Do you trade binary (over X threshold) or scalar (100-125 bucket)? Why?

Continue Learning:

Try on Ballast Markets:

Disclaimer

This content is for educational purposes only and does not constitute financial advice. Prediction markets involve risk, including total loss of capital. Binary and scalar markets have different risk profiles. Start with small positions and only risk capital you can afford to lose.