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A deep dive into why predicting distributions beats predicting yes/no.

The Fundamental Difference

Binary Markets

β€œWill Bitcoin be above $100,000 on December 31?” Options: Yes or No Payout: Yes = $1, No = $1

Continuous Markets (Skepsis)

β€œWhat will Bitcoin’s price be on December 31?” Options: Any range within the market bounds Payout: $1 per share if outcome lands in your range

Visual Comparison

Binary: One Data Point

Question: "BTC > $100K by Dec 31?"

Yes: 45% β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–‘β–‘β–‘β–‘β–‘β–‘β–‘β–‘β–‘β–‘β–‘β–‘β–‘β–‘β–‘β–‘β–‘β–‘β–‘β–‘
No:  55% β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–‘β–‘β–‘β–‘β–‘β–‘β–‘β–‘β–‘β–‘β–‘β–‘

Information: "Market thinks ~45% chance of crossing $100K"
Unknown: Will it be $100,001 or $500,000? Both are "Yes"

Continuous: Full Distribution

Question: "Where will BTC be on Dec 31?"

$80K-$85K:   3%  β–ˆβ–ˆ
$85K-$90K:   8%  β–ˆβ–ˆβ–ˆβ–ˆ
$90K-$95K:   15% β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ
$95K-$100K:  22% β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ
$100K-$105K: 25% β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ  ← Mode (most likely)
$105K-$110K: 15% β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ
$110K-$120K: 9%  β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ
$120K+:      3%  β–ˆβ–ˆ

Information: Full probability landscape
- Expected value visible
- Uncertainty visible
- Tail risks visible

Information Density

What Binary Markets Tell You

A single binary market at 45% β€œYes” tells you:
  • There’s a 45% chance of crossing the threshold
  • That’s it

What Continuous Markets Tell You

A continuous distribution tells you:
  • Expected value: Where the market thinks it’ll land
  • Confidence: Is the distribution narrow (confident) or wide (uncertain)?
  • Skew: Is the market more bullish or bearish?
  • Tail risk: What’s the chance of extreme outcomes?
  • Mode vs Mean: Most likely outcome vs average expected outcome

Edge Cases: Where Binary Fails

The β€œAlmost Right” Problem

Binary market: β€œWill BTC hit $100K?”
ScenarioBTC PriceBetResult
A$99,999Yes❌ LOSE
B$100,001Yesβœ… WIN
You were right about BTC being β€œaround $100K” in both cases. Binary punishes you in Scenario A. Continuous market: β€œWhere will BTC be?”
ScenarioBTC PriceRange BetResult
A$99,99998Kβˆ’98K-102Kβœ… WIN
B$100,00198Kβˆ’98K-102Kβœ… WIN
Your actual belief (around $100K) is captured and rewarded.

The β€œPrecision Penalty” Problem

Binary framing forces false precision:
"Will GPT-5 launch before June 1, 2025?"

You think: "Probably April-August 2025"
Binary forces: Pick June 1 as the cutoff

If GPT-5 launches June 15:
- You were basically right (summer 2025)
- Binary says: WRONG
Continuous market:
"When will GPT-5 launch?"

Your bet: April-August 2025 range
GPT-5 launches June 15
Result: βœ… WIN (exactly as you predicted)

The β€œMissing Nuance” Problem

Binary: β€œWill it rain tomorrow?”
  • Doesn’t capture: How much rain?
  • Drizzle and monsoon both = β€œYes”
  • No way to express β€œprobably light rain”
Continuous: β€œHow much rainfall tomorrow?”
  • 0.0-0.1 inches: 30%
  • 0.1-0.5 inches: 45% ← You bet here
  • 0.5-1.0 inches: 20%
  • 1.0+ inches: 5%
Your prediction matches your actual belief.

Capital Efficiency

Binary: Multiple Markets Needed

To express β€œBTC will be between 95Kβˆ’95K-105K,” you need:
Market 1: "BTC > $95K?" β†’ Buy Yes
Market 2: "BTC > $105K?" β†’ Buy No

Two transactions
Two sets of fees
Two positions to track
Capital spread across markets

Continuous: One Market

Range: $95K-$105K
One transaction
One fee
One position
Capital concentrated
Result: Same belief, half the friction.

Price Discovery

Binary Markets: Threshold Games

In binary markets, traders fight over the threshold:
"BTC > $100K?"
Currently: 48% Yes

Trader A thinks BTC will be $102K β†’ Buys Yes
Trader B thinks BTC will be $98K β†’ Buys No
Trader C thinks BTC will be $150K β†’ Buys Yes (same as A!)

The market can't distinguish A and C's very different views.

Continuous Markets: Full Spectrum

"Where will BTC be?"

Trader A (thinks $102K) β†’ Bets $100K-$105K
Trader B (thinks $98K) β†’ Bets $95K-$100K  
Trader C (thinks $150K) β†’ Bets $140K-$160K

Each view has its own odds
Market shows full range of beliefs
Much richer information

When Binary Markets Work

Binary isn’t always wrong. They work well when:

1. The Question is Naturally Binary

  • β€œWill [candidate] win the election?” (1st or not 1st)
  • β€œWill [company] go bankrupt?” (exists or doesn’t)
  • β€œWill [law] pass?” (passes or doesn’t)

2. Threshold is Meaningful

  • β€œWill inflation be above 3%?” (policy threshold)
  • β€œWill [movie] make $100M opening?” (industry benchmark)

3. Extremes Don’t Matter

  • β€œWill [team] make playoffs?” (whether they dominate or barely qualify doesn’t change the outcome)

When Continuous Markets Excel

1. Magnitude Matters

  • Price predictions (How high? How low?)
  • Measurements (How much? How many?)
  • Timing (When exactly?)

2. Uncertainty is Important

  • Is the market confident or uncertain?
  • What are the tail risks?
  • What’s the range of likely outcomes?

3. Nuance Adds Value

  • Weather (temperatures, rainfall amounts)
  • Economic indicators (inflation rate, unemployment)
  • Performance metrics (revenue, users, etc.)

The Hybrid Future

At Skepsis, we believe continuous markets can handle most prediction needs. But we’re also exploring:

Derived Binary Markets

From a continuous market, you can derive any binary question:
Continuous: "Where will BTC be Dec 31?"

Derived binaries (from same underlying):
- "BTC > $100K?" β†’ Sum of probability above $100K
- "BTC > $90K?" β†’ Sum of probability above $90K
- "BTC between $95K-$105K?" β†’ Sum of that range
One continuous market = infinite binary markets

Summary

AspectBinaryContinuous
InformationSingle probabilityFull distribution
ExpressivenessThreshold onlyAny range
Edge casesPunishes β€œalmost right”Rewards accuracy
Capital efficiencyMultiple marketsOne market
Price discoveryLimitedRich
NuanceNonePreserved
Best forNaturally binary eventsNumerical outcomes

Try the Difference

Experience continuous markets yourself:
Make a continuous prediction: Launch Skepsis β†’

Next Steps

EconomicsHow the money flows in continuous marketsEconomics
vs PolymarketDirect comparison with the leading binary platformvs Polymarket