POLYMARKET · PREDICTION MARKET · SPORTS

Will Croatia advance to the knockout stages at the 2026 FIFA World Cup?

YES · live

74.5¢

NO · live

25.5¢

▸ Advanced metrics · M2M bundle

polymarket · will-croatia-advance-to-the-knockout-stages-at-the-2026-fifa-world-cup · fresh · feed 2s old

24h sparkline · 60 pts▼ —

realized vol (ann.)

115.82%

max drawdown

3.27%

sharpe

—

ulcer index

1.83%

RMS drawdown

pain index

1.26%

mean drawdown

mod. VaR 95%

0.00%

Cornish-Fisher

martin ratio

—

ret / ulcer

CDaR 95%

2.64%

cond. drawdown

gain/pain

0.20

Σgain / Σ|loss|

sterling

—

ret / CDaR

omega (θ=0)

0.20

upside/downside

roll spread

0.6 bps

implied (price-only)

bars used

850

store

spread

—

24h Δ

—

flow lean

—

carry

flat

signalNEUTRALconfidence 20%

Same bundle via M2M API: /api/m2m/pm-will-croatia-advance-to-the-knockout-stages-at-the-2026-fifa-world-cup/bundle · venue execution: polymarket →

LIVEPOLL0SRCFRESH2.3s⏱--:--:-- UTCNEXT8.0sUP0s--:--HIST0/30

▶ STREAMING·HYPERLIQUID·POLYMARKET·0 POLLS·SRC FRESH·UPTIME 0s·NEXT POLL 8.0s·CC0 OPEN DATA·HYPO.MARKETS·▶ STREAMING·HYPERLIQUID·POLYMARKET·0 POLLS·SRC FRESH·UPTIME 0s·NEXT POLL 8.0s·CC0 OPEN DATA·HYPO.MARKETS·

YES · live

74.5¢

NO · live

25.5¢

YES price · live 24h

25 ticks · last 74.50¢

YES / NO split · live

Σ 100.00% · fair

Σ-sides total = 100.00% (tight rounding)

H(p) entropy = 0.819 / 1.00 bits (82%) · high uncertainty

YES

74.5%74.5¢1.34×▬ +0.00pp

25.5%25.5¢3.92×▬ +0.00pp

Σ 100.00% · arb gap 0.00pp

Per-tick activity · |Δp| in basis points · live

Σ 400bp moved · peak 200bp · n=24 ticks

Live numerics · pulse on poll

LIVE NUMERICS8 metrics·POLL 0

⏱snapshot age

2.3s

▲YES mid

74.50¢ (74.50%)

▼NO mid

25.50¢ (25.50%)

ΣΣ sides

100.00%

⚖arb gap

0.000pp

$24h vol $

$27.7k

≋liquidity $

$24.2k

◳history points

25 ticks (live)

§1 · 24h price history (YES + NO tokens)

YES price · CLOB mid

25 YES observations from clob.polymarket.com · last 74.50¢

NO price · CLOB mid

25 NO observations from clob.polymarket.com · last 25.50¢

§2 · Distribution of Δp

Histogram of hourly increments

n=24

Q-Q plot · standardised Δp vs N(0,1)

reference line = identity (perfect normality). Heavy upper-right tail = fat positive tail.

§3 · Sample moments

Descriptive statistics · 5-number summary · shape diagnostics

SAMPLE MOMENTS · N=25LEPTOKURTIC · FAT TAILS (G₂=2.49)

μ MEAN76.34¢95% CI: [76.03¢, 76.65¢]

σ STD DEV0.80ppσ² = 0.640 · CV = 1.05%

med MEDIAN76.50¢Q₁ 76.50¢ · Q₃ 76.50¢

FIVE-NUMBER SUMMARY · BOX PLOTrange 4.00pp · IQR 0.00pp (1.349σ→1.08pp)

SKEWNESS · G₁-0.666left-skewed

−3−10+1+3

EXCESS KURTOSIS · G₂2.485leptokurtic · fat tails

−30+2+4+6

μ ↔ medianμ < med · left-tailed|μ−med| / σ = 0.20

σ × 1.349 ↔ IQRdiverges from normalratio = 0.00

range ↔ σwide tails (range > 4σ)range / σ = 5.00

μ = mean YES probability · σ = standard deviation · 95% CI = μ ± 1.96·SE. Skew/kurt diagnose departure from normality.

§5 · Time-series structure

Regime & autocorrelation diagnostics

TIME-SERIES STRUCTUREREGIME: MEAN-REVERTING · ADF rejects unit root

ρ(1) AUTOCORR-0.049within white-noise band

ρ(2) AUTOCORR-0.053lag-2 not significant

H · HURST EXPONENT1.169strongly persistent

OLS TREND · t-STAT-3.962significant @ α=0.05

HURST EXPONENT [0, 1]strongly persistent · H = 1.169

H = 1.169STRONGLY PERSISTENT

0
anti-persistent0.45
mean-reverting0.5
random walk0.55
persistent1
strongly trending

AUTOCORRELATION FUNCTION · ρ(k) for k=1..5WHITE NOISE · no significant lags

OLS TREND · t-STAT · [-5, +5]SIGNIFICANT @ 1% (|t|=3.96)

−5 reject−1.960 retain H₀+1.96+5 reject

REGIME CLASSIFICATIONMEAN-REVERTING · ADF rejects unit rootfrom Hurst + ρ(1) joint diagnosis

PREDICTABILITY · score 1.00very high · strong structure|ρ(1)| + 2·|H − 0.5| heuristic

TREND SIGNIFICANCESIGNIFICANT @ 1% (|t|=3.96)α=0.05 critical |t|=1.96 · α=0.01 |t|=2.58

ρ(k) = lag-k sample autocorrelation · H = R/S Hurst exponent · t = OLS-trend t-statistic. Significance bands at ±2/√n approximate the 95% white-noise envelope. α=0.05 critical |t|=1.96; α=0.01 |t|=2.58.

§6 · Microstructure

Market quality · two-sided pricing · activity

MICROSTRUCTURE · MARKET QUALITYPERFECT · ARB-FREE Σ=100.00%

MARKET ID2070776

SLUGwill-croatia-adv…fa-world-cup

CATEGORYSports

TWO-SIDED PRICINGFAVOURS YES (75¢)

PRIMARY · YES74.50¢implied prob 74.50% · decimal odds 1.34×

COUNTER · NO25.50¢implied prob 25.50% · decimal odds 3.92×

74.50¢

25.50¢

Σ-SIDES ARBITRAGE TESTPERFECT · ARB-FREE Σ=100.00%

0%50%100% · target110%

Σ = 100.00% · |1 − Σ| = 0.000pp

24H ACTIVITY · LIQUIDITYACTIVE

24H VOLUME27.65k USD 24h

LIQUIDITY24.18k USD

MARKET QUALITYPERFECT · ARB-FREE Σ=100.00%|1−Σ| ≤ 0.5pp ⇒ fair · > 2pp ⇒ inefficient

PRICING SKEWFAVOURS YES (75¢)|primary − counter| = 0.490 · entropy 0.819 bits

LIQUIDITY DEPTHACTIVE100k+ deep · 10k+ active · 1k+ modest · 100+ thin

Σ-sides = YES + NO implied probabilities. Perfect arb-free Σ = 100%. |1−Σ| > 2pp suggests synthetic outright arbitrage.

§7 · Position sizing & edge analysis

Probability split · YES vs NO · Kelly · entropy · arbitrage

FAIR MARKET · no edge

Probability scale (YES)

0%25%50%
fair75%100%

Implied decimal odds

YES1.34×(75¢)NO3.92×(26¢)

Kelly bet-size (% of bankroll) K* = 0.00%

K* full

0.00%

½K half

0.00%

¼K quarter

0.00%

Entropy H(p̂) = 0.819 bits (82% of max) · high uncertainty

0 (certain)0.250.50.751.00 (max)

Σ-sides = 100.00% · |1 − Σ| = 0.00pp · tight cross-venue rounding

K* full = (b·p − q)/b · ½K and ¼K are conservative fractions of the full-Kelly bet. Entropy in bits — log₂(2)=1 is maximum uncertainty for a binary market.

§8 · Time decay & θ projection

Time decay & theta projection

⏱ URGENCY · LOWresolves 2026-06-28 00:00 UTC

7days

12hrs

50min

YES →$1.00(P = 74.5%)

NO →$0.00(P = 25.5%)

current: $0.7450 · expected return per side: $0.26 on YES hit · $0.74 on NO hit

Theta progression · θ ∝ σ / √t_remainingθ_now = 3.919 pp/day

now7.53d left

3.919 pp/day×1.00

−25%5.65d left

4.525 pp/day×1.15

−50%3.77d left

5.543 pp/day×1.41

−75%1.88d left

7.838 pp/day×2.00

−90%18.08h left

12.394 pp/day×3.16

θ approximation: σ/√T (expected daily move magnitude). The cone shows ±√(p̂(1−p̂)) widening as time decays, funneling to {0, 1} at resolution. Theta accelerates as √(t_left)→0.

§9 · Hourly return heatmap

24-hour signed Δp grid · green = up · red = down

0 up bars · 2 down · best 0.00% · worst -2.00% · typical |Δ| 0.167%

§10 · Equity curve & underwater drawdown

Cumulative compounded return + running peak-to-trough

final equity 0.9604 (-3.96%) · max DD -3.96% · time-under-water 24/25 bars

§11 · Rolling-window statistics (w = 6 bars)

Rolling annualised Sharpe ratio · green positive · red negative

latest -38.210 · range [-38.21, 0.00] · μ -8.044 · positive Sharpe = excess-return-per-risk earned by buying-and-holding through this window

Rolling annualised volatility (%)

latest 76.42% · range [0.00%, 76.42%] · μ 16.09% · σ̂ scaled to annualised (×√8760)

Rolling lag-1 autocorrelation ρ(1)

latest -0.233 · |ρ| > 0.3 ⇒ regime with persistence (ρ > 0) or reversal (ρ < 0) · |ρ| ≤ 0.1 = consistent with random walk

§12 · Hypothesis tests (α = 0.05)

Formal inference at 5% significance

2 of 5 REJECT · mixed evidence2 reject·3 pass·1 n/a·α = 0.05

𝒩

Jarque-Bera

REJECT H₀***

H₀: Δp ~ Normal(μ, σ²)

STATISTIC

124.7193

p-VALUE (log scale)

< 0.0001

10⁻⁴10⁻³10⁻²10⁻¹1

Ljung-Box(h=5)

FAIL TO REJECTns

H₀: No serial autocorrelation up to lag 5

STATISTIC

0.1683

p-VALUE (log scale)

0.9987

10⁻⁴10⁻³10⁻²10⁻¹1

Dickey-Fuller (τ_μ)

FAIL TO REJECTns

H₀: p has a unit root (non-stationary)

STATISTIC

-2.4648

p-VALUE (log scale)

0.1309

10⁻⁴10⁻³10⁻²10⁻¹1

Wald-Wolfowitz runs

N/An/a

H₀: Sign sequence of Δ is random

STATISTIC

—

p-VALUE (log scale)

—

KPSS (μ stationarity)

REJECT H₀*

H₀: p IS level-stationary

STATISTIC

0.5283

p-VALUE (log scale)

0.0353

10⁻⁴10⁻³10⁻²10⁻¹1

Variance ratio q=3

FAIL TO REJECTns

H₀: Δp is a random walk · VR = 1

STATISTIC

-1.1446

p-VALUE (log scale)

0.2524

10⁻⁴10⁻³10⁻²10⁻¹1

Each row states an explicit null H₀, the test statistic, an approximated p-value, and the decision. REJECT means evidence against H₀. KPSS complements ADF (rejecting both ⇒ ambiguous; rejecting one ⇒ clean verdict).

§13 · Spectral analysis (DFT periodogram)

Power spectrum of Δp · ‖X̂(k)‖²/n

dominant period ≈ 3.00h (freq 0.333) · concentrates 18.2% of total energy · Σ|X̂|²/n = 3.667e-4

▸ Depth section using sovereign-store price series (850 bars · effective 1752616 bars/year) — annualisation reflects native polling cadence, not upstream timeframes.

§14 · Honest position analytics

A binary-market analytics module framed in horizon time (days to resolution, not annualised). Estimators that need a model probability q as a first-class input (Kelly, KL divergence, Bayesian posterior, Mark-to-Market MC) only render when q is provided externally. Sweep an exploratory q at the interactive simulator →

§15 · Horizon returns

Returns · per bar / per day / per horizon

Horizon 7.5 d · σ/bar 0.088pp · expected |Δp| over horizon 1.18ppterminal variance p(1−p) = 0.1900 · n = 850✓ n = 850

μ per bar

-0.002pp

average Δp · drift

σ per bar

0.088pp

one-bar volatility · logit-free

Per-day movedaily

0.43pp

σ × √24

Per-horizon move8d

1.18pp

σ × √180.8369313888889

Terminal variancebinary

0.1900

p(1−p) at resolution

Current pricep

74.5¢

latest snapshot

Note: annualised Sharpe/Sortino are omitted — they are not meaningful for a bounded fixed-horizon binary contract that snaps to {0, 1} at resolution.

Annualised metrics are intentionally omitted — they don't apply to bounded probability series that resolve at a fixed date.

§16 · Tail risk

VaR · ES · max drawdown

VaR₉₅ 0.15pp · ES₉₅ 0.18pp · method parametric · drift-correcteddrift -0.002pp/bar · quantised: yes · median step 2.00pp · unique ratio 0.00✓ n = 850

VaR 95%

0.15pp

1.645·σ (parametric) of Δp

ES 95%

0.18pp

mean of the tail

Max drawdown

3.3pp

peak 76.5¢ → trough 74.0¢

Median step

2.00pp

price bucket granularity

Price series is bucketed (cent grid). Empirical quantiles collapse to grid points — parametric N(0, σ²) used instead.

Empirical quantiles unless the price series is bucketed (PM cent grid), in which case parametric N(0, σ²) is used to avoid grid collapse.

§17 · Odds conversion

Odds conversion · every dialect a bettor thinks in

Implied probabilityP

74.5%

= price

Decimal oddsEU

1.342

total return per $1

AmericanUS

-292

risk $292 to win $100

FractionalUK

0.34 / 1

profit per $1 risked

Profit per $100stake

+$34.23

clean dollar framing

underdog (+)favorite (-)your price

Price → implied probability → decimal odds → American moneyline → fractional. Five views of the same number, plus the moneyline curve.

§18 · Binary entropy

Binary entropy · uncertainty as bits of information

Market entropyH(p)

0.819 bit

max 1.0 at p = 0.5

Your entropyH(q)

0.819 bit

Δ +0.000 bit vs market

Surprise · YES−log₂ p

0.42 bit

self-information

Surprise · NO−log₂(1−p)

1.97 bit

self-information

Market entropy only — model entropy requires an external q.

§19 · Model-dependent surfaces

§ Edge / Kelly / KL · no model probability provided

External model required

The position-economics, Kelly, KL-divergence, Bayesian and Monte-Carlo surfaces require a model probability q as input — a number independent of the market price p.

The previous build defaulted q to a tape-momentum heuristic derived from p; that produces apparent edge that is structurally guaranteed to be small and is not a useful skill signal. The auto-derived path has been removed.

To explore these surfaces with a hypothetical q, open the interactive simulator and drag the MODEL P(YES) slider. To wire a real model, POST to the NOSTRADAMUS hook (TBD) or pass ?q=… on the simulator URL.

§∞ · Provenance & attestation

Upstream (snapshot): gamma-api.polymarket.com
Upstream (history): clob.polymarket.com
YES token ID: 67715735941429794717067696771416793168660820179681905042643596996616149977203
NO token ID: 40250089939564440648546929051371693169444630979782549254386419912545923219451
Snapshot fetched: 2026-06-20 11:09:44 UTC
Snapshot age: 2.3s
History points: 25 CLOB mids
Page rendered: 2026-06-20 11:09:47 UTC
Storage policy: no persistence — fetched on every request
SHA-256 attestation: 0a2e5fd28460a8b994161f95afd82cd4dcf259d386dc0f510224e1385a598af6 · deterministic hash of source snapshot
Open data licence: CC0 / public domain

§∞-2 · Related markets · explore more

HL PREDSpain88.5¢HL PREDEcuador86.5¢HL PREDBelgium67.7¢POLYMARKETWill USA win the 2026 FIFA World Cup?3¢POLYMARKET Iran agrees to end enrichment of uranium by June 30?5¢POLYMARKETWill Paraguay win the 2026 FIFA World Cup?0¢HL PERPBTC-USD perpetual$63,628 HL PERPHYPE-USD perpetual$70.63 HL PERPETH-USD perpetual$1,726.3

Also see: /arb opportunities · RSS feed · more in Sports

Market depth

▸ live order book · Polymarket YES

Depth within 1bp

bid $0 · ask $0

Depth within 5bp

bid $0 · ask $0

Depth within 10bp

bid $0 · ask $0

Depth within 50bp

bid $0 · ask $0

Mid price

0.745000

(best bid + best ask) / 2

Spread

134.2bp

(bestAsk − bestBid) / mid

Imbalance (whole book)

-0.335

ask-heavy

Imbalance (top-5)

-0.811

ask-heavy top-of-book

Slippage scenarios

▸ live book walk · Polymarket YES

Simulating a market order at three notionals against the live book. Slippage = avg execution price vs. mid, in basis points. Worst fill = price of the deepest level touched. Live JSON: /api/asset/pm-will-croatia-advance-to-the-knockout-stages-at-the-2026-fifa-world-cup/slippage?size=10000&side=buy

Side	Notional	Avg fill	Slippage	Worst fill	Levels	Status
BUY	$1.00K	0.757195	163.69bp	0.760000	2	FILLED
BUY	$10.00K	0.766561	289.41bp	0.770000	3	FILLED
BUY	$100.00K	0.791656	626.25bp	0.990000	20	PARTIAL
SELL	$1.00K	0.735585	126.38bp	0.730000	2	FILLED
SELL	$10.00K	0.521038	3006.21bp	0.090000	40	FILLED
SELL	$100.00K	0.344642	5373.93bp	0.010000	48	PARTIAL

Risk metrics

▸ sovereign store · 850 barsperiods/year ≈ 1.75M

Realized vol (annualised)

154.07%

σ per bar = 0.001164

Mean return (annualised)

-5468.74%

μ per bar = -0.000031

Sharpe (rf=0)

-35.50

annualised; risk-free assumed zero

Max drawdown

3.27%

peak 0.77 → trough 0.74 over 443 bars

/api/asset/pm-will-croatia-advance-to-the-knockout-stages-at-the-2026-fifa-world-cup/risk · same metrics, JSON