POLYMARKET · PREDICTION MARKET · SPORTS

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

YES · live
69.5¢
NO · live
30.5¢

▸ Advanced metrics · M2M bundle

polymarket · will-scotland-advance-to-the-knockout-stages-at-the-2026-fifa-world-cup · fresh · feed 9s old
24h sparkline · 60 pts▼ —
realized vol (ann.)
85.34%
max drawdown
0.72%
sharpe
—
ulcer index
0.15%
RMS drawdown
pain index
0.03%
mean drawdown
mod. VaR 95%
0.00%
Cornish-Fisher
martin ratio
—
ret / ulcer
CDaR 95%
0.03%
cond. drawdown
gain/pain
3.00
Σgain / Σ|loss|
sterling
—
ret / CDaR
omega (θ=0)
3.00
upside/downside
roll spread
0.8 bps
implied (price-only)
bars used
362
store
spread
—
24h Δ
—
flow lean
—
carry
flat
signalNEUTRALconfidence 20%
Same bundle via M2M API: /api/m2m/pm-will-scotland-advance-to-the-knockout-stages-at-the-2026-fifa-world-cup/bundle · venue execution: polymarket →
LIVEPOLL0SRCFRESH8.5s⏱--:--:-- UTC8NEXT8.0sUP0s--:--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
69.5¢
NO · live
30.5¢
YES price · live 24h
n=25 · μ=0.7550 · σ=0.0677 · range [0.6400, 0.8300] · R²=0.649▼ FALLING -12.03%σ HIGH 8.96%LAST 0.69500.83000.78250.73500.68750.6400μ = 0.7550max 0.8300min 0.6400dataMA(5)OLS R²=0.65μ lineμ ± σ bandmaxminlive endpoint
25 ticks · last 69.50¢
YES / NO split · live
YES 69.5%NO 30.5%YES69.5%69.50¢ · odds 1/1.44
Σ 100.00% · fair
Σ-sides total = 100.00% (tight rounding)
H(p) entropy = 0.887 / 1.00 bits (89%) · high uncertainty
YES
69.5%69.5¢1.44×▬ +0.00pp
NO
30.5%30.5¢3.28×▬ +0.00pp
Σ 100.00% · arb gap 0.00pp
Per-tick activity · |Δp| in basis points · live
n=24 · Σ=3,850 · μ=160.4 · σ=291.5 · CV=1.82BURSTY · concentratedcumulative energy ↗ · 50% by h=1403376751,0121,350μ = 1601,35050%h1h5h9h13h17h21#1 peak#2-3> μactivequietμ linecum energy
Σ 3850bp moved · peak 1350bp · n=24 ticks
Live numerics · pulse on poll
LIVE NUMERICS8 metrics·POLL 0
⏱snapshot age
8.5s
▲YES mid
69.50¢ (69.50%)
▼NO mid
30.50¢ (30.50%)
ΣΣ sides
100.00%
⚖arb gap
0.000pp
$24h vol $
$62.3k
≋liquidity $
$70.0k
◳history points
25 ticks (live)

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

YES price · CLOB mid
n=25 · μ=0.7550 · σ=0.0677 · range [0.6400, 0.8300] · R²=0.649▼ FALLING -12.03%σ HIGH 8.96%LAST 0.69500.83000.78250.73500.68750.6400μ = 0.7550max 0.8300min 0.6400dataMA(5)OLS R²=0.65μ lineμ ± σ bandmaxmin
25 YES observations from clob.polymarket.com · last 69.50¢
NO price · CLOB mid
n=25 · μ=0.2450 · σ=0.0677 · range [0.1700, 0.3600] · R²=0.649▲ RISING +45.24%σ EXTREME 27.61%LAST 0.30500.36000.31250.26500.21750.1700μ = 0.2450max 0.3600min 0.1700dataMA(5)OLS R²=0.65μ lineμ ± σ bandmaxmin
25 NO observations from clob.polymarket.com · last 30.50¢

§2 · Distribution of Δp

Histogram of hourly increments
n=24 · 10 bins · μ=-0.0074 · σ=0.0306 · skew=-2.08 (left-skewed) · kurt=6.99 (leptokurtic (fat tails))14117401-12.52ppbin -12.52pp · n=1 · 7.1% peakbin -12.52pp · n=1 · 7.1% peak-10.57pp-8.62pp-6.67pp1-4.72ppbin -4.72pp · n=1 · 7.1% peakbin -4.72pp · n=1 · 7.1% peak1-2.77ppbin -2.77pp · n=1 · 7.1% peakbin -2.77pp · n=1 · 7.1% peak14-0.83ppbin -0.83pp · n=14 · 100.0% peakbin -0.83pp · n=14 · 100.0% peak51.12ppbin 1.12pp · n=5 · 35.7% peakbin 1.12pp · n=5 · 35.7% peak13.07ppbin 3.07pp · n=1 · 7.1% peakbin 3.07pp · n=1 · 7.1% peak15.02ppbin 5.02pp · n=1 · 7.1% peakbin 5.02pp · n=1 · 7.1% peakμΔ < 0 · loss barsΔ ≈ 0 · flatΔ > 0 · gain barsN(μ,σ²) referenceμ line · ±σ band shaded
n=24
Q-Q plot · standardised Δp vs N(0,1)
n=24 · skew=-2.40 · kurt=8.77 · near 8 / mid 15 / far 1 · OLS slope=0.83 intercept=-0.00LEPTOKURTIC — FAT TAILSUPPER TAIL NORMALLOWER TAIL NORMAL-3σ-3σ-2σ-2σ-1σ-1σ+0σ+0σ+1σ+1σ+2σ+2σ+3σ+3σΔ=-2.00σsample ↓marginal: sample bars + theoretical N(0,1) curve →theoretical Φ⁻¹(p) →↑ sample z-quantile|Δ| < 0.3σ · on the line|Δ| < 1σ · moderate|Δ| ≥ 1σ · outliery = x refOLS fit
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=25PLATYKURTIC · THIN TAILS (G₂=-1.83)
μ MEAN75.50¢95% CI: [72.85¢, 78.15¢]
σ STD DEV6.77ppσ² = 45.771 · CV = 8.96%
med MEDIAN79.00¢Q₁ 68.50¢ · Q₃ 81.50¢
FIVE-NUMBER SUMMARY · BOX PLOTrange 19.00pp · IQR 13.00pp (1.349σ→9.13pp)
min 64.00¢Q₁ 68.50¢med 79.00¢Q₃ 81.50¢max 83.00¢μ
SKEWNESS · G₁-0.259approximately symmetric
−3−10+1+3
EXCESS KURTOSIS · G₂-1.829platykurtic · thin tails
−30+2+4+6
μ ↔ medianμ < med · left-tailed|μ−med| / σ = 0.52
σ × 1.349 ↔ IQRdiverges from normalratio = 0.70
range ↔ σconcentrated (range < 4σ)range / σ = 2.81
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: INDETERMINATE · weak signal at n=24
ρ(1) AUTOCORR+0.070within white-noise band
ρ(2) AUTOCORR-0.354lag-2 not significant
H · HURST EXPONENT0.895strongly persistent
OLS TREND · t-STAT-6.517significant @ α=0.05
HURST EXPONENT [0, 1]strongly persistent · H = 0.895
H = 0.895STRONGLY 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
k=1+0.070k=2-0.354k=3+0.005k=4+0.041k=5+0.0520+1−1+0.41−0.41+ momentum (ρ > +0.41)− reversal (ρ < −0.41)noise (within band)±2/√n threshold
OLS TREND · t-STAT · [-5, +5]SIGNIFICANT @ 1% (|t|=6.52)
−5 reject−1.960 retain H₀+1.96+5 reject
REGIME CLASSIFICATIONINDETERMINATE · weak signal at n=24from Hurst + ρ(1) joint diagnosis
PREDICTABILITY · score 0.86very high · strong structure|ρ(1)| + 2·|H − 0.5| heuristic
TREND SIGNIFICANCESIGNIFICANT @ 1% (|t|=6.52)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 ID2070741
SLUGwill-scotland-ad…fa-world-cup
CATEGORYSports
TWO-SIDED PRICINGFAVOURS YES (70¢)
PRIMARY · YES69.50¢implied prob 69.50% · decimal odds 1.44×
COUNTER · NO30.50¢implied prob 30.50% · decimal odds 3.28×
69.50¢
30.50¢
Σ-SIDES ARBITRAGE TESTPERFECT · ARB-FREE Σ=100.00%
0%50%100% · target110%
Σ = 100.00% · |1 − Σ| = 0.000pp
24H ACTIVITY · LIQUIDITYACTIVE
24H VOLUME62.29k USD 24h
LIQUIDITY70.03k USD
MARKET QUALITYPERFECT · ARB-FREE Σ=100.00%|1−Σ| ≤ 0.5pp ⇒ fair · > 2pp ⇒ inefficient
PRICING SKEWFAVOURS YES (70¢)|primary − counter| = 0.390 · entropy 0.887 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
YES 69.5%NO 30.5%YES p̂69.5%H = 0.887 / 1.00 bits
Probability scale (YES)
0%25%50%
fair75%100%
Implied decimal odds
YES1.44×(70¢)NO3.28×(31¢)
Kelly bet-size (% of bankroll) K* = 0.00%
K* full
0.00%
½K half
0.00%
¼K quarter
0.00%
Entropy H(p̂) = 0.887 bits (89% 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
15hrs
16min
7.64 days·θ = 33.144 pp/day
YES →$1.00(P = 69.5%)
NO →$0.00(P = 30.5%)
current: $0.6950 · expected return per side: $0.31 on YES hit · $0.69 on NO hit
0%25%50%75%100%YES $1NO $0NOW+3.8dRESOLVESP projection · σ=6.77% · path funnel to settle at YES=1 or NO=0
Theta progression · θ ∝ σ / √t_remainingθ_now = 33.144 pp/day
now7.64d left
33.144 pp/day×1.00
−25%5.73d left
38.271 pp/day×1.15
−50%3.82d left
46.872 pp/day×1.41
−75%1.91d left
66.287 pp/day×2.00
−90%18.33h left
104.809 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
HOURLY RETURN HEATMAP · n=24 bars · best 6.00% · worst -13.50% · typical |Δ| 1.60%BEARISH SESSION -9.50%BEST+6.00%16hWORST-13.50%14hTYPICAL |Δ|1.60%mean absoluteCUMULATIVE-9.50%Σ signed ΔSTREAK▬ 0flat-runASIA · 00-08 UTCμ +0.43% · Σ +3.00%EUROPE · 08-16 UTCμ -2.25% · Σ -18.00%US · 16-24 UTCμ +0.69% · Σ +5.50%CUMULATIVE Δ PATH · final -9.50%+4.00%-15.00%0.00% · 1h0.00% · 1h·1h3.00% · 2h3.00% · 2h3.00%2h-0.50% · 3h-0.50% · 3h-0.50%3h1.50% · 4h1.50% · 4h1.50%4h-0.50% · 5h-0.50% · 5h-0.50%5h-0.50% · 6h-0.50% · 6h-0.50%6h0.00% · 7h0.00% · 7h·7h-0.50% · 8h-0.50% · 8h-0.50%8h-1.00% · 9h-1.00% · 9h-1.00%9h0.00% · 10h0.00% · 10h·10h0.00% · 11h0.00% · 11h·11h1.50% · 12h1.50% · 12h1.50%12h-0.50% · 13h-0.50% · 13h-0.50%13h-13.50% · 14h-13.50% · 14h-13.50%14h▼ WORST-4.00% · 15h-4.00% · 15h-4.00%15h6.00% · 16h6.00% · 16h6.00%16h★ BEST-2.00% · 17h-2.00% · 17h-2.00%17h0.00% · 18h0.00% · 18h·18h-1.00% · 19h-1.00% · 19h-1.00%19h1.00% · 20h1.00% · 20h1.00%20h0.50% · 21h0.50% · 21h0.50%21h1.00% · 22h1.00% · 22h1.00%22h0.00% · 23h0.00% · 23h·23h0.00% · 24h0.00% · 24h·24hTIME PATTERNUS-led (+5.50%)RUNSup max 3 · down max 3BREADTH29% up · 42% down · 29% flat
7 up bars · 10 down · best 6.00% · worst -13.50% · typical |Δ| 1.604%

§10 · Equity curve & underwater drawdown

Cumulative compounded return + running peak-to-trough
EQUITY & DRAWDOWN ANALYSIS · n=25 barsSEVERE DRAWDOWN -10.30%FINAL-10.30%MAX DD-18.21%RECOVERYONGOING · 20 barsMAX RUN-UP+4.02%UNDERWATER21/25 (84%)STREAK▬ 0EQUITY CURVE · end 0.8970 · peak 1.0402 · range [0.8508, 1.0402]1.04020.8508break-even = 1★ PEAK 1.0402UNDERWATER DRAWDOWN · max -18.21% · severe0%-18.21%▼ TROUGH -18.21%TOP DRAWDOWN PERIODS · 2 total#1 -18.21%bar 6-25 · 20 bars · ONGOING#2 -0.50%bar 4-4 · 1 bars · recoveredDD SEVERITYsevere (max -18.21%)RECOVERYongoing · 20 barsTIME UNDER WATER84% of session · 21/25 bars
final equity 0.8970 (-10.30%) · max DD -18.21% · time-under-water 21/25 bars

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

Rolling annualised Sharpe ratio · green positive · red negative
n=19 · +5 / −12 (26% positive) · μ=-14.71 · σ=37.34UNPROFITABLE STRATEGYLAST 30.86 (+1.22σ vs μ)103.6151.810.00-51.81-103.61μ = -14.7132.2932.2932.2932.29-9.74-9.74-17.82-17.82-103.61-103.61-76.42-76.420.000.00-9.06-9.06-37.78-37.78-46.17-46.17-24.78-24.78-29.76-29.76-34.04-34.04-35.39-35.390.000.0025.1725.17-6.50-6.5030.8630.8630.8630.86v > 0 · positivev < 0 · negativeμ mean lineμ ± σ bandlatest bar (outlined)
latest 30.857 · range [-103.61, 32.29] · μ -14.715 · positive Sharpe = excess-return-per-risk earned by buying-and-holding through this window
Rolling annualised volatility (%)
n=19 · μ=261.5064 · σ=233.2320 · range [35.2278, 618.5410] · R²=0.079▼ FALLING -47.67%σ EXTREME 89.19%LAST 70.9718618.5410472.7127326.8844181.056135.2278μ = 261.5064max 618.5410min 35.2278dataMA(3)OLS R²=0.08μ lineμ ± σ bandmaxmin
latest 70.97% · range [35.23%, 618.54%] · μ 261.51% · σ̂ scaled to annualised (×√8760)
Rolling lag-1 autocorrelation ρ(1)
n=19 · +6 / −13 (32% positive) · μ=-0.147 · σ=0.210MEAN-REVERSIONLAST -0.239 (-0.44σ vs μ)0.6380.3190.000-0.319-0.638μ = -0.147-0.452-0.452-0.286-0.286-0.379-0.379-0.072-0.072-0.363-0.363-0.133-0.1330.1430.143-0.058-0.0580.0210.0210.1160.1160.0190.019-0.025-0.025-0.059-0.0590.0600.060-0.638-0.638-0.297-0.2970.0050.005-0.152-0.152-0.239-0.239v > 0 · positivev < 0 · negativeμ mean lineμ ± σ bandlatest bar (outlined)
latest -0.239 · |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 6 REJECT · mixed evidence2 reject·4 pass·α = 0.05
𝒩

Jarque-Bera

REJECT H₀***

H₀: Δp ~ Normal(μ, σ²)

STATISTIC
152.0228
p-VALUE (log scale)
< 0.0001
α
10⁻⁴10⁻³10⁻²10⁻¹1
p < α · rejection zonenon-normal · fat tails or skew present
ρ

Ljung-Box(h=5)

FAIL TO REJECTns

H₀: No serial autocorrelation up to lag 5

STATISTIC
3.8320
p-VALUE (log scale)
0.5760
α
10⁻⁴10⁻³10⁻²10⁻¹1
p ≥ α · null retainedconsistent with white noise
Ψ

Dickey-Fuller (τ_μ)

FAIL TO REJECTns

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

STATISTIC
-1.0606
p-VALUE (log scale)
0.7294
α
10⁻⁴10⁻³10⁻²10⁻¹1
p ≥ α · null retainedrandom-walk behaviour (crit ≈ -2.86)
±

Wald-Wolfowitz runs

FAIL TO REJECTns

H₀: Sign sequence of Δ is random

STATISTIC
-0.1219
p-VALUE (log scale)
0.9030
α
10⁻⁴10⁻³10⁻²10⁻¹1
p ≥ α · null retainedsigns appear random (9 runs)
χ

KPSS (μ stationarity)

REJECT H₀*

H₀: p IS level-stationary

STATISTIC
0.7185
p-VALUE (log scale)
0.0119
α
10⁻⁴10⁻³10⁻²10⁻¹1
p < α · rejection zonenon-stationary (crit 0.463)
χ

Variance ratio q=3

FAIL TO REJECTns

H₀: Δp is a random walk · VR = 1

STATISTIC
-0.2778
p-VALUE (log scale)
0.7812
α
10⁻⁴10⁻³10⁻²10⁻¹1
p ≥ α · null retainedVR 0.915 ≈ 1 (RW behaviour)
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
n=12 bins · noise floor μ=1.07e-3 · top T=4.80h (19.2%) · top-3 cover 44.5%1 SIGNIFICANT CYCLEcumulative energy ↗ (1 bin above 2× noise)2.5e-31.9e-31.2e-36.2e-40.0e+0μ noise floor2× noise (significance)period 24.0 · power 1.26e-3 · 9.8% energyperiod 24.0 · power 1.26e-3 · 9.8% energyperiod 12.0 · power 4.02e-4 · 3.1% energyperiod 12.0 · power 4.02e-4 · 3.1% energyperiod 8.0 · power 1.08e-3 · 8.5% energyperiod 8.0 · power 1.08e-3 · 8.5% energyperiod 6.0 · power 1.05e-3 · 8.2% energyperiod 6.0 · power 1.05e-3 · 8.2% energyperiod 4.8 · power 2.47e-3 · 19.2% energyperiod 4.8 · power 2.47e-3 · 19.2% energyperiod 4.0 · power 1.60e-3 · 12.5% energyperiod 4.0 · power 1.60e-3 · 12.5% energyperiod 3.4 · power 1.64e-3 · 12.8% energyperiod 3.4 · power 1.64e-3 · 12.8% energyperiod 3.0 · power 1.19e-3 · 9.3% energyperiod 3.0 · power 1.19e-3 · 9.3% energyperiod 2.7 · power 1.17e-3 · 9.1% energyperiod 2.7 · power 1.17e-3 · 9.1% energyperiod 2.4 · power 3.69e-4 · 2.9% energyperiod 2.4 · power 3.69e-4 · 2.9% energyperiod 2.2 · power 2.82e-4 · 2.2% energyperiod 2.2 · power 2.82e-4 · 2.2% energyperiod 2.0 · power 3.01e-4 · 2.3% energyperiod 2.0 · power 3.01e-4 · 2.3% energy50% by T=4.0h#1 dominantT=4.80h#2T=3.43h#3T=4.00hT=2hT=3hT=4hT=6hT=8hT=12hT=16hT=24h← shorter cycle (high freq · Nyquist=½) · period T (bars per cycle) · longer cycle (low freq · 1/n) →#1 dominant#2 peak#3 peak> 2× noisenoiseμ floor2μ sig.cum energy
dominant period ≈ 4.80h (freq 0.208) · concentrates 19.2% of total energy · Σ|X̂|²/n = 1.282e-2

▸ Depth section using sovereign-store price series (389 bars · effective 1752129 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 7.6 d · σ/bar 0.505pp · expected |Δp| over horizon 6.83ppterminal variance p(1−p) = 0.2120 · n = 389✓ n = 389
μ per bar
-0.031pp
average Δp · drift
σ per bar
0.505pp
one-bar volatility · logit-free
Per-day movedaily
2.47pp
σ × √24
Per-horizon move8d
6.83pp
σ × √183.27528416666667
Terminal variancebinary
0.2120
p(1−p) at resolution
Current pricep
69.5¢
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 0.86pp · ES₉₅ 1.07pp · method parametric · drift-correcteddrift -0.031pp/bar · quantised: yes · median step 0.50pp · unique ratio 0.04✓ n = 389
VaR 95%
0.86pp
1.645·σ (parametric) of Δp
ES 95%
1.07pp
mean of the tail
Max drawdown
16.0pp
peak 81.5¢ → trough 68.5¢
Median step
0.50pp
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
69.5%
= price
Decimal oddsEU
1.439
total return per $1
AmericanUS
-228
risk $228 to win $100
FractionalUK
0.44 / 1
profit per $1 risked
Profit per $100stake
+$43.88
clean dollar framing
-1000-5000+500+1000020406080100you · 69.5%implied probability (%)American odds
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)
0.887 bit
max 1.0 at p = 0.5
Your entropyH(q)
0.887 bit
Δ +0.000 bit vs market
Surprise · YES−log₂ p
0.52 bit
self-information
Surprise · NO−log₂(1−p)
1.71 bit
self-information
0.000.260.530.791.050.00.20.40.60.81.0marketmodelprobabilityH (bits)
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
2795605969001235670719617494663880900657443274144613117847190598195501764261
NO token ID
7264202565197835457949070489112354687713546453465613908439694825827123043640
Snapshot fetched
2026-06-20 08:43:20 UTC
Snapshot age
8.5s
History points
25 CLOB mids
Page rendered
2026-06-20 08:43:28 UTC
Storage policy
no persistence — fetched on every request
SHA-256 attestation
011c96bc9b17073fa07b3e33e48b8e50b3acd1c731fef8262c06f109141cf05d · deterministic hash of source snapshot
Open data licence
CC0 / public domain

§∞-2 · Related markets · explore more

HL PREDSpain88.4¢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 Egypt win the 2026 FIFA World Cup?0¢HL PERPBTC-USD perpetual$63,428HL PERPHYPE-USD perpetual$70.73HL PERPETH-USD perpetual$1,722.9

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

Market depth

▸ live order book · Polymarket YES
Depth within 1bp
$0
bid $0 · ask $0
Depth within 5bp
$0
bid $0 · ask $0
Depth within 10bp
$0
bid $0 · ask $0
Depth within 50bp
$0
bid $0 · ask $0
Mid price
0.695000
(best bid + best ask) / 2
Spread
143.9bp
(bestAsk − bestBid) / mid
Imbalance (whole book)
+0.463
bid-heavy
Imbalance (top-5)
+0.579
bid-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-scotland-advance-to-the-knockout-stages-at-the-2026-fifa-world-cup/slippage?size=10000&side=buy

SideNotionalAvg fillSlippageWorst fillLevelsStatus
BUY$1.00K0.70000071.94bp0.7000001FILLED
BUY$10.00K0.708022187.37bp0.7100002FILLED
BUY$100.00K0.8097871651.61bp0.99000018PARTIAL
SELL$1.00K0.676591264.88bp0.6700003FILLED
SELL$10.00K0.670653350.31bp0.6700003FILLED
SELL$100.00K0.5948651440.79bp0.01000041PARTIAL

Risk metrics

▸ sovereign store · 389 barsperiods/year ≈ 1.75M
Realized vol (annualised)
894.31%
σ per bar = 0.006756
Mean return (annualised)
-71925.93%
μ per bar = -0.000411
Sharpe (rf=0)
-80.43
annualised; risk-free assumed zero
Max drawdown
15.95%
peak 0.81 → trough 0.69 over 27 bars

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