POLYMARKET · PREDICTION MARKET · SPORTS

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

YES · live
66.5¢
NO · live
33.5¢

▸ Advanced metrics · M2M bundle

polymarket · will-scotland-advance-to-the-knockout-stages-at-the-2026-fifa-world-cup · fresh · feed 13s old
24h sparkline · 60 pts▼ —
realized vol (ann.)
140.63%
max drawdown
4.32%
sharpe
—
ulcer index
1.87%
RMS drawdown
pain index
0.86%
mean drawdown
mod. VaR 95%
0.00%
Cornish-Fisher
martin ratio
—
ret / ulcer
CDaR 95%
4.32%
cond. drawdown
gain/pain
0.43
Σgain / Σ|loss|
sterling
—
ret / CDaR
omega (θ=0)
0.43
upside/downside
roll spread
1.0 bps
implied (price-only)
bars used
577
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 →
LIVEPOLL0SRCWARMING13.1s⏱--:--:-- UTC8NEXT8.0sUP0s--:--HIST0/30
▶ STREAMING·HYPERLIQUID·POLYMARKET·0 POLLS·SRC WARMING·UPTIME 0s·NEXT POLL 8.0s·CC0 OPEN DATA·HYPO.MARKETS·▶ STREAMING·HYPERLIQUID·POLYMARKET·0 POLLS·SRC WARMING·UPTIME 0s·NEXT POLL 8.0s·CC0 OPEN DATA·HYPO.MARKETS·
YES · live
66.5¢
NO · live
33.5¢
YES price · live 24h
n=25 · μ=0.7500 · σ=0.0696 · range [0.6400, 0.8300] · R²=0.696▼ FALLING -15.82%σ HIGH 9.27%LAST 0.66500.83000.78250.73500.68750.6400μ = 0.7500max 0.8300min 0.6400dataMA(5)OLS R²=0.70μ lineμ ± σ bandmaxminlive endpoint
25 ticks · last 66.50¢
YES / NO split · live
YES 66.5%NO 33.5%YES66.5%66.50¢ · odds 1/1.50
Σ 100.00% · fair
Σ-sides total = 100.00% (tight rounding)
H(p) entropy = 0.920 / 1.00 bits (92%) · high uncertainty
YES
66.5%66.5¢1.50×▬ +0.00pp
NO
33.5%33.5¢2.99×▬ +0.00pp
Σ 100.00% · arb gap 0.00pp
Per-tick activity · |Δp| in basis points · live
n=24 · Σ=4,150 · μ=172.9 · σ=290.8 · CV=1.68BURSTY · concentratedcumulative energy ↗ · 50% by h=1303376751,0121,350μ = 1731,35050%h1h5h9h13h17h21#1 peak#2-3> μactivequietμ linecum energy
Σ 4150bp moved · peak 1350bp · n=24 ticks
Live numerics · pulse on poll
LIVE NUMERICS8 metrics·POLL 0
⏱snapshot age
13.1s
▲YES mid
66.50¢ (66.50%)
▼NO mid
33.50¢ (33.50%)
ΣΣ sides
100.00%
⚖arb gap
0.000pp
$24h vol $
$63.0k
≋liquidity $
$65.4k
◳history points
25 ticks (live)

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

YES price · CLOB mid
n=25 · μ=0.7500 · σ=0.0696 · range [0.6400, 0.8300] · R²=0.696▼ FALLING -15.82%σ HIGH 9.27%LAST 0.66500.83000.78250.73500.68750.6400μ = 0.7500max 0.8300min 0.6400dataMA(5)OLS R²=0.70μ lineμ ± σ bandmaxmin
25 YES observations from clob.polymarket.com · last 66.50¢
NO price · CLOB mid
n=25 · μ=0.2500 · σ=0.0696 · range [0.1700, 0.3600] · R²=0.696▲ RISING +59.52%σ EXTREME 27.82%LAST 0.33500.36000.31250.26500.21750.1700μ = 0.2500max 0.3600min 0.1700dataMA(5)OLS R²=0.70μ lineμ ± σ bandmaxmin
25 NO observations from clob.polymarket.com · last 33.50¢

§2 · Distribution of Δp

Histogram of hourly increments
n=24 · 10 bins · μ=-0.0083 · σ=0.0308 · skew=-1.96 (left-skewed) · kurt=6.44 (leptokurtic (fat tails))13107301-12.52ppbin -12.52pp · n=1 · 7.7% peakbin -12.52pp · n=1 · 7.7% peak-10.57pp-8.62pp-6.67pp1-4.72ppbin -4.72pp · n=1 · 7.7% peakbin -4.72pp · n=1 · 7.7% peak2-2.77ppbin -2.77pp · n=2 · 15.4% peakbin -2.77pp · n=2 · 15.4% peak13-0.83ppbin -0.83pp · n=13 · 100.0% peakbin -0.83pp · n=13 · 100.0% peak51.12ppbin 1.12pp · n=5 · 38.5% peakbin 1.12pp · n=5 · 38.5% peak13.07ppbin 3.07pp · n=1 · 7.7% peakbin 3.07pp · n=1 · 7.7% peak15.02ppbin 5.02pp · n=1 · 7.7% peakbin 5.02pp · n=1 · 7.7% 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=-2.22 · kurt=7.88 · near 10 / mid 13 / far 1 · OLS slope=0.86 intercept=-0.00LEPTOKURTIC — FAT TAILSUPPER TAIL NORMALLOWER TAIL NORMAL-3σ-3σ-2σ-2σ-1σ-1σ+0σ+0σ+1σ+1σ+2σ+2σ+3σ+3σΔ=-1.91σsample ↓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=-1.91)
μ MEAN75.00¢95% CI: [72.27¢, 77.73¢]
σ STD DEV6.96ppσ² = 48.375 · CV = 9.27%
med MEDIAN79.00¢Q₁ 68.00¢ · Q₃ 81.50¢
FIVE-NUMBER SUMMARY · BOX PLOTrange 19.00pp · IQR 13.50pp (1.349σ→9.38pp)
min 64.00¢Q₁ 68.00¢med 79.00¢Q₃ 81.50¢max 83.00¢μ
SKEWNESS · G₁-0.123approximately symmetric
−3−10+1+3
EXCESS KURTOSIS · G₂-1.907platykurtic · thin tails
−30+2+4+6
μ ↔ medianμ < med · left-tailed|μ−med| / σ = 0.58
σ × 1.349 ↔ IQRdiverges from normalratio = 0.70
range ↔ σconcentrated (range < 4σ)range / σ = 2.73
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+0.058within white-noise band
ρ(2) AUTOCORR-0.351lag-2 not significant
H · HURST EXPONENT0.977strongly persistent
OLS TREND · t-STAT-7.258significant @ α=0.05
HURST EXPONENT [0, 1]strongly persistent · H = 0.977
H = 0.977STRONGLY 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+0.058k=2-0.351k=3-0.015k=4+0.027k=5+0.0320+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|=7.26)
−5 reject−1.960 retain H₀+1.96+5 reject
REGIME CLASSIFICATIONINDETERMINATE · weak signal at n=24from Hurst + ρ(1) joint diagnosis
PREDICTABILITY · score 1.00very high · strong structure|ρ(1)| + 2·|H − 0.5| heuristic
TREND SIGNIFICANCESIGNIFICANT @ 1% (|t|=7.26)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 (67¢)
PRIMARY · YES66.50¢implied prob 66.50% · decimal odds 1.50×
COUNTER · NO33.50¢implied prob 33.50% · decimal odds 2.99×
66.50¢
33.50¢
Σ-SIDES ARBITRAGE TESTPERFECT · ARB-FREE Σ=100.00%
0%50%100% · target110%
Σ = 100.00% · |1 − Σ| = 0.000pp
24H ACTIVITY · LIQUIDITYACTIVE
24H VOLUME63.02k USD 24h
LIQUIDITY65.44k USD
MARKET QUALITYPERFECT · ARB-FREE Σ=100.00%|1−Σ| ≤ 0.5pp ⇒ fair · > 2pp ⇒ inefficient
PRICING SKEWFAVOURS YES (67¢)|primary − counter| = 0.330 · entropy 0.920 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 66.5%NO 33.5%YES p̂66.5%H = 0.920 / 1.00 bits
Probability scale (YES)
0%25%50%
fair75%100%
Implied decimal odds
YES1.50×(67¢)NO2.99×(34¢)
Kelly bet-size (% of bankroll) K* = 0.00%
K* full
0.00%
½K half
0.00%
¼K quarter
0.00%
Entropy H(p̂) = 0.920 bits (92% 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
14hrs
11min
7.59 days·θ = 34.073 pp/day
YES →$1.00(P = 66.5%)
NO →$0.00(P = 33.5%)
current: $0.6650 · expected return per side: $0.33 on YES hit · $0.67 on NO hit
0%25%50%75%100%YES $1NO $0NOW+3.8dRESOLVESP projection · σ=6.96% · path funnel to settle at YES=1 or NO=0
Theta progression · θ ∝ σ / √t_remainingθ_now = 34.073 pp/day
now7.59d left
34.073 pp/day×1.00
−25%5.69d left
39.345 pp/day×1.15
−50%3.80d left
48.187 pp/day×1.41
−75%1.90d left
68.147 pp/day×2.00
−90%18.22h left
107.750 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| 1.73%BEARISH SESSION -12.50%BEST+6.00%15hWORST-13.50%13hTYPICAL |Δ|1.73%mean absoluteCUMULATIVE-12.50%Σ signed ΔSTREAK↘ 1down-runASIA · 00-08 UTCμ +0.36% · Σ +2.50%EUROPE · 08-16 UTCμ -1.44% · Σ -11.50%US · 16-24 UTCμ -0.06% · Σ -0.50%CUMULATIVE Δ PATH · final -12.50%+4.00%-15.00%3.00% · 1h3.00% · 1h3.00%1h-0.50% · 2h-0.50% · 2h-0.50%2h1.50% · 3h1.50% · 3h1.50%3h-0.50% · 4h-0.50% · 4h-0.50%4h-0.50% · 5h-0.50% · 5h-0.50%5h0.00% · 6h0.00% · 6h·6h-0.50% · 7h-0.50% · 7h-0.50%7h-1.00% · 8h-1.00% · 8h-1.00%8h0.00% · 9h0.00% · 9h·9h0.00% · 10h0.00% · 10h·10h1.50% · 11h1.50% · 11h1.50%11h-0.50% · 12h-0.50% · 12h-0.50%12h-13.50% · 13h-13.50% · 13h-13.50%13h▼ WORST-4.00% · 14h-4.00% · 14h-4.00%14h6.00% · 15h6.00% · 15h6.00%15h★ BEST-2.00% · 16h-2.00% · 16h-2.00%16h0.00% · 17h0.00% · 17h·17h-1.00% · 18h-1.00% · 18h-1.00%18h1.00% · 19h1.00% · 19h1.00%19h0.50% · 20h0.50% · 20h0.50%20h1.00% · 21h1.00% · 21h1.00%21h0.00% · 22h0.00% · 22h·22h0.00% · 23h0.00% · 23h·23h-3.00% · 24h-3.00% · 24h-3.00%24hTIME PATTERNAsia-led (+2.50%)RUNSup max 3 · down max 3BREADTH29% up · 46% down · 25% flat
7 up bars · 11 down · best 6.00% · worst -13.50% · typical |Δ| 1.729%

§10 · Equity curve & underwater drawdown

Cumulative compounded return + running peak-to-trough
EQUITY & DRAWDOWN ANALYSIS · n=25 barsSEVERE DRAWDOWN -12.99%FINAL-12.99%MAX DD-18.21%RECOVERYONGOING · 21 barsMAX RUN-UP+4.02%UNDERWATER22/25 (88%)STREAK↘ 1EQUITY CURVE · end 0.8701 · 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 5-25 · 21 bars · ONGOING#2 -0.50%bar 3-3 · 1 bars · recoveredDD SEVERITYsevere (max -18.21%)RECOVERYongoing · 21 barsTIME UNDER WATER88% of session · 22/25 bars
final equity 0.8701 (-12.99%) · max DD -18.21% · time-under-water 22/25 bars

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

Rolling annualised Sharpe ratio · green positive · red negative
n=19 · +4 / −13 (21% positive) · μ=-16.69 · σ=35.67UNPROFITABLE STRATEGYLAST -5.21 (+0.32σ vs μ)103.6151.810.00-51.81-103.61μ = -16.6932.2932.29-9.74-9.74-17.82-17.82-103.61-103.61-76.42-76.420.000.00-9.06-9.06-37.78-37.78-46.17-46.17-24.78-24.78-29.76-29.76-34.04-34.04-35.39-35.390.000.0025.1725.17-6.50-6.5030.8630.8630.8630.86-5.21-5.21v > 0 · positivev < 0 · negativeμ mean lineμ ± σ bandlatest bar (outlined)
latest -5.209 · range [-103.61, 32.29] · μ -16.689 · positive Sharpe = excess-return-per-risk earned by buying-and-holding through this window
Rolling annualised volatility (%)
n=19 · μ=261.7433 · σ=233.0993 · range [35.2278, 618.5410] · R²=0.033▲ RISING +3.32%σ EXTREME 89.06%LAST 140.1321618.5410472.7127326.8844181.056135.2278μ = 261.7433max 618.5410min 35.2278dataMA(3)OLS R²=0.03μ lineμ ± σ bandmaxmin
latest 140.13% · range [35.23%, 618.54%] · μ 261.74% · σ̂ scaled to annualised (×√8760)
Rolling lag-1 autocorrelation ρ(1)
n=19 · +7 / −12 (37% positive) · μ=-0.118 · σ=0.204CLOSE TO MARTINGALELAST 0.100 (+1.07σ vs μ)0.6380.3190.000-0.319-0.638μ = -0.118-0.286-0.286-0.379-0.379-0.072-0.072-0.363-0.363-0.133-0.1330.1430.143-0.058-0.0580.0210.0210.1160.1160.0190.019-0.025-0.025-0.059-0.0590.0600.060-0.638-0.638-0.297-0.2970.0050.005-0.152-0.152-0.239-0.2390.1000.100v > 0 · positivev < 0 · negativeμ mean lineμ ± σ bandlatest bar (outlined)
latest 0.100 · |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
124.6278
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
3.6580
p-VALUE (log scale)
0.6020
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
-0.9047
p-VALUE (log scale)
0.7872
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
0.2279
p-VALUE (log scale)
0.8197
α
10⁻⁴10⁻³10⁻²10⁻¹1
p ≥ α · null retainedsigns appear random (10 runs)
χ

KPSS (μ stationarity)

REJECT H₀**

H₀: p IS level-stationary

STATISTIC
0.7571
p-VALUE (log scale)
0.0090
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
-0.4166
p-VALUE (log scale)
0.6770
α
10⁻⁴10⁻³10⁻²10⁻¹1
p ≥ α · null retainedVR 0.873 ≈ 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=1.11e-3 · top T=4.80h (17.7%) · top-3 cover 43.9%1 SIGNIFICANT CYCLEcumulative energy ↗ (1 bin above 2× noise)2.3e-31.8e-31.2e-35.9e-40.0e+0μ noise floor2× noise (significance)period 24.0 · power 8.63e-4 · 6.5% energyperiod 24.0 · power 8.63e-4 · 6.5% energyperiod 12.0 · power 6.40e-4 · 4.8% energyperiod 12.0 · power 6.40e-4 · 4.8% energyperiod 8.0 · power 8.75e-4 · 6.6% energyperiod 8.0 · power 8.75e-4 · 6.6% energyperiod 6.0 · power 1.36e-3 · 10.2% energyperiod 6.0 · power 1.36e-3 · 10.2% energyperiod 4.8 · power 2.35e-3 · 17.7% energyperiod 4.8 · power 2.35e-3 · 17.7% energyperiod 4.0 · power 1.59e-3 · 12.0% energyperiod 4.0 · power 1.59e-3 · 12.0% energyperiod 3.4 · power 1.89e-3 · 14.2% energyperiod 3.4 · power 1.89e-3 · 14.2% energyperiod 3.0 · power 8.51e-4 · 6.4% energyperiod 3.0 · power 8.51e-4 · 6.4% energyperiod 2.7 · power 1.58e-3 · 11.9% energyperiod 2.7 · power 1.58e-3 · 11.9% energyperiod 2.4 · power 2.18e-4 · 1.6% energyperiod 2.4 · power 2.18e-4 · 1.6% energyperiod 2.2 · power 5.01e-4 · 3.8% energyperiod 2.2 · power 5.01e-4 · 3.8% energyperiod 2.0 · power 5.51e-4 · 4.2% energyperiod 2.0 · power 5.51e-4 · 4.2% 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 17.7% of total energy · Σ|X̂|²/n = 1.326e-2

▸ Depth section using sovereign-store price series (604 bars · effective 1752324 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 0.415pp · expected |Δp| over horizon 5.60ppterminal variance p(1−p) = 0.2228 · n = 604✓ n = 604
μ per bar
-0.025pp
average Δp · drift
σ per bar
0.415pp
one-bar volatility · logit-free
Per-day movedaily
2.03pp
σ × √24
Per-horizon move8d
5.60pp
σ × √182.19905111111112
Terminal variancebinary
0.2228
p(1−p) at resolution
Current pricep
66.5¢
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 0.71pp · ES₉₅ 0.88pp · method parametric · drift-correcteddrift -0.025pp/bar · quantised: yes · median step 1.00pp · unique ratio 0.03✓ n = 604
VaR 95%
0.71pp
1.645·σ (parametric) of Δp
ES 95%
0.88pp
mean of the tail
Max drawdown
18.4pp
peak 81.5¢ → trough 66.5¢
Median step
1.00pp
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
66.5%
= price
Decimal oddsEU
1.504
total return per $1
AmericanUS
-199
risk $199 to win $100
FractionalUK
0.50 / 1
profit per $1 risked
Profit per $100stake
+$50.38
clean dollar framing
-1000-5000+500+1000020406080100you · 66.5%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)
0.920 bit
max 1.0 at p = 0.5
Your entropyH(q)
0.920 bit
Δ +0.000 bit vs market
Surprise · YES−log₂ p
0.59 bit
self-information
Surprise · NO−log₂(1−p)
1.58 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 09:47:50 UTC
Snapshot age
13.1s
History points
25 CLOB mids
Page rendered
2026-06-20 09:48:03 UTC
Storage policy
no persistence — fetched on every request
SHA-256 attestation
96d3ae24e0b94dbb4faccc0393d1e4eb4e90464785fef84ad15aee5b4a2c1b35 · deterministic hash of source snapshot
Open data licence
CC0 / public domain

§∞-2 · Related markets · explore more

HL PREDSpain88.4¢HL PREDEcuador86.3¢HL PREDBelgium67.7¢POLYMARKETWill USA win the 2026 FIFA World Cup?3¢POLYMARKET Iran agrees to end enrichment of uranium by June 30?6¢POLYMARKETWill Egypt win the 2026 FIFA World Cup?0¢HL PERPBTC-USD perpetual$63,632HL PERPHYPE-USD perpetual$70.72HL PERPETH-USD perpetual$1,728.1

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
0.665000
(best bid + best ask) / 2
Spread
150.4bp
(bestAsk − bestBid) / mid
Imbalance (whole book)
+0.572
bid-heavy
Imbalance (top-5)
+0.843
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$1.00K0.684289290.06bp0.6900003FILLED
BUY$10.00K0.719047812.74bp0.88000014FILLED
BUY$100.00K0.8467852733.61bp0.99000025PARTIAL
SELL$1.00K0.66000075.19bp0.6600001FILLED
SELL$10.00K0.66000075.19bp0.6600001FILLED
SELL$100.00K0.5843551212.71bp0.01000032PARTIAL

Risk metrics

▸ sovereign store · 604 barsperiods/year ≈ 1.75M
Realized vol (annualised)
738.52%
σ per bar = 0.005579
Mean return (annualised)
-59108.55%
μ per bar = -0.000337
Sharpe (rf=0)
-80.04
annualised; risk-free assumed zero
Max drawdown
18.40%
peak 0.81 → trough 0.67 over 503 bars

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