NOSTRADAMUS · Position Analytics Engine
SIMULATOR Will USA qualify for FIFA World Cup Quarterfinals?
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A live, interactive instrument for dissecting a single binary position. Sweep the inputs and watch every indicator recompute — payoff geometry, Kelly growth, Bayesian posterior, KL divergence, cost waterfall, Monte-Carlo equity fan, forecast calibration. Companion to the live /feed/kalshi-kxwcround-26quar-usa page.
▲ YES EDGE · +0.018 · f★ 3.3% · deploy 1.6% · net 1.06pp
§1 · Position economics
YES · Expected P/L per share +0.0181@ model P(YES) = 0.468
P/L per sharemarket pricemodel Pprofit zoneloss zone
Profit is linear in the eventual settlement price.
f★ = 3.28% · g(f★) = 0.066%deploy 1.64% · g = 0.049%
g(f)f★ optimumdeployed fgrowth zone
Underbet leaves growth on the table; overbet destroys capital. The interior maximum is f★.
§2 · The trade ticket
YES @ 0.450 · EV +$16stake $411 · 1.64% of bankroll
Deployed stakestake
$411
1.64% of bankroll
Sharesunits
912
each pays $1 if YES
Max payoutwin
$912
gross, if win
Max profitwin
+$502
net of cost
Max losslose
-$411
binary settles to $0
Payout multiple×
×2.22
$1 → $2.22
Risk:RewardR:R
1.22 : 1
win $1.22 per $1
Expected P/LE[P/L]
+$16
probability-weighted
| Outcome | P(model) | P/L | Contribution |
|---|---|---|---|
| Resolves YES (win) | 46.8% | +$502 | +$235 |
| Resolves against (lose) | 53.2% | -$411 | -$218 |
| Expected value | 100.0% | — | +$16 |
What you actually win and lose. The bottom table tabulates probability-weighted P/L by outcome.
§3 · Break-even & cushion
Cushion +1.8 pprelative edge +4.0%
Required win ratebreak-even
45.0%
price = implied probability
Model win rateP(win)
46.8%
what you forecast
Cushionedge
+1.8 pp
margin of safety
Fair pricemodel
0.468
where you think it should trade
The market price equals the win rate you must beat to make money.
§4 · Odds conversion
Implied probabilityP
45.0%
= price
Decimal oddsEU
2.222
total return per $1
AmericanUS
+122
$100 wins $122
FractionalUK
1.22 / 1
profit per $1 risked
Profit per $100stake
+$122.22
clean dollar framing
underdog (+)favorite (-)your price
Five views of the same number.
§4b · Time & annualized return
APR 70% · APY 98%ROI 4.0% over 21d · 17.4 turns/yr
Time to resolvehorizon
21.0 d
504h capital lockup
Raw ROIper resolve
+4.0%
APR (simple)scaled
+70%
ROI × 365/days
APY (compounded)if redeployed
+98%
(1+ROI)^(365/d) − 1
Daily expectedper day
+0.19%
geometric, per day held
Capital turns/yrvelocity
×17.4
how often this slot recycles
simple APRcompounded APYyour horizon
Rank positions by APR, not raw ROI. A thin edge tomorrow beats a fat edge next year.
§5 · Costs & net edge
Net edge +1.06 pperosion 42% · break-even w/ fees 45.8%
gross edgefrictionnet edgefee 0 bps · spread 1.50¢
The number that decides whether to trade.
§6 · Sizing menu
Full Kellyf★
$821
3.28% · g = 0.066%
Half Kelly½ f★
$411
1.64% · g = 0.049%
Quarter Kelly¼ f★
$205
0.82% · g = 0.029%
Flat 1%1%
$250
1.00% · g = 0.034%
Flat 2%2%
$500
2.00% · g = 0.056%
Flat 5%5%
$1,250
5.00% · g = 0.048%
Recommended¼ f★
$205
survives model error
Quarter-Kelly is the industry default — survives model error far better than full Kelly.
§7 · Information theory
Market entropyH(p)
0.993 bit
max 1.0 at p = 0.5
Your entropyH(q)
0.997 bit
Δ +0.004 bit vs market
Surprise · YES−log₂ p
1.15 bit
self-information
Surprise · NO−log₂(1−p)
0.86 bit
self-information
H(p) peaks at p = 0.5 (one bit of irreducible doubt).
NOISE · D_KL(q ‖ p) = 0.0007 nat (0.0009 bit)belief ≈ market — stand down
YES contributionNO contributionbelief ‖ marketnoise
Zero KL ⇒ you know nothing the crowd doesn't.
§8 · Bayesian inference
MARKET PRICE INSIDE 95% CIposterior μ 0.468 · CI [0.35, 0.59] · κ 68.2
Posterior meanE[θ]
0.468
Beta(31.9, 36.3)
95% credible intervalHDI
[0.35, 0.59]
price INSIDE → weak edge
Concentrationκ
68.2
pseudo-obs behind belief
Disagreementvs crowd
+1.8 pp
posterior − price
market prior (dashed)model posterior95% credible bandmarket price
When the market price falls outside the 95% credible interval, your disagreement is statistically meaningful.
§9 · Tail risk · Monte-Carlo (mode A · single position to resolution)
E[P/L] +7.2% · P(YES) 48.3% · VaR₉₅ 100.0%400 paths · 504 bars to resolution
Expected P/Lper $1
+7.22%
P(YES) empiricalq
48.3%
Best pathmax
+122.2%
Worst pathmin
-100.0%
VaR 95%5%
100.0%
CVaR 95%ES
100.0%
median path25/75 + 5/95 bandsentry pricemodel q
Logit-space mean-reverting walk + terminal flip with probability q. Answers: 'what happens to THIS one position'. Distinct from the repeated-edge fan below.
§9b · Tail risk · Monte-Carlo (mode B · repeated independent edges)
Median CAGR/bet 0.04% · ruin rate 0.0%400 paths × 120 bets · f deploy 1.64%
Sharpe / betμ/σ
0.035
μ 0.06% · σ 1.8%
Sortino / betμ/σ↓
0.039
downside-only denominator
VaR 95%5%
-1.6%
per-bet worst-case
CVaR 95%ES
-1.6%
mean tail loss
Max drawdownMDD
-3.6%
Calmar 0.01
Ruin rate≤50%
0.0%
P(equity ever ≤ 50%)
median25/75 band5/95 bandruin line
Answers a different question: 'if I could find this exact edge forever, what is the bankroll trajectory'. Compounds 120 sequential resolutions which is NOT what happens to a single position.
§10 · Base-rate & macro context
ANCHORED · supported by convictionanchor gap -13.1pp · crowd gap -14.9pp
Anchor gapmodel − base
-13.1 pp
Crowd gapprice − base
-14.9 pp
Verdictdiscipline
ANCHORED
Reference-class anchoring prevents narrative-driven blowups.
§11 · Forecast quality (synthetic ledger)
SKILL POSITIVE · in-sample BSS 20.2% · AUC 0.768out-of-sample BSS (5-fold) 20.2% ± 2.7% · Brier 0.1996 · log-loss 0.5933 · n 1600✓ n = 1600
BrierBS
0.1996
lower = better · ō 0.50
BSSvs base
20.2%
improvement over base rate
ReliabilityREL
0.0048
miscalibration · want ↓
ResolutionRES
0.0555
decisiveness · want ↑
Log lossLL
0.5933
cross-entropy
AUCROC
0.768
0.5 coin · 1.0 oracle
calibration curveROCUNC (irreducible)RES (skill, ↑)REL (miscalib, ↓)
Computed on a seeded synthetic forecast ledger. Reseed (⟳) to redraw.
§12 · Journal vitals (synthetic ledger)
PROFITABLE · PF 1.21 · expectancy +0.104R180 trades · win 50.6% · Sharpe 0.060
Total P/Lnet
+$4,682
on $45,000 cycled
Win ratehit %
50.6%
91 W / 89 L
Profit factorPF
1.21
$ won / $ lost
Expectancyper trade
+$26.01
avg $ per position
R-expectancyper risk
+0.104R
in units of risk taken
Avg win / losspayoff
$295.95 / -$250.00
ratio 1.18 : 1
Sharpe / traderisk-adj
0.060
μR / σR
Closing line valueCLV
+2.04 pp
avg edge vs close
cumulative P/Lprofitable zonered zonesynthetic · seeded from asset
The scorecard every trader checks. Synthetic ledger seeded from the asset slug — recomputes against your real fill history once wired.