Sharpe Ratio
PublishedEfficiency: how much pace does a driver extract per unit of chaos?
Mathematics & Statistics · Purdue · Class of 2027
Prabhat M
Quantitative research: rigorous models that explain why, not just predict that.
Most recently: a pre-registered study of how prediction markets priced all 104 matches of the 2026 World Cup. The market was better calibrated than my own model, the visible gap between venues turned out to be mostly house margin rather than disagreement, and the dislocation that opens at a goal is mostly untradeable once you check the depth behind it. See the study.
- Focus
- Quant Trading & Research · Prediction Markets
- Based
- West Lafayette, IN
- Status
- Open to FT 2027
86World Cup matches captured tick-by-tick on both venues, out of the tournament's 104
11Predictions pre-registered before kickoff, graded in public after: 5 pass, 2 fail, 4 inconclusive
01
About
Currently
Wrapping up xResidual, my pre-registered study of how prediction markets priced the 2026 World Cup, including a September audit pass over the full pipeline. Finalizing the QuantF1 methodology paper for arXiv submission.
I'm a Math and Statistics senior at Purdue, graduating May 2027. My work sits at the intersection of quantitative finance, sports analytics, and applied machine learning. What interests me most is the mechanism behind a result: models whose predictions come with reasons attached.
Over the past two years I've self-built an implementation library covering the core syllabus of a graduate-level quantitative finance program: option pricing through exotics, credit risk models, factor models, portfolio optimization, time series analytics. More recently, I've been developing QuantF1: a hierarchical Bayesian study of how far a Formula 1 driver's skill can be separated from their machinery. The methodology paper is in preparation for arXiv.
Co-founder of UltraRice, fiscally sponsored by The Hack Foundation (d.b.a. Hack Club), a 501(c)(3) nonprofit. UltraRice works on ultrasonic rice fortification for malnutrition in India, started at 17 and funded with $20,000+ in non-dilutive grants from Tyler Cowen's Emergent Ventures India (Mercatus Center, George Mason University) on the strength of independent research. Public financials at bank.hackclub.com/ultrarice. Before that, The Knowledge Society (2022), where UltraRice began as an end-of-year moonshot. Selected for the 2026 IMC Trading US Chess Academy, one of 20 brackets nationwide, finishing 7th in the qualifier.
Languages
- Python
- C++ (intermediate)
- SQL
- R
Quant Methods
- Hierarchical Bayesian (PyMC)
- Market Microstructure
- Monte Carlo & Exotics
- Time Series (ARIMA/GARCH)
- Factor Models & Optimization
- Walk-Forward Validation
- Kelly Sizing
Infrastructure
- Azure · AWS
- Docker
- systemd
- CI/CD · GitHub Actions
- SQLite
- Git
02
Research
FlagshipThree threads of one instinct: rigorous models that explain why, not just predict that: risk-adjusted sports analytics, prediction-market efficiency, and systematic quantitative finance.
Sports Analytics
QuantF1
FlagshipA hierarchical Bayesian study of 76,000 F1 laps (2022–25, PyMC/NUTS, AR(1) Student-t) examining how far a driver's skill can be separated from their machinery. Championship-points variance decomposes into roughly 70% pace, 26% conversion, 4% luck, isolating conversion as a measurable within-team skill; the cross-team split is only weakly identified, swinging 47–71% on the removal of a single team switch. Paper: arXiv, in preparation.
What surprised me. The within-team comparison is the part that identifies cleanly: teammates share machinery, so conversion separates as a measurable skill. The cross-team split does not. Removing a single mid-season team switch swings the variance share from 47% to 71%, which means the headline "how much is the driver" number rests on a handful of driver moves rather than on 76,000 laps. The honest version of this study reports that fragility instead of picking the flattering number, and that constraint shaped the whole paper.
The Series
- The Sharpe Ratio of a Driver: What Quant Finance Can Teach Us About Formula 1 Performance
- The Sortino Ratio of a Driver: Measuring Controlled Aggression in F1
- The Execution Profile of a Driver: Measuring Performance Beyond the Results Table
- The Alpha of a Driver: Separating Skill from Machinery in Formula 1
- The Physics of Failure: Measuring Drawdown and Recovery in Formula 1
Analytical Framework
Sortino Ratio
PublishedControlled Aggression: which mistakes actually matter?
Execution Profile
PublishedBehavior: how is performance delivered?
Alpha
PublishedSkill vs Machinery: separating the driver from the car.
Drawdown and Recovery
PublishedResilience: what happens when things go wrong?
Regime Sensitivity
Forthcoming · arXivContext: when does a driver's execution work?
Consistency
Forthcoming · arXivRepeatability: is this structural skill or situational brilliance?
Prediction Markets
xResidual
Complete · 2026 World CupA six-week live study of how prediction markets, Kalshi and Polymarket benchmarked against bookmaker consensus, priced all 104 matches of the 2026 World Cup. Eleven falsifiable predictions were pre-registered before kickoff on June 11 and graded in public when the tournament closed on July 19. The record, predictions, code and grading all stay up, together with a September correction that withdrew one of the study's findings after a follow-up audit.
What the Study Found
0.487The market's Brier score against my pre-registered model's 0.503, calibration slope 1.07 against my 0.87. Better calibrated than my model, though the gap itself is not significant (paired p = 0.25)
0.17ppMedian de-vigged gap between the two venues across the 20 days both books normalized. The visible spread is mostly house margin, not disagreement: 5.6% overround on Kalshi against 2.1% on Polymarket
12.0¢Median price move at a goal. The book empties on both venues, so only about 9% of goals were harvestable, and which ones could not be called in advance. Both pre-registered tradability tests came back null
$38Locked profit across about $4,855 of capacity in the entire World Cup cross-venue arbitrage, from a pre-tournament snapshot walking both books level by level net of fees. The deepest book nets $0
The headline result is a negative one, and it is the point: a visible 12-cent dislocation opens at every goal, and the books empty before most of it can be taken. A second surviving result points the same way: the market under-reacts, booking about a third of the model's fair move across the 8 matches whose goal timeline validates against the final score, and undershooting on all 22 goals where the quote moved.
What nearly went wrong. My first pass at the harvest ledger returned +10.2¢ on 100% of goals. A number that good is not a discovery, it is a bug you have not found yet: the ledger credited a follower with the full price move while assuming the quote it was lifting would still be resting there. At the instant of a goal it is not. Gating on real depth inverted the result.
Correction, September 2026. A follow-up audit withdrew the study's cross-venue lead-lag finding: one venue's price had been read at a coarser sampling rate than the other's, and a market with no lead at all reproduces the published result. The correction sorts every result by whether it survives, the figures above are the ones that do, and the original write-up stays online unedited behind a banner.
How the Pre-Registered Calls Landed
5 / 2 / 4Pass, fail, inconclusive across eleven predictions, after the September regrade. P1, one of the two named primaries, still passes; the two failures are published below, not quietly dropped
P6The other named primary, "the deeper venue leads price discovery", moved from PASS to INCONCLUSIVE when the lead was withdrawn. Logged as addendum A-P6 rather than edited in place
+0.020Nats per match the de-vigged market beat me by on log score (0.825 vs 0.845). It won 35 of 72 matches outright: the gap is margin, not frequency, and is not significant (p = 0.34)
59%Of 222 directional calls closed with positive CLV, median +0.68pp. But the mean is −2.81pp: a minority of large adverse moves swamps it
The two that failed. P3 predicted the mean de-vigged cross-venue title gap would stay within 1pp through the final; graded at the close it was 3.98pp, because once teams resolve, Kalshi's winner field stops being a probability distribution at all. P10 predicted the documented goal-overreaction fade would net positive; it returned −0.285pp per trade. There was nothing to fade: the market under-reacts to goals rather than over-reacting. I said in advance that publishing either result was the point.
Where the CLV actually came from. Split by market, the advance-to-knockout lane closed 74% positive at +4.03pp mean; the deeper reach-round lanes all carried negative mean CLV (reach-QF: 50% positive, −7.06pp). The simulated paper-trading book finished +$148 on a notional $1,452, no capital at risk, and split by lane it says more than the total does. The advance lane made +$181 and is the one market where closing-line value also backs the model. The reach-round lane made +$88 with no such support, so that part is outcome rather than edge, and the two lanes flagged as edgeless before trading lost $117. Two cautions: the 21 advance positions resolve on one group stage, so their hit rate is nearer one correlated bet than 21 independent edges, and the CLV is measured on the model's forecasts rather than the fills.
The Pipeline
Expectation Baseline
BaselineWorld Football Elo over 49k historical results, paired with a Skellam goal model.
Monte Carlo Engine
SimulationFormat-aware tournament sim: 40k iterations, FIFA best-thirds rules, Transfermarkt squad-value blending, and an empirical-Bayes confederation-bias correction.
Residual Analysis
CoreLog-score and standardized z-scores with honest sigma discipline: expectation vs. outcome.
Market Microstructure
MarketsOrder-book depth, spreads, and imbalance across Kalshi and Polymarket. The cross-venue price-discovery analysis built on this stage was later withdrawn; the capture itself was always full-resolution on both venues.
Calibration
ValidationCORP isotonic reliability diagrams with consistency bands and three devig methods: falsifiable predictions pre-registered, graded in public on Jul 19.
In-Play Capture
In-PlayMillisecond-stamped websocket capture of both order books across 86 matches, with auto goal-shock detection and the goal-overreaction fade test (P10).
Built to Be Trusted
Always-on collection
Price logging ran 24/7 on an always-on Azure VM via systemd timers for the full six weeks, capturing 86 of the 104 matches on both venues; the rest were missed or caught on one venue only.
Content-hash provenance
Every build stamps the git SHA, model parameters, and input fingerprints, and flags any published card that has drifted from the model behind it.
142 tests
Across the math core, calibration, microstructure, simulation invariants, the confederation-bias correction, and data-integrity guards.
Systematic Trading & Derivatives
Quantitative Finance
Implementation work spanning derivatives, portfolio construction, and systematic trading, including a prediction-market forecasting system that ran on a daily GitHub Actions schedule through the 2026 season.
Quant-Finance Repository
Quant-Finance
End-to-end research and implementation library covering Black-Scholes, Monte Carlo for Asian/Barrier/Lookback/Rainbow exotics, Merton credit model, factor models, portfolio optimization, and time series analytics.
- Options pricing: Black-Scholes & Monte Carlo for Asian / Barrier / Lookback / Rainbow exotics
- Credit risk: Merton, Black-Cox, Jarrow-Turnbull
- Factor models: CAPM, Fama-French 3/5, Carhart, AQR style premia
- Portfolio optimization: Markowitz, Black-Litterman, reinforcement learning
- Sentiment-driven trading pipeline (VADER + FinBERT); backtesting engine with realistic transaction costs; live paper-trading bot
- Companion multi-asset signal track: walk-forward, out-of-sample validation; ~0.7 Sharpe on the Numerai signal competition
- Financial Models
- Portfolio Management
- Trading Strategy
- Time Series
- Live Paper Trading
ML@Purdue · Applied Prediction Markets
TSA Forecasting for Kalshi
Contributor on ML@Purdue team project (PM: Eubene In) building a production forecasting system for Kalshi's weekly TSA checkpoint contracts. Owned the ARIMA/SARIMAX baseline track and walk-forward benchmark harness; implemented quarter-Kelly position sizing.
- Best baseline (ENSEMBLE_BASIC, fold-wise retraining): R² 0.67 · MAE 142.7k · 95.88% PI coverage
- Empirical finding: retraining frequency matters more than model complexity for this problem
- Production track: AutoGluon ensembles with Newey-West HAC standard errors
- Paper-traded on a daily GitHub Actions schedule from March 2026
Seen enough? I'm open to full-time quant trading and research roles for 2027 — ask for a résumé or get in touch.
03
Experience & Education
SLMs & Agentic AI Intern, Hexaware Technologies
Built a multi-detector statistical anomaly ensemble (robust MAD z-scores, Mahalanobis distance on shrinkage covariance, trajectory deviation), validated against held-out anomaly classes and reported honestly where it failed to generalize. Diagnosed a covariance-estimation bias mis-scaling the Mahalanobis statistic, halving the false-positive rate at constant recall.
Research Assistant, Purdue College of Liberal Arts Research Academy
Designed large-scale multi-agent simulation experiments for statistical analysis and hypothesis testing under partial information, with reproducible Python pipelines for out-of-sample evaluation. Modeled sequential decision-making under uncertainty, achieving a 25% improvement in task accuracy through data-driven intervention design.
Software Engineering Intern, Hotkeys Holding LLC
Engineered low-latency retrieval pipelines in Python using vector databases and Gemini APIs, cutting document-lookup latency ~90% and enabling sub-200ms real-time inference. Designed caching and batching workflows that reduced LLM response time 95% on cache hits, with end-to-end instrumentation for latency, throughput, and retrieval quality.
Education
Purdue University
B.S. Mathematics & Statistics
Quantitative Coursework
- Mathematical Probability
- Statistical Theory
- Introduction to Time Series
- Linear Algebra
- Vector Calculus
- Discrete Mathematics
- Data Structures
- Computer Architecture
- Assembly Language
In progress · Fall 2026 Foundations of Analysis · Elementary Stochastic Processes
Competitions & Honors
- Jump Trading Probability Cup: Top 20% (343 forecasts, +2.8 RBP vs. crowd)
- Putnam (2025)
- ICPC Regional (2024)
- IMC Trading US Chess Academy: 7th, Qualifier Bracket (2026)
- CICSE Chess Nationals: Tamil Nadu Rep (2023)
04
Writing
Eleven articles across four tracks: prediction markets, the QuantF1 series, applied machine learning, and neurosymbolic AI.
Prediction Markets
Cross-venue microstructure from xResidual. Its central lead-lag claim was later withdrawn; see the correction.
- The Edge That Isn't: A Real Lead Nobody Can TradeAug 2026 · withdrawn
QuantF1 Research
Separating driver skill from machinery. The full series is listed in section 02.
- The Sharpe Ratio of a DriverOct 2025
- The Sortino Ratio of a DriverOct 2025
- The Execution Profile of a DriverJan 2026
- The Alpha of a DriverJan 2026
- The Physics of FailureFeb 2026
Machine Learning
Neural networks, recommenders, and adversarial robustness.
- Adversarial Attacks on Neural NetworksMay 2024
- Hybrid Neural Network for Movie RecommendationsFeb 2023
The recommender write-up is cited in Lavreniuk and Potapova (2025), Applied Information Technologies, Vasyl' Stus Donetsk National University.
Neurosymbolic AI
Hybrid symbolic-neural systems, written before the wave.
Earlier work · applied ML and neurosymbolic AI, 2023–24
Repositories behind the articles above: a neurosymbolic disease-triage service (Flask, Dockerized, CI/CD), a study of adversarial attacks and defenses (FGSM, PGD, C&W), and the hybrid movie recommender that drew the citation above.
05
Get in Touch
I'm looking for full-time quantitative trading and research roles starting after I graduate in May 2027. If you'd rather evaluate the work than take my word for it, xResidual is public end to end: the pre-registration, the public grading, and the code. I'll send a résumé the same day you ask, and I'm glad to walk through any part of the work.