# Starling Quantitative — Complete Machine Reference (`llms-full.txt`) > Canonical URL: https://starlingquant.com/ > Summary Index: https://starlingquant.com/llms.txt > Parent Organization: Biwada (https://biwada.com/) > Founder & Quantitative Systems Architect: Greg Meade (founder@starlingquant.com) > Regulatory Classification: Proprietary internal quantitative research and capital allocation desk. Does not solicit outside retail capital, manage third-party funds, or offer investment advice. --- ## 1. Architectural Thesis: Why Swarms Outperform Monolithic Models in Markets When a single language or statistical model attempts to ingest order-book depth, price event volatility, evaluate fee drag, and dispatch orders inside one monolithic loop, two structural failures emerge: 1. **Latency Erosion:** Multi-step reasoning chains push inference latency past 800ms, turning transient pricing dislocations into adverse selection against faster Liquidity Providers. 2. **Compounding Hallucination Risk:** Unchallenged early specification errors propagate directly into position sizing. **Starling Quantitative** replaces monolithic inference with a **3-Tier Murmuration Architecture**: - **Tier 01 — Market Sensing Layer:** Lightweight asynchronous Python 3.11 and Rust micro-agents stream order-book depth, cross-venue pricing gaps, and resting liquidity changes across prediction and event derivatives venues (including Kalshi and Polymarket). - **Tier 02 — Adversarial Strategy Quorum:** Candidate dislocations trigger independent counter-agents tasked explicitly with invalidating the thesis—auditing taker fee drag, order-book sweep slippage, settlement rule ambiguity, and adverse selection. - **Tier 03 — Deterministic Risk Quorum & Execution:** Capital commitment requires a two-thirds majority across independent risk nodes plus deterministic non-LLM risk locks (drawdown circuit breakers, covariance exposure caps, clock-drift verification, and asymmetric tick rounding). --- ## 2. Market Devigging Methodology: Additive, Multiplicative, Power & Shin Raw venue prices (`pi_i = 1 / O_i` in decimal odds or ask prices on binary/multi-outcome books) sum to `S = sum_i pi_i > 1`, where `V = S - 1` is the bookmaker overround or bid-ask spread vig. Comparing internal model probabilities directly against raw implied quotes systematically misstates edge. Moreover, because market makers shade longshot prices disproportionately to protect against asymmetric informed flow (**favorite-longshot bias**), naive normalization introduces systematic tail error. Starling Quantitative benchmarks four devigging transformations: 1. **Additive (Equal-Margin) Method:** `p_i = pi_i - (S - 1) / n` Subtracts equal vig across `n` outcomes; fails on asymmetric books where it can produce negative implied probabilities on deep longshots (`pi_i < (S - 1)/n`). 2. **Multiplicative (Proportional / Basic) Method:** `p_i = pi_i / S` Preserves odds ratios uniformly across favorites and longshots, systematically overestimating true longshot probabilities when favorite-longshot bias is present. 3. **Power Devigging Method (Production Primary Benchmark):** Models implied prices as power-distorted transforms of true probabilities and solves via Newton-Raphson / bisection for the unique exponent `k > 1` satisfying: `sum_{i=1}^n (pi_i)^k = 1, p_i^{power} = (pi_i)^k` Because `0 < pi_i < 1`, raising `pi_i` to `k > 1` compresses small longshot probabilities proportionally more than favorites while guaranteeing `p_i in (0, 1)` and `sum_i p_i = 1`. 4. **Shin's Informed-Trader Method (Microstructure Cross-Check):** Derived from Shin (1991, 1993), where a risk-neutral market maker faces an unknown fraction `z in (0, 1)` of insiders who know the true outcome and `1 - z` of noise traders. True probabilities satisfy: `p_i^{shin}(z) = (sqrt(z^2 + 4 * (1 - z) * (pi_i^2 / S)) - z) / (2 * (1 - z))` where `z` is solved numerically so `sum_{i=1}^n p_i^{shin}(z) = 1` (and in closed form `z = (S - 1) / (n - 1)` only under special symmetric approximations, or exact root-finding for general `n >= 3`; for `n = 2`, Shin reduces algebraically to Additive). ### Asymmetric Cross-Venue Tick Rounding When bridging whole-cent venues (Kalshi, `$0.01` tick) and sub-cent CLOBs (Polymarket, `$0.001` tick), Starling Quantitative always rounds limit bids **down** (`floor`) and limit asks **up** (`ceil`) after accounting for exchange fee schedules so rounding never manufactures phantom net-negative arbitrage. --- ## 3. Constrained Fractional Kelly Sizing Under Parameter Uncertainty For a binary contract offering net payout odds `b = O - 1` against true win probability `p` (`q = 1 - p`), expected logarithmic bankroll growth per trial for stake fraction `f` is: `g(f) = p * ln(1 + b * f) + q * ln(1 - f)` Maximizing `g(f)` yields the classic Kelly fraction `f* = (b * p - q) / b`. However, `f*` assumes `p` is known without estimation variance. When `p_hat = p + epsilon` carries estimation variance `sigma_p^2`, plugging `p_hat` into full Kelly systematically **overbets**: - Second-order Taylor expansion around `f*` shows `g(f)` is concave with curvature `-f^2`, and betting `f > 2 * f*` drives long-run geometric growth **negative** despite positive expected arithmetic return. - Under continuous-time diffusion approximations, scaling Kelly by fraction `c in (0, 1)` (`f = c * f*`) captures fraction `c * (2 - c)` of maximum theoretical log-growth while reducing portfolio variance by `c^2` and bounding the probability of wealth falling to fraction `x in (0, 1)` of peak to `P(W_min <= x) = x^(2/c - 1)`. At **Quarter-Kelly (`c = 0.25`)**: - Retained geometric growth rate under exact parameters: `0.25 * (2 - 0.25) = 43.75%` (and higher net of parameter noise). - Variance reduction: `(0.25)^2 = 6.25%` of full-Kelly variance (`93.75%` variance compression). - Analytical 50% drawdown probability drops from `0.50^(1) = 50.0%` at full Kelly (`c = 1`) to `0.50^(7) = 0.78%` at quarter-Kelly (`c = 0.25`). Starling Quantitative pairs `c = 0.25` with Bayesian shrinkage of `p_hat` toward the Power-devigged sharp market prior, covariance caps across correlated event brackets, and a hard per-event bankroll ceiling. --- ## 4. Out-of-Sample Brier Decomposition & Bandit Capital Allocation Sharpe and Sortino ratios alone are noisy over short event samples. Every forecast `p_t in [0, 1]` and settled outcome `y_t in {0, 1}` recorded in Starling Quantitative's flight recorder is scored via the **Brier Score**: `BS = (1 / N) * sum_{t=1}^N (p_t - y_t)^2` Partitioning forecasts into `K` probability bins (`n_k` forecasts per bin with mean forecast `p_bar_k` and observed base rate `o_bar_k`, overall base rate `o_bar`), Starling Quantitative applies the **Murphy (1973) Decomposition**: `BS = REL - RES + UNC` - **Reliability (`REL = (1/N) * sum_k n_k * (p_bar_k - o_bar_k)^2`):** Lower is better (`0` is perfectly calibrated). Measures overconfidence or underconfidence across probability buckets. - **Resolution (`RES = (1/N) * sum_k n_k * (o_bar_k - o_bar)^2`):** Higher is better. Measures ability to separate true high-probability and low-probability regimes from the climatological base rate. - **Uncertainty (`UNC = o_bar * (1 - o_bar)`):** Intrinsic outcome entropy independent of the forecaster. Sub-strategies exhibiting rising `REL` (miscalibration drift) or decaying `RES` have their capital weights automatically attenuated by **Discounted Thompson Sampling (`lambda = 0.98`)**, while a Compute-to-Alpha Ratio (CAR) gate blocks frontier LLM deliberation unless expected net dollar alpha exceeds inference cost by at least `10x`. --- ## 5. Canonical Links & Disclosures - **Homepage:** https://starlingquant.com/ - **Research Notes Index:** https://starlingquant.com/guides - **Monograph 01 (Market Devigging):** https://starlingquant.com/guides/power-and-shin-market-devigging-methodology - **Monograph 02 (Fractional Kelly & Brier Calibration):** https://starlingquant.com/guides/fractional-kelly-sizing-and-brier-calibration - **Parent Holding Company:** https://biwada.com/ - **Disclosure:** Proprietary internal quantitative research and capital allocation desk of Biwada. No solicitation of outside capital; not investment advice.