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Quantitative Premier League Prediction Markets on Solana: Poisson xG vs. Bookmaker Overround on worm.wtf

#solana #web3 #python #datascience

Why Traditional Sportsbooks Bleed Expected Value (EV)

In traditional sportsbooks, every Premier League 1X2 market embeds a 5.5% to 8.5% overround (vig) into the implied probabilities. Even if your bivariate Poisson Expected Goals (xG) model accurately predicts match outcomes, the bookmaker margin systematically erodes long-term profitability.

On-chain leveraged prediction markets on Solana like worm.wtf (@wormwtf) change this microstructure completely: every outcome trades as a live market percentage (0%–100%) directly on Solana with up to 3x leverage and weekly Matchweek USDC trader pools.

1. Modeling Premier League Matchweek Probabilities with Bivariate Poisson xG

Given home attack strength $\lambda_{\text{home}}$ and away attack strength $\lambda_{\text{away}}$ adjusted for opponent xGA (Expected Goals Against), the probability of scoreline $(i, j)$ follows:

import math

def poisson_pmf(k: int, lam: float) -> float:
    return (lam ** k) * math.exp(-lam) / math.factorial(k)

def match_1x2_probs(xg_home: float, xg_away: float, max_goals: int = 8):
    p_home, p_draw, p_away = 0.0, 0.0, 0.0
    for h in range(max_goals + 1):
        for a in range(max_goals + 1):
            p = poisson_pmf(h, xg_home) * poisson_pmf(a, xg_away)
            if h > a: p_home += p
            elif h == a: p_draw += p
            else: p_away += p
    return {"home": round(p_home, 4), "draw": round(p_draw, 4), "away": round(p_away, 4)}
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2. Identifying Positive EV (+EV) Edges & Quarter-Kelly Sizing

When the Poisson model probability $p_{\text{model}}$ exceeds the live market implied probability $p_{\text{worm}}$ on worm.wtf, we size positions using Quarter-Kelly ($0.25 f^*$) to cap drawdown variance:

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