In a perfectly efficient market, it should be impossible to construct a portfolio of bets on the same event that guarantees profit regardless of outcome. This is the arbitrage-free constraint, and it requires that probabilities assigned to all outcomes of the same event sum to approximately 100% (plus margin). Any consistent violation of this constraint across markets exposes an exploitable inconsistency.
Cross-market consistency testing checks whether the implied probabilities embedded in different markets for the same event are mutually compatible. If the 1X2 market implies a 55% home win probability, the Asian Handicap −0.5 line should imply something close to 55% as well (the probability of winning by any margin = probability of home win in 1X2). If the AH −0.5 line implies only 48%, either the 1X2 or the AH market is mispriced relative to the other — and exploiting the gap is a form of arbitrage within a bookmaker's own markets.
Given 1X2 probabilities from a Poisson model, the probability for any Asian handicap line can be derived from the same scoreline distribution matrix. The AH −1.5 line (home team wins by 2+) is simply the sum of all scoreline probabilities where home goals minus away goals ≥ 2. If the Poisson model gives AH −1.5 a 35% probability but the bookmaker prices it at 1.90 (implied 52.6%), there is a massive inconsistency — one of these prices is wrong, and the analytical question is which market the bookmaker prices more carefully.
The over/under probability for any total is derived from the same Poisson scoreline distribution. In the PunterStat FDCO dataset, the Premier League 2023/24 had 52.3% of matches finishing over 2.5 goals. A model that prices over 2.5 goals at 48% for an average Premier League match is inconsistent with the historical base rate. Similarly, if the over 2.5 probability implied by the bookmaker's 1X2 pricing (via Poisson back-calculation) is 54% but the over/under market implies only 48%, the two markets are inconsistent — and one is offering value relative to the other.
A systematic cross-market consistency check for each match involves: (1) derive the full Poisson scoreline distribution; (2) calculate implied probabilities for 1X2, AH −0.5, AH −1.5, AH +0.5, Over/Under 2.5, Over/Under 3.5; (3) compare each derived probability to the bookmaker's offered price in each market; (4) bet the market with the largest positive discrepancy relative to your model. This approach, applied across all available markets for each fixture, maximises the probability of finding exploitable inconsistencies without requiring a more accurate base model.
Cross-market consistency is one of the most underused analytical tools in sports betting. Because bookmakers price 1X2, Asian handicap, and totals markets using different trading teams and different update frequencies, inconsistencies between the same bookmaker's own markets are more common than inconsistencies between different bookmakers on the same market. In FDCO data analysis, the most reliable cross-market inconsistencies arise in the AH quarter-line markets (−0.75, −1.25, −1.75) which are less closely monitored than the main −0.5 and −1.5 lines. These quarter-line markets derive their probabilities from the full scoreline distribution, and bookmakers who copy rather than compute often get them measurably wrong relative to their own 1X2 pricing.
