How we calculate fair value.

Philosophy

Sports betting markets are informationally rich but structurally fragmented. Forty or more sportsbooks price the same event simultaneously, each with different customer bases, risk tolerances, and pricing update frequencies. The challenge is not the absence of information — it is the extraction of a coherent fair value signal from a noisy, heterogeneous set of quotes.

BaseCase does not build predictive models. We do not forecast game outcomes from player statistics, injury reports, or historical performance. Instead, we treat the aggregate sportsbook market as a distributed estimation system and attempt to identify the most accurate probability estimate implied by the collective pricing of informed participants. When an individual book deviates from this estimate, we surface the discrepancy.

Data Infrastructure

Sportsbook odds are ingested via The Odds API, covering licensed US and international sportsbooks including Pinnacle, DraftKings, FanDuel, BetMGM, Caesars, ESPN BET, BetRivers, Bovada, and approximately thirty others. Prediction market data is sourced from Kalshi (CFTC-regulated) and Polymarket.

The system operates on a 60-second refresh cycle, archiving every price movement to a time-series database. This produces a proprietary minute-level dataset of cross-book pricing dynamics — line movement patterns, arb duration distributions, and book-specific latency profiles — that is not available through historical API endpoints.

De-Vigging

Raw sportsbook odds include vigorish. A standard -110/-110 market implies 52.4% + 52.4% = 104.8%, but the true probabilities must sum to 100%. Removing this margin — de-vigging — is foundational to any fair value estimate.

The most common approach, multiplicative normalization, simply divides each implied probability by the total. This is algebraically convenient but empirically weak: it assumes the overround is distributed uniformly across outcomes, ignoring the well-documented favorite-longshot bias (Shin 1991, Snowberg & Wolfers 2010).

We use the power method introduced by Clarke, Kovalchik, and Ingram (2017), which raises each implied probability to a constant exponent k such that the de-vigged values sum to 1. The exponent is found by binary search. This naturally corrects for favorite-longshot bias: longshot probabilities shrink more than favorites, matching the empirical distribution of how sportsbooks actually allocate their margin.

Clarke et al. showed this method "universally outperforms the multiplicative method" and "outperforms or is comparable to the Shin method" across datasets spanning tennis, horse racing, and greyhound racing. We apply the power method independently to each sportsbook before any cross-book aggregation.

Fair Value Estimation

After de-vigging each book individually, we compute a fair value estimate for each selection by aggregating across books. The aggregation is not a simple average or median. We use a weighted combination of book probabilities, where the weights are calibrated empirically on historical data using standard supervised learning techniques.

The key insight from our calibration work is that no single sportsbook is universally sharpest across all sports. Book coverage, pricing sophistication, and calibration accuracy vary significantly by sport and by season. A book that is the most accurate pricer of NBA games may have minimal coverage of college basketball. A book with excellent calibration in one season may deteriorate the next. The weight vectors we deploy reflect these asymmetries.

This finding is consistent with independent research. Pikkit's 2024 sharpness study, using a different methodology (measuring which books' lines other books converge toward), found a similar convergence among major sportsbooks in the post-PASPA era: "No book really stands out... even the top recreational books don't fall too far behind the sharper ones."

We maintain the distinction between fair value estimation (producing the best probability estimate) and edge detection (finding profitable deviations from that estimate). These objectives are related but not identical, and optimizing for one does not necessarily optimize for the other. Our architecture reflects this distinction.

Calibration

The weights used in our fair value model are derived from a historical calibration study spanning multiple complete seasons and covering tens of thousands of games across four major North American sports. The study uses a standard Brier score framework to evaluate each sportsbook's probabilistic accuracy, followed by regularized regression to estimate optimal blending weights.

Several challenges arise in this type of calibration that are worth noting for transparency:

Selection bias in book coverage. A sportsbook that only prices marquee games will appear sharper than one that prices every game, because marquee games have more efficient markets and are easier to predict. Brier score rankings must be interpreted carefully in the presence of uneven coverage. We account for this by computing head-to-head calibration only on matched events where both books are present.

Snapshot timing. Our historical dataset captures odds at a fixed daily snapshot, not the true closing line. The best-informed betting occurs in the final hours before game start, and some books may be sharper at close than our snapshot captures. This caveat applies uniformly to all books in the comparison, so relative rankings are preserved, but the absolute calibration levels may be conservative.

Regime change. The US sports betting market has changed substantially since the repeal of PASPA in 2018. The competitive landscape, the flow of information between books, and the sophistication of pricing teams are all evolving. Weights derived from historical data may not perfectly generalize to future seasons. We address this through rolling window refits and by reserving holdout data for out-of-sample validation.

Edge Detection

An edge exists when a sportsbook's implied probability for an outcome diverges from our fair value estimate by more than a sport-specific threshold. The threshold varies by sport because the signal-to-noise ratio of detected edges varies dramatically across sports. Some sports have inherently higher variance per game, reducing the informativeness of any single probability estimate.

We additionally cap both the maximum edge percentage and the maximum expected value to filter noise from the signal. Extremely large edges are empirically dominated by longshot bets where small probability miscalibrations create large percentage deviations, and by data feed errors or stale prices. Our historical analysis confirms that edges beyond a certain threshold have win rates below breakeven.

Expected value (EV) is computed in the standard way: the product of the fair probability and the offered payout, minus the complement probability times the stake. Positive EV indicates a bet where the expected return exceeds the cost if the fair probability estimate is correct.

Signal Quality Assessment

Not all detected edges are equal. We compute several quality metrics for each opportunity:

Line movement confirmation. We monitor whether other sportsbooks' prices move in the direction that confirms the detected edge. If multiple books independently adjust their lines in the same direction, it increases confidence that the mispricing is real rather than idiosyncratic. The predictive value of this signal varies substantially by sport.

Closing line value (CLV). After each game starts, we record the closing odds at the book where the edge was detected. If the closing odds moved toward our fair value estimate (confirming we got a better price than the final market), that edge had positive CLV. Over large samples, consistently positive CLV is the strongest indicator of a sustainable edge.

Outlier detection. Each detected edge is z-scored against the cross-book consensus. Extreme outliers (z > 3) are flagged as suspected pricing errors — platform glitches, stale data feeds, or coordinated errors across books sharing the same pricing engine. These opportunities are displayed separately with appropriate warnings.

Arbitrage Detection

True arbitrage exists when the combined implied probability of all outcomes across two or more sportsbooks falls below 100%, guaranteeing a profit regardless of outcome with appropriate stake allocation.

Our scanner evaluates every cross-book pair for each event. Identified arbitrage opportunities are scored on multiple dimensions: how long the opportunity has persisted (a proxy for stability and executability), the width of the profit margin (wider margins are more robust to execution slippage), and the statistical normality of each leg's pricing relative to the broader market. These factors are combined into a composite quality score.

Arbitrage windows in sports betting are typically brief. Our 60-second refresh cycle means opportunities may have closed between detection and display. The quality score helps users distinguish between stable, executable opportunities and fleeting or suspicious ones.

Position Sizing

Each opportunity is accompanied by a suggested position size computed via the Kelly Criterion — specifically, a fractional Kelly (one-quarter of the theoretical optimum). Full Kelly is growth-optimal under perfect probability estimation but is well known to produce unacceptable drawdowns when estimates are noisy (Thorp 2006, MacLean et al. 2011).

Fractional Kelly reduces bankroll volatility while preserving most of the long-run growth rate. We further apply sport-specific ceilings to Kelly sizing, reflecting the empirical finding that edge estimates in some sports carry substantially more noise than others.

Cross-Platform Comparison

Sportsbooks and prediction markets are structurally distinct. Sportsbooks are quote-driven markets where the house sets prices and adjusts based on flow. Prediction markets are order-driven continuous double auctions where participants trade binary contracts.

We display sportsbook fair value alongside prediction market prices for matching events but do not blend them into a single estimate. The two ecosystems have different participant bases, different liquidity profiles, and different regulatory constraints. When they disagree, the disagreement itself is informative.

Limitations

BaseCase is an informational tool. It does not place bets, manage accounts, or guarantee outcomes. All probability estimates are market-implied, not model-derived, and are subject to the limitations of the underlying market.

Our fair value estimates are backward-looking in the sense that they aggregate the current pricing of sportsbooks. They do not incorporate private information, sentiment analysis, or any form of fundamental modeling. When the collective market is wrong, our estimates will also be wrong.

Detected edges represent pricing discrepancies, not guaranteed profits. Odds can change between detection and execution. Books may limit accounts or void bets on suspected errors. Arbitrage execution requires simultaneous placement across platforms, which introduces latency and rejection risk.

The calibration weights underpinning the fair value model are derived from historical data and may not generalize perfectly to future market conditions. We mitigate this through out-of-sample validation and periodic refitting, but stationarity is an assumption, not a guarantee.

References