Chapter 34: Key Takeaways -- Prop Bets and Player Markets

1. The Multiplicative Projection Framework Is the Foundation

Every player prop projection follows the same core structure: Projected Stat = Minutes x Per-Minute Rate x Opponent Adjustment x Context Adjustments. Minutes projection is the single most important and most uncertain input, because a 15% error in minutes cascades through every stat category. Per-minute rates should use exponentially weighted moving averages over a 15-20 game window to balance recency and stability.

2. Pace and Usage Rate Drive the Biggest Adjustments

Pace measures how many possessions a game generates, directly scaling the opportunity set for every counting stat. Usage rate determines how a player converts possessions into statistical production. When a teammate is absent, the remaining players absorb that usage proportionally, and star players absorb disproportionately more. These two adjustments alone can shift a projection by 10-15%, making them the highest-leverage modeling inputs after minutes.

3. Opponent Defense Adjustments Must Be Position-Specific

A blanket "good defense / bad defense" assessment is insufficient. Opponent adjustments should measure how many of a specific stat the opponent allows to a specific position. A team that shuts down opposing point guards may be average against centers, and vice versa. The adjustment factor is a simple ratio of the opponent's position-specific stat allowed to the league average.

4. Correlation Between SGP Legs Creates Systematic Edge

Same-game parlay legs are not independent. A team winning correlates positively with its star scoring over his points prop (rho ~ 0.22 in NBA data) and negatively with the opposing star's points. Game total over correlates positively with all player scoring overs. When a sportsbook's correlation model underestimates these dependencies, the true joint probability exceeds the implied probability, creating positive expected value.

5. The Gaussian Copula Provides a Tractable Correlation Model

The Gaussian copula transforms correlated normal variables into uniform marginals, then maps them to the leg-specific outcome space. This approach handles any number of legs with arbitrary pairwise correlations, naturally produces a valid joint distribution, and is computationally efficient via Monte Carlo simulation. Its main limitation -- the assumption of linear (Gaussian) dependence -- is acceptable for the moderate correlations seen in SGP legs.

6. Projection System Accuracy Comes from Ensemble Methods

No single input source dominates. The best prop projection systems combine recent game logs (EWMA rates), season-long baselines, opponent matchup data, Vegas-implied game environments, and usage redistribution from injury news. Bayesian stabilization prevents overreaction to small samples early in the season by shrinking extreme observed rates toward the positional prior.

7. Alternate Lines and Combination Stats Are Often Mispriced

Sportsbooks model the core lines (e.g., points over/under at the median) with high precision, but alternate lines (e.g., over 35.5 points at +400) are more vulnerable to distributional misspecification. If a player's statistical distribution has fat tails (positive excess kurtosis), alternate overs are systematically underpriced by books using normal distribution models. Combination stats (PRA, P+A) require proper variance calculation that accounts for inter-stat correlations.

8. Public Bias Toward Overs Creates Contrarian Value

Empirical data shows that roughly 60-70% of public money flows to the over on star player props, particularly points. Sportsbooks shade their lines in response, setting the over side slightly higher than the true median. This systematic bias creates modest but consistent value on the under side of star player scoring props, particularly in nationally televised games where casual bettors are most active.

9. Game Script and Environment Are Underexploited

The expected game script, derived from the point spread and total, drives predictable adjustments to player usage patterns. Large underdogs pass more (boosting QB and WR props), while large favorites run more (boosting RB props and suppressing pass volume). Similarly, pace-up game environments (high Vegas totals) boost all counting stats. Stacking multiple correlated overs in a favorable environment amplifies the edge.

10. Disciplined Execution Requires Bankroll Rules and Edge Thresholds

Even with an accurate projection system, profitability requires discipline. Props should only be bet when the estimated edge exceeds a minimum threshold (typically 3-5% after accounting for vig). Individual prop bets should be sized at 1-3% of bankroll, and same-game exposure on a single event should be capped at 5-10% of bankroll. Tracking actual results against projections and continuously recalibrating the model is essential for long-term profitability.