NFL Week 9 Player Props & Projections

Lines and prices are real DraftKings numbers (FACT). The projected mean, the model's over probability, and the edge are derived from a rules-based projection engine (DERIVED). Edge = model_over_prob - no_vig(over_implied_prob).

Passing Yards

Normal approximation: P(yards ≥ line) for Normal(projected mean, SD≈95). Passing yards are roughly symmetric, so the normal fit is reasonable near the line.

Rushing Yards

Normal approximation: P(yards ≥ line) for Normal(projected mean, SD≈35). Rushing yards are right-skewed (breakaway runs), so a symmetric normal understates the upper tail — overs are biased slightly low.

Receiving Yards

Normal approximation: P(yards ≥ line) for Normal(projected mean, SD≈35). Receiving yards are right-skewed (long catches), so a symmetric normal understates the upper tail — overs are biased slightly low.

Receptions

Poisson tail: P(receptions ≥ ⌈line⌉) on the projected mean. Reception counts are mildly overdispersed (target share varies), but Poisson is a reasonable fit at standard lines.

Passing TDs

Poisson tail: P(passing TDs ≥ ⌈line⌉) on the projected mean.

Anytime TD

Bernoulli: P(≥1 TD) = 1 − P(0) under Poisson(expected rushing + receiving TDs). A QB's passing TDs are not anytime-TD scoring events, so only rushing + receiving TDs feed the rate.

• These edges are NOT betting advice. An edge is the gap between a rules-based projection and the book's line — a projection, not a prediction. The slice-18 backtest confirmed the projection engine is not yet calibrated for props; treat every edge as directional context only.
• The slice-18 prop backtest (2024 DraftKings, walk-forward) found EVERY market miscalibrated: line-market ECE ran ~0.09–0.16 against a 0.03 well-calibrated bar, and the model's Brier was worse than the book's no-vig line on all five, so NO market cleared the pre-registered promotion bar — edges stay directional-only, not actionable. As with MLB props, the root cause is the projection engine, not the probability layer — and the follow-up diagnostic sharpened it: the SDs are already about right (residual ≈ assumed), but the projection means carry too little edge to beat the sharp line (on the yards markets the most-confident overs even go over LESS often), so no market's Brier beats the book. Because that edge is invariant to any recalibration, no isotonic/SD fix can promote these markets — only better projection means could.
• Yardage probabilities use a symmetric normal approximation; rushing and receiving yards are right-skewed, so overs on those markets are biased slightly low (real overs marginally better than reported).
• Player names are resolved to nflverse ids by exact lookup only; a name we cannot resolve unambiguously is dropped and counted (num_unmatched / num_ambiguous), never guessed — a wrong player would be a correctness bug.
• Integer lines are treated as 'over wins on ≥ ⌈line⌉', which slightly overstates the over vs. sportsbook push rules; the near-universal half-point lines are unaffected.