Expected-GP model (gp_expectancy.py → gp_expectancy.csv)

Built 2026-07 for the 2026-27 projection stack: project_rosters_2026_27.py values every player at his per-82 rate; this model supplies the missing availability multiplier, ExpGPFrac2026 (expected fraction of an 82-game schedule played).

Data

• Panel: 16 seasons (2010-2025 season keys) from roster_toi_2010_2020.csv + roster_toi.csv, regular-season games only (game_id[4:6] == "02"; coverage verified complete: 12,590 + 6,560 distinct games).
• GP-fraction = distinct games ÷ hardcoded schedule length {2012: 48, 2019: 71, 2020: 56, else 82}, clipped to [0, 1]. The observed-max-GP denominator was rejected: midseason trades push individual maxima to 84-85, which would deflate everyone else.
• Interior gap seasons (absent between first and last NHL appearance — e.g. Kucherov's injury-wiped 2020-21) are filled with 0.0 as prediction inputs, but never used as evaluation targets (using them would condition on the known return).
• Ages from player_bio.csv birthDate, as of Oct 1 of the season year.
• Goalies excluded from all analysis/tuning — a backup's GP-fraction is rotation policy, not health. They are still written to the CSV (pos = G) with the same estimator; treat that number as "share of games dressed and used", not injury expectation. The projection stack already handles goalie workload via starts.

Q1 — Persistence

Games-missed is clearly persistent, but much of the pooled 0.63 is the regular-vs-fringe axis; within established regulars the health signal itself is r ≈ 0.35 — real, but noisy enough that heavy shrinkage is warranted. Multi-season averages carry essentially the same signal as last season alone at the pooled level; the model bake-off below settles the weighting question.

Q2 — Age effect beyond persistence

Residuals of the tuned model (actual − predicted) regressed on age (2012-2025, eligible skater rows): about −0.010 fraction (≈ −0.9 GP) per year of age past 27, flattening slightly after 30. Confirmed model-free in the healthy cohort (last-2-season mean ≥ 0.85):

The gradient is real but small (~5 GP from age 22 to 36 for a healthy player).

Q3 — Model bake-off (walk-forward MAE, targets 2018-2025)

Eligibility per target season: skater, appeared that season, ≥ 1 prior panel season, last-2 prior mean ≥ 0.25 (semi-regular gate). n = 5,179 predictions. Rookie (first) seasons are never targets. No-history players get the league mean fraction (μ₂₀₂₆ = 0.763 for this population; regulars run ~0.82-0.85).

Tuning grid: decay ∈ {0.3…1.0}, shrink k ∈ {0…3} pseudo-seasons toward the trailing-3-season league mean; the surface is flat near the optimum ((0.4, 0.25) and (0.3, 0.5) are within 0.0011). Steep decay wins: last season carries most of the health signal; older seasons add a little; heavy shrinkage is not needed once recency-weighting is in place (k = 0.25 ≈ a quarter-season of league-mean ballast, which mostly regularizes stale or one-season histories).

Age adjustment dropped. It failed walk-forward in every form tried: full spec (+0.0034 MAE), slope-only fit on regulars with no intercept (+0.0020), single hinge at 28 (+0.0041), and even when evaluated only on regulars (0.1509 → 0.1557). The Q2 gradient (~0.01/yr) is an order of magnitude smaller than residual noise (MAE 0.18), and fitting it walk-forward adds estimation error faster than it removes bias. Per the design rule — age adjustment only if it survives the walk-forward test — ExpGPFrac2026 is age-free. Bias check: eval-window mean predicted 0.770 vs actual 0.755.

Final model: pred = (Σ 0.3^lag · frac + 0.25 · μ) / (Σ 0.3^lag + 0.25), lag measured back from 2025-26, clipped to [0.02, 1].

Q4 — The catastrophic tail

P(fraction < 0.40 | last-2-season mean ≥ 0.85), i.e. a lost season for a previously healthy skater:

The tail is age-dependent — roughly 2× as likely at 30+ as under 25 — even though age adds nothing to the point prediction. If the season simulator ever samples GP rather than using the expectation, it should draw catastrophes at ~2.5% (U25) / ~5.5% (30+) on top of the continuous part; the expectation already prices the average of this tail.

Sanity gates

Mean ExpGPFrac2026 among skaters with 2025-26 fraction ≥ 0.5: 0.823 — inside the expected 0.80-0.85 band for regulars.

Output

gp_expectancy.csv — 1,328 players (everyone with ≥ 1 GP in 2023-24 through 2025-26; 132 goalies flagged by pos): playerId, name, pos, Age2026, Frac2023/24/25, NSeasons, ExpGPFrac2026, ExpGP82.

Hook-up note for project_rosters_2026_27.py: expected value per roster slot ≈ ProjValue82 × ExpGPFrac2026 (plus replacement-level fill for the missing games, if modeled). Rookies absent from the CSV: use the league mean fraction for regulars (~0.82) rather than 0.763, since a projected roster slot conditions on being a regular.