NBA Home Court Advantage — Regression Results

Author

Justin Pietsch

Published

July 4, 2026

Auto-generated by home_court_analysis.py — do not edit manually.
Re-run MPLBACKEND=Agg python3 home_court.py to refresh.


════════════════════════════════════════════════════════════════════════
NBA HOME COURT ADVANTAGE — REGRESSION ANALYSIS
════════════════════════════════════════════════════════════════════════
Game-level logistic regression. Outcome: home_win (1/0) per game.
All data from cache/ — same source as the plots above.


─── THE OVERALL DECLINE — IS IT STATISTICALLY REAL? ────────────────────
   Primary: binomial GLM (events/trials per season, weights by game count).
   Cross-check: OLS with Newey–West HAC SEs (maxlags=1).
   Per-era slopes use same methods on era subsets.

   Regular season  (43 seasons, 1984–2026)
   Binomial GLM: -0.244 pp/yr  95% CI [-0.280, -0.209]  (p = <0.001  ***,  total ≈ -10.3 pp)
   OLS / HAC:    -0.250 pp/yr  95% CI [-0.296, -0.204]  (p = <0.001  ***,  R² = 0.745,  total: -10.5 pp)

   Era              N   GLM pp/yr     GLM p   OLS pp/yr     HAC p     
   ────────────  ────  ──────────  ────────  ──────────  ────────  ───
   1984–94         11      -0.522    <0.001      -0.506     0.019  ***
   1995–01          7      +0.201     0.462      +0.229     0.205     
   2002–04          3      +1.136     0.256      +1.135     0.312     
                       ⚠ n=3: too few seasons — treat as illustrative only
   2005–17         13      -0.179     0.085      -0.180     0.002     
   2018–22          5      -1.183     0.009      -1.191     0.009   **
   2023–26          4      -0.773     0.223      -0.772     0.216     
                       ⚠ n=4: too few seasons — treat as illustrative only

   Playoffs  (42 seasons, 1984–2026)
   Binomial GLM: -0.225 pp/yr  95% CI [-0.359, -0.091]  (p = <0.001  ***,  total ≈ -9.5 pp)
   OLS / HAC:    -0.216 pp/yr  95% CI [-0.356, -0.076]  (p = <0.001  ***,  R² = 0.195,  total: -9.1 pp)

   Era              N   GLM pp/yr     GLM p   OLS pp/yr     HAC p     
   ────────────  ────  ──────────  ────────  ──────────  ────────  ───
   1984–94         11      +0.250     0.629      +0.234     0.262     
   1995–01          7      +0.385     0.719      +0.312     0.782     
   2002–04          3      +6.551     0.095      +6.398     0.097     
                       ⚠ n=3: too few seasons — treat as illustrative only
   2005–17         13      -0.442     0.255      -0.445     0.323     
   2018–22          4      -2.129     0.207      -2.155     0.184     
                       ⚠ n=4: too few seasons — treat as illustrative only
   2023–26          4      -1.409     0.558      -1.408     0.003     
                       ⚠ n=4: too few seasons — treat as illustrative only


─── STRUCTURAL BREAK TEST — WHERE DID THE DECLINE SHIFT? ───────────────
   QLR supremum Chow F: Chow test at every candidate year, outer 15% trimmed.
   Conditional p-values assume the break year is known (single-test reference).
   Andrews (1993) QLR critical values, k=2, π₀=0.15:
   10% → 7.12  |  5% → 8.85  |  1% → 12.37

   Regular season  (N = 43 seasons, candidates: 1991–2019)
   Supremum Chow F = 10.22  at year 1999  [p < 5%   **]
   Subperiod slopes:  before 1999: -0.652 pp/yr  |  after 1999: -0.255 pp/yr

   Top candidate break years:
     Year    Chow F     Cond. p   Slope before   Slope after
   ──────  ────────  ──────────  ─────────────  ────────────
     1999     10.22      <0.001         -0.652        -0.255
     2003      8.39      <0.001         -0.482        -0.308
     1998      8.30      <0.001         -0.673        -0.235
     1992      7.59       0.002         -0.022        -0.182
     2000      6.60       0.003         -0.562        -0.253

   Bootstrap 95% CI for break year (B=500 residual resamples): [1993, 2002]
   ► Break is robustly in 1993–2002: supports 'late 1990s'
     framing; no single year can be pinpointed with precision.

   Playoffs  (N = 42 seasons, candidates: 1991–2018)
   Supremum Chow F = 3.23  at year 2006  [n.s. at 10%]
   Subperiod slopes:  before 2006: -0.287 pp/yr  |  after 2006: -0.651 pp/yr

   Top candidate break years:
     Year    Chow F     Cond. p   Slope before   Slope after
   ──────  ────────  ──────────  ─────────────  ────────────
     2006      3.23       0.051         -0.287        -0.651
     2008      2.88       0.068         -0.201        -0.727
     2007      2.83       0.072         -0.231        -0.677
     2004      2.36       0.108         -0.319        -0.532
     2013      1.75       0.188         -0.031        -0.404

   Bootstrap 95% CI for break year (B=500 residual resamples): [1993, 2018]
   ► Break not significant; CI of [1993, 2018] is wide
     and unreliable — no stable break location to report.


─── CUSUM TEST — PARAMETER STABILITY  (complement to structural break test above) 
   CUSUM (Brown-Durbin-Evans): cumulative recursive residuals from the linear
   trend. Exit from the 5% critical band = structural instability detected.
   QLR (§1b) finds the single strongest break; CUSUM tests global stability.
   Agreement → increased confidence; discrepancy → worth investigating.

   Regular season  (N = 43 seasons)
   Exceeds 5% critical band: no — stable within bounds
   Peak |CUSUM| = 14.000 at year 2019  (5% bound at that point = ±16.086)
   Peak is 87% of the 5% boundary.
   ► CUSUM stays inside bounds even though the structural break test found a break:
     the slope change around 1999 is gradual (-0.65 → -0.25 pp/yr),
     not a sharp level jump — CUSUM has lower power for slope-only breaks.

   Playoffs  (N = 42 seasons)
   Exceeds 5% critical band: no — stable within bounds
   Peak |CUSUM| = 5.820 at year 2026  (5% bound at that point = ±17.987)
   Peak is 32% of the 5% boundary.


─── BAYESIAN CHANGE-POINT MODEL — HOW MANY BREAKS, AND WHERE? ──────────
   Model comparison: k=0 (linear), k=1 (one break), k=2 (two breaks), k=3 (three breaks).
   BIC-based marginal likelihood. Uniform prior over k and break locations.
   Piecewise WLS (weights = game counts); minimum 3 seasons per segment.
   Regular season only.

   N = 43 seasons, 1984–2026
   Candidate break positions: min segment size = 3 seasons

   ─ Posterior model probabilities ─
   (Uniform prior over k ∈ {0,1,2,3} and over all valid break locations)

   Model                       BF vs k=0  Posterior P(k)
   ─────────────────────────  ──────────  ──────────────
   k=0  (no break)                  1.0           1.4%
   k=1  (one break)                14.2          19.3%
   k=2  (two breaks)               29.9          40.5%
   k=3  (three breaks)             28.6          38.8%

   ─ k=1 posterior over break year ─
   MAP break year:     1999
   95% HPD interval:   1992–2003
   Posterior-weighted slopes:
     Pre-break:  -0.577 pp/yr  (±0.170 posterior SD)
     Post-break: -0.255 pp/yr  (±0.032 posterior SD)

   Top break-year probabilities (k=1):
     Year   P(τ=year | k=1)
   ──────  ────────────────
     1999            50.1%  ██████████████████████████████
     2003            17.7%  ██████████
     1998            11.5%  ██████
     2000             6.1%  ███
     1992             3.9%  ██
     2002             3.3%  ██
     2001             1.9%  █
     1993             1.9%  █

   ─ k=2 MAP break years: 1992 and 2020 ─

   ─ k=3 MAP break years: 1988, 1998, and 2020 ─
   ► BF(k=1 vs k=0) = 14.2: strong evidence for at least one structural break.
   ► BF(k=2 vs k=1) = 2.1  BF(k=3 vs k=2) = 1.0


─── IS THE DECLINE LEAGUE-WIDE? — PER-FRANCHISE HCA SLOPE DECOMPOSITION 
   Regular-season team-season HCA gap = home win% − road win% (nets out
   each team's overall strength). Each franchise gets its own year-slope
   by OLS; the pooled cluster-robust slope is the league-wide decline.
   A method-of-moments split separates the true between-team spread in
   those slopes from sampling noise (same idiom as franchise HCA and
   referee bias). Near-zero true spread → the decline is league-wide.

   Panel: 1,223 team-seasons; per-team slopes fit for 31 franchises (≥10 seasons)

   League-wide slope (pooled, cluster-robust):  -0.490 pp/yr  (SE 0.026, p = <0.001  ***)
   Observed SD of per-team slopes:              0.213 pp/yr
   Noise-adjusted true between-team SD:         0.000 pp/yr
   Share of observed spread that is noise:      100%

   Per-franchise raw slopes (extremes; both within noise of the league rate):
   Steepest decline:  -1.160 pp/yr  (New Orleans Pelicans)
   Shallowest/rising: -0.082 pp/yr  (LA Clippers)
   Franchises with a positive (rising) raw slope: 0/31
   After EB shrinkage every franchise collapses to ≈-0.49 pp/yr.

   ► Once sampling noise is removed, franchises barely differ: most of the
     raw spread in team slopes is noise, and the shrunken slopes collapse
     onto one shared league rate. The decline is broadly league-wide, not
     driven by a handful of franchises losing their edge.
   ► Playoffs are excluded: per-franchise playoff samples are far too small
     for a season-by-season panel; the playoff decline is league-wide (§1, §5).


─── WHERE IS HOME COURT HEADING? — STATE-SPACE FORECAST ────────────────
   A local-linear-trend state-space model on the season-level home
   win % lets the underlying level drift with its own slope, then
   extrapolates a few seasons forward with prediction intervals (the
   fan). Regular season and playoffs fit separately. This is a forward
   projection of the current slope, not a claim about future rule
   changes; the intervals widen with the horizon to show that.

   Regular season  (1984–2026, 43 seasons)
   Current smoothed level:  54.9%   (trend slope -0.3 pp/yr)

     Season   Forecast      95% interval
   ────────  ─────────  ────────────────
       2027      54.6%  [ 51.1,  58.1]
       2028      54.3%  [ 50.4,  58.3]
       2029      54.0%  [ 49.7,  58.4]
       2030      53.8%  [ 49.0,  58.5]
       2031      53.5%  [ 48.4,  58.6]

   Playoffs  (1984–2026, 42 seasons)
   Current smoothed level:  58.8%   (trend slope -0.3 pp/yr)

     Season   Forecast      95% interval
   ────────  ─────────  ────────────────
       2027      58.4%  [ 46.8,  70.0]
       2028      58.1%  [ 46.4,  69.8]
       2029      57.8%  [ 45.9,  69.6]
       2030      57.4%  [ 45.4,  69.4]
       2031      57.1%  [ 44.9,  69.3]


─── FOUL & SHOOTING DIFFERENTIALS BY ERA  (home minus away, per game) ──
   Negative foul diff = refs call fewer fouls on the home team.
   Positive fta_diff = home team attempted more free throws.
   Trend = slope of trend line (change per season year); pp = percentage points.

   Regular season  (N = 49,107 games)

   Era              Foul diff      FTA diff      FG% (pp)     eFG% (pp) 3PA rate (pp)      3P% (pp)      FT% (pp)
   ──────────────────────────────────────────────────────────────────────────────────────────────────────────────
   1984–94              -1.23         +1.97         +1.57         +1.56         -0.35         +1.12         +0.27
   1995–01              -0.59         +0.92         +1.16         +1.20         -0.11         +0.83         +0.35
   2002–04              -0.52         +0.84         +1.48         +1.62         +0.08         +1.66         +0.07
   2005–17              -0.79         +1.15         +1.17         +1.25         -0.10         +0.70         +0.26
   2018–22              -0.33         +0.53         +0.81         +0.93         +0.24         +0.46         -0.01
   2023–26              -0.25         +0.46         +0.70         +0.95         +0.44         +0.88         +0.76
   ──────────────────────────────────────────────────────────────────────────────────────────────────────────────
   Trend/yr         +0.022***     -0.036***     -0.021***     -0.015***     +0.018***     -0.007        +0.003   

   Playoffs  (N = 3,292 games)

   Era              Foul diff      FTA diff      FG% (pp)     eFG% (pp) 3PA rate (pp)      3P% (pp)      FT% (pp)
   ──────────────────────────────────────────────────────────────────────────────────────────────────────────────
   1984–94              -1.58         +2.35         +1.56         +1.47         -0.85         -0.21         +0.52
   1995–01              -1.22         +1.66         +1.31         +1.40         -0.20         +1.55         +0.58
   2002–04              -1.04         +1.71         +1.92         +1.88         -0.32         +0.60         +0.00
   2005–17              -1.43         +2.36         +1.56         +1.57         -0.36         +0.39         +0.22
   2018–22              -0.67         +1.30         +1.00         +1.30         +0.88         +0.86         +0.26
   2023–26              -0.68         +1.09         +0.96         +1.02         -0.21         +0.75         +2.12
   ──────────────────────────────────────────────────────────────────────────────────────────────────────────────
   Trend/yr         +0.020 **     -0.021        -0.015        -0.009        +0.028  *     +0.015        +0.009   


─── FOUL & FTA DIFFERENTIAL — PER-GAME SPREAD VS. THE AVERAGE EDGE ─────
   P10/P90 = 10th/90th percentile of the per-game home-minus-away gap.
   width = P90 - P10, the typical night-to-night swing around the average.
   home-favored = share of games where the gap ran the home team's way.

   Regular season
      early   FTA  mean=+1.97  P10=-12  P90=+16  width=28  home-favored=56%
              Foul mean=-1.23  P10=-8  P90=+6  width=14  home-favored=56%
      late    FTA  mean=+0.46  P10=-11  P90=+12  width=23  home-favored=49%
              Foul mean=-0.25  P10=-6  P90=+6  width=12  home-favored=48%

      fta: average edge fell 77%, game-to-game spread narrowed only 18%
      foul: average edge fell 80%, game-to-game spread narrowed only 14%

   Playoffs
      early   FTA  mean=+2.35  P10=-11  P90=+16  width=27  home-favored=57%
              Foul mean=-1.58  P10=-8  P90=+5  width=13  home-favored=58%
      late    FTA  mean=+1.09  P10=-10  P90=+11  width=21  home-favored=56%
              Foul mean=-0.68  P10=-6  P90=+5  width=11  home-favored=52%

      fta: average edge fell 54%, game-to-game spread narrowed only 22%
      foul: average edge fell 57%, game-to-game spread narrowed only 15%


─── REFEREE CREW HOME FOUL BIAS (PLAYOFFS) ─────────────────────────────
   foul_diff = PF_home − PF_away  (negative = home team fouled less = home-favoring)
   Officials with <50 playoff games excluded.
   t-tests use per-game SDs (real test). BH = Benjamini-Hochberg FDR 5% correction.

   47 officials with ≥50 playoff games
   45/47 (96%) show negative mean foul diff (home-favoring)
   Individually significant (p<0.05, real t-test):    29/47
   Survive Benjamini-Hochberg correction (FDR 5%):    29/47
   League mean foul_diff across officials: -1.098 fouls/game

   Variance decomposition (career level, method of moments):
   Observed SD across officials: 0.645 fouls/game
   Mean within-official SE:      0.500 fouls/game
   Estimated true between-SD:    0.407 fouls/game
   ► Sampling noise explains 60% of observed spread.

   Last playoff season worked, most home-favoring officials:
   Ron Garretson        last worked 2017-18
   Joe Crawford         last worked 2014-15
   Eddie Rush           last worked 2011-12

   Top 10 most home-favoring (by shrunken mean foul_diff):
   Official                     N games  Raw diff  Shrunken         p      BH-p
   ────────────────────────── ───────── ───────── ───────── ───────── ─────────
   Ron Garretson                    143    -2.385    -1.734    <0.001    <0.001
   Joe Crawford                     160    -2.288    -1.717    <0.001    <0.001
   Eddie Rush                       100    -2.530    -1.664    <0.001    <0.001
   Rodney Mott                       69    -2.232    -1.499    <0.001     0.001
   James Capers                     199    -1.764    -1.478    <0.001    <0.001
   Bob Delaney                       80    -2.175    -1.412    <0.001     0.004
   Eric Lewis                        79    -1.759    -1.368    <0.001     0.003
   Sean Wright                      108    -1.639    -1.344    <0.001     0.002
   David Jones                       51    -1.843    -1.274     0.015     0.026
   Bill Spooner                     111    -1.495    -1.258     0.003     0.009

   Bottom 10 least home-favoring (by shrunken mean foul_diff):
   Official                     N games  Raw diff  Shrunken         p      BH-p
   ────────────────────────── ───────── ───────── ───────── ───────── ─────────
   Tyler Ford                        61    -0.344    -0.889     0.602     0.629
   Jason Phillips                    96    -0.615    -0.865     0.148     0.205
   Kevin Scott                       57    -0.351    -0.836     0.529     0.579
   Courtney Kirkland                 85    -0.353    -0.817     0.501     0.575
   Mark Lindsay                      54    -0.111    -0.799     0.858     0.858
   David Guthrie                    113    -0.398    -0.775     0.367     0.442
   Tony Brothers                    213    -0.559    -0.773     0.092     0.143
   Josh Tiven                       103    -0.252    -0.731     0.588     0.629
   Ben Taylor                        53    +0.151    -0.715     0.806     0.824
   Joe Forte                         51    +0.451    -0.713     0.527     0.579

   Era variance decomposition — does official spread compress over time?
   Era            N off     Mean    Raw SD   True SD   Noise %
   ──────────── ─────── ──────── ───────── ───────── ─────────
   1995–01           14   -2.239     2.076     0.000      100%
   2002–04           27   -0.781     1.813     0.722       84%
   2005–17           43   -1.232     0.975     0.477       76%
   2018–22           33   -0.737     1.056     0.469       80%
   2023–26           25   -0.753     0.702     0.000      100%


─── SHOT ZONE DIFFERENTIALS BY ERA  (home minus road % of FGA) ─────────
   Positive = home team takes a higher share of FGA from that zone.
   Trend = slope of trend line (change per season year). Data from 1996–97 onward.

   Regular season  (N = 30 seasons)

   Era          Paint (RA+Non-RA)         Mid-Range          Corner 3     Above Break 3
   ────────────────────────────────────────────────────────────────────────────────────
   1995–01                  +1.28             -1.24             +0.16             -0.20
   2002–04                  +1.18             -1.24             +0.29             -0.23
   2005–17                  +1.26             -1.19             +0.12             -0.19
   2018–22                  +0.55             -0.77             +0.18             +0.04
   2023–26                  +0.24             -0.72             +0.21             +0.26
   ────────────────────────────────────────────────────────────────────────────────────
   Trend/yr             -0.041***         +0.025***         +0.000            +0.015 **

   Playoffs  (N = 28 seasons)

   Era          Paint (RA+Non-RA)         Mid-Range          Corner 3     Above Break 3
   ────────────────────────────────────────────────────────────────────────────────────
   1995–01                  +1.71             -1.67             +0.46             -0.50
   2002–04                  +2.08             -1.82             +0.10             -0.36
   2005–17                  +1.78             -1.50             +0.10             -0.39
   2018–22                  +0.72             -1.62             +0.48             +0.42
   2023–26                  +1.35             -1.11             +0.10             -0.34
   ────────────────────────────────────────────────────────────────────────────────────
   Trend/yr             -0.036            +0.015            -0.004            +0.025   


─── MEDIATION — BOX-SCORE CHANNELS AS SHARES OF HCA LEVEL AND TREND ────
   How much of the home edge, and of its decline, flows through the
   measured channels: shooting (eFG%), referee fouls, turnovers, and
   rebounds? Linear-probability model of home_win on the four
   home-minus-away differentials; cluster-robust SEs by season.
   Level identity:  mean win % = intercept + Σ coef × mean diff.
   Trend identity:  total pp/yr = unmediated pp/yr + Σ coef × channel trend/yr.
   Foul diff carries the free-throw-attempt channel; FT% diff is
   excluded (mean ≈ +0.3 pp, negligible). Channels are proximate —
   how HCA expresses itself in the box score — so this is an
   accounting decomposition, not deep causation.

   Regular season  (N = 49,104 games, home win % = 60.1, level above coin flip = +10.1 pp)
   Channel-model R² = 0.615 — share of game-outcome variance the four channels carry.

   Level decomposition  (coef × mean diff):
   Channel            Mean diff   pp per unit   Contribution  % of level
   ────────────────  ──────────  ────────────  ─────────────  ──────────
   eFG% diff (pp)         +1.27      +3.42 ***      +4.4 pp         43%
   Foul diff              -0.73      -1.98 ***      +1.4 pp         14%
   TOV diff               -0.38      -3.38 ***      +1.3 pp         13%
   REB diff               +1.52      +1.67 ***      +2.5 pp         25%
   ────────────────  ──────────  ────────────  ─────────────  ──────────
   Unexplained                                       +0.5 pp          5%

   Trend decomposition  (pp of home win % per year):
   Total trend (home_win ~ year): -0.244 pp/yr  (p = <0.001  ***)

   Channel           Trend in diff/yr        95% CI (diff/yr)     Contribution  % of trend
   ────────────────  ────────────────  ──────────────────────  ───────────────  ──────────
   eFG% diff (pp)         -0.0151 ***      [-0.0224, -0.0078]    -0.0516 pp/yr         21%
   Foul diff              +0.0222 ***      [+0.0168, +0.0275]    -0.0438 pp/yr         18%
   TOV diff               +0.0193 ***      [+0.0142, +0.0244]    -0.0651 pp/yr         27%
   REB diff               -0.0443 ***      [-0.0517, -0.0370]    -0.0738 pp/yr         30%
   ────────────────  ────────────────  ───────────────  ──────────
   Sum, channels                         -0.2344 pp/yr         96%
   Unmediated                            -0.0097 pp/yr          4%

   ► Regular season: channels carry 95% of the HCA level and 96% of its decline.

   Playoffs  (N = 3,292 games, home win % = 64.1, level above coin flip = +14.1 pp)
   Channel-model R² = 0.598 — share of game-outcome variance the four channels carry.

   Level decomposition  (coef × mean diff):
   Channel            Mean diff   pp per unit   Contribution  % of level
   ────────────────  ──────────  ────────────  ─────────────  ──────────
   eFG% diff (pp)         +1.46      +3.18 ***      +4.6 pp         33%
   Foul diff              -1.25      -1.95 ***      +2.4 pp         17%
   TOV diff               -0.92      -3.33 ***      +3.1 pp         22%
   REB diff               +1.80      +1.67 ***      +3.0 pp         21%
   ────────────────  ──────────  ────────────  ─────────────  ──────────
   Unexplained                                       +0.9 pp          7%

   Trend decomposition  (pp of home win % per year):
   Total trend (home_win ~ year): -0.225 pp/yr  (p = <0.001  ***)

   Channel           Trend in diff/yr        95% CI (diff/yr)     Contribution  % of trend
   ────────────────  ────────────────  ──────────────────────  ───────────────  ──────────
   eFG% diff (pp)         -0.0087          [-0.0290, +0.0116]    -0.0278 pp/yr         12%
   Foul diff              +0.0204 **       [+0.0070, +0.0339]    -0.0396 pp/yr         18%
   TOV diff               +0.0066          [-0.0086, +0.0218]    -0.0218 pp/yr         10%
   REB diff               -0.0374 **       [-0.0630, -0.0118]    -0.0622 pp/yr         28%
   ────────────────  ────────────────  ───────────────  ──────────
   Sum, channels                         -0.1514 pp/yr         67%
   Unmediated                            -0.0734 pp/yr         33%

   ► Playoffs: channels carry 93% of the HCA level and 67% of its decline.
   ► Note: playoff differentials fold in the seed-quality gap (the
     home team is usually the better team) — see the seeding
     decomposition for that control.

   ─ Bootstrap 95% CIs on the shares (season block resample, B=500) ─
   Resamples whole seasons with replacement and recomputes the shares;
   the band is the 2.5–97.5 percentile across resamples. Wide bands
   (especially in the playoffs) mean the point share is loosely pinned.

   Regular season  (B = 500 resamples)
   Channel            % level           95% CI   % trend           95% CI
   ────────────────  ────────  ───────────────  ────────  ───────────────
   eFG% diff (pp)         43%  [  +40,  +46]%       21%  [  +11,  +28]%
   Foul diff              14%  [  +13,  +16]%       18%  [  +14,  +22]%
   TOV diff               13%  [  +10,  +14]%       27%  [  +20,  +34]%
   REB diff               25%  [  +23,  +27]%       30%  [  +25,  +38]%
   ────────────────
   Channels carry 95% of the level (95% CI [91, 97]%) and 96% of the decline (95% CI [87, 107]%).

   Playoffs  (B = 500 resamples)
   Channel            % level           95% CI   % trend           95% CI
   ────────────────  ────────  ───────────────  ────────  ───────────────
   eFG% diff (pp)         33%  [  +27,  +38]%       12%  [  -28,  +38]%
   Foul diff              17%  [  +14,  +21]%       18%  [   +7,  +41]%
   TOV diff               22%  [  +17,  +27]%       10%  [  -13,  +39]%
   REB diff               21%  [  +17,  +25]%       28%  [   +9,  +55]%
   ────────────────
   Channels carry 93% of the level (95% CI [86, 102]%) and 67% of the decline (95% CI [38, 107]%).

   ─ Are the channel trends downstream of the 3-point shift? ─
   Each differential's year-trend, before and after controlling for the
   game's 3PA rate. A trend that survives the control is an independent
   driver; one that collapses faded with the move to the perimeter.

   Regular season  (N = 49,104 games)
   Channel              Trend/yr    Trend/yr | 3PA   Absorbed
   ────────────────  ───────────  ────────────────  ─────────
   eFG% diff (pp)      -0.0151***         +0.0166*        210%
   Foul diff           +0.0222***         +0.0108**        51%
   TOV diff            +0.0193***         +0.0088*         54%
   REB diff            -0.0443***         -0.0408***         8%

   ► Survives the 3PA control: TOV diff, REB diff — not fully
     explained by the shooting revolution.

   Playoffs  (N = 3,292 games)
   Channel              Trend/yr    Trend/yr | 3PA   Absorbed
   ────────────────  ───────────  ────────────────  ─────────
   eFG% diff (pp)      -0.0087           +0.0105         220%
   Foul diff           +0.0204**         +0.0025          88%
   TOV diff            +0.0066           -0.0061         194%
   REB diff            -0.0374**         -0.0531*        -42%

   ► Survives the 3PA control: REB diff — not fully
     explained by the shooting revolution.

   ─ Coefficient stability by era (regular season only) ─
   Re-fitting the LPM within each era to check whether the channel
   coefficients are stable across 43 seasons.
   (pp per unit of each home-minus-away differential)

   Era            N games      eFG%     Fouls       TOV       REB
   ────────────  ────────  ────────  ────────  ────────  ────────
   1984–94         11,272    +3.39    -2.05    -3.19    +1.69
   1995–01          7,777    +3.42    -1.98    -3.49    +1.65
   2002–04          3,567    +3.61    -2.20    -3.25    +1.57
   2005–17         15,749    +3.44    -2.01    -3.57    +1.69
   2018–22          5,829    +3.43    -1.83    -3.41    +1.70
   2023–26          4,910    +3.28    -1.63    -3.20    +1.61

   Pooled (all seasons):  eFG%=+3.42  Fouls=-1.98  TOV=-3.38  REB=+1.67  (pp per unit)
   ► Stable coefficients validate the pooled decomposition.
     Large era-to-era shifts would mean the 'share' percentages are
     a blend of heterogeneous effects and should be interpreted with caution.


─── MEDIATION ROBUSTNESS — SENSITIVITY TO UNMEASURED CONFOUNDING ───────
   Robustness check on the mediation. The decomposition assumes the four
   box-score channels are the path home advantage takes; a hidden cause
   correlated with both a channel and the outcome could bias its share.
   For each channel this reports the partial R² with home_win and the
   robustness value (RV, Cinelli & Hazlett 2020): the minimum share of
   the residual variation in BOTH that channel and home_win a confounder
   would have to explain to drive the channel's coefficient to zero.
   Higher RV = harder to explain away. This bounds robustness to a hidden
   cause; it does not prove the channel causes home wins.

   Regular season  (N = 49,104 games, residual dof = 49,098)

   Channel        partial R²   robustness value  Interpretation
   ────────────  ───────────  ─────────────────  ────────────────────────────────────────
   Shooting            48.1%              60.5%  a confounder must explain ≥ 60.5% of both to zero it out
   Fouls               10.5%              28.9%  a confounder must explain ≥ 28.9% of both to zero it out
   Turnovers           21.9%              40.7%  a confounder must explain ≥ 40.7% of both to zero it out
   Rebounding          17.6%              36.8%  a confounder must explain ≥ 36.8% of both to zero it out


   Playoffs  (N = 3,292 games, residual dof = 3,286)

   Channel        partial R²   robustness value  Interpretation
   ────────────  ───────────  ─────────────────  ────────────────────────────────────────
   Shooting            45.9%              59.0%  a confounder must explain ≥ 59.0% of both to zero it out
   Fouls                9.2%              27.1%  a confounder must explain ≥ 27.1% of both to zero it out
   Turnovers           20.1%              39.1%  a confounder must explain ≥ 39.1% of both to zero it out
   Rebounding          17.5%              36.6%  a confounder must explain ≥ 36.6% of both to zero it out



─── REST DIFFERENTIAL — WIN % BY BUCKET AND ERA STABILITY ──────────────
   Buckets: away team more rested (rest_diff < 0), equal rest, and home
   team more rested (rest_diff > 0). Games without a prior game to
   compute rest from are excluded.

   Regular season  (N = 48,424, baseline home win % = 60.1%)

   Bucket             N games   Home win %   vs. baseline
   ────────────────  ────────  ───────────  ─────────────
   Away more rest       8,736        57.6%          -2.6 pp
   Equal rest          23,453        59.3%          -0.9 pp
   Home more rest      16,235        62.8%          +2.7 pp

   Chi-square (H0: home win % equal across buckets): χ²(2) = 79.22,  p = <0.001  ***

   Rest effect by era (bivariate logistic within each era):
   Era                 N   log-odds/day   ≈pp/day         p     
   ────────────  ───────  ─────────────  ────────  ────────  ───
   1984–94        11,123         +0.047      +1.1     0.007   **
   1995–01         7,669         +0.072      +1.7    <0.001  ***
   2002–04         3,516         +0.044      +1.1     0.135     
   2005–17        15,520         +0.054      +1.3    <0.001  ***
   2018–22         5,749         +0.065      +1.6     0.012    *
   2023–26         4,847         +0.113      +2.8    <0.001  ***

   Rest × era interaction (LR test): χ²(5) = 4.54,  p = 0.474  
   ► no evidence the rest effect changed across eras.

   Playoffs  (N = 2,956, baseline home win % = 62.8%)

   Bucket             N games   Home win %   vs. baseline
   ────────────────  ────────  ───────────  ─────────────
   Away more rest          99        67.7%          +4.9 pp
   Equal rest           2,713        61.9%          -0.8 pp
   Home more rest         144        75.0%         +12.2 pp

   Chi-square (H0: home win % equal across buckets): χ²(2) = 11.06,  p = 0.004  **

   Rest effect by era (bivariate logistic within each era):
   Era                 N   log-odds/day   ≈pp/day         p     
   ────────────  ───────  ─────────────  ────────  ────────  ───
   1984–94           706         +0.027      +0.6     0.748     
   1995–01           440         +0.193      +4.5     0.061     
   2002–04           217         +0.136      +3.2     0.365     
   2005–17           986         +0.118      +2.7     0.080     
   2018–22           304         -0.038      -0.9     0.792     
   2023–26           303         +0.147      +3.6     0.209     

   Rest × era interaction (LR test): χ²(5) = 2.82,  p = 0.727  
   ► no evidence the rest effect changed across eras.


─── REST, ALTITUDE, AND TIME ZONE — DO THEY MATTER? ────────────────────
   Bivariate logistic regression — each factor tested independently.
   N regular season: 48,424   N playoffs: 2,956

   Factor                           ── Regular season ──         ──── Playoffs ────    
                                 log-odds    ≈pp         p       log-odds    ≈pp         p     
   ────────────────────────────  ────────  ─────  ────────  ───  ────────  ─────  ────────  ───
   Rest diff (per day)             +0.065   +1.6    <0.001  ***    +0.101   +2.4     0.010   **
                    95% CI (pp)            [+1.2,+2.0]                           [+0.6,+4.2]
   Altitude home (DEN/UTA)         +0.329   +7.9    <0.001  ***    -0.069   -1.6     0.633     
                    95% CI (pp)            [+6.1,+9.7]                           [-8.2,+5.0]
   Time zone diff (per zone)       -0.016   -0.4     0.086         +0.045   +1.0     0.330     
                    95% CI (pp)            [-0.8,+0.1]                           [-1.1,+3.1]

   ► Rest matters in both contexts — +1.6 pp/day regular
     season, +2.4 pp/day playoffs (larger in playoffs).
   ► Altitude home advantage is real in the regular season (+7.9 pp)
     but absent in playoffs — Denver/Utah team strength is a confound.
   ► Time zones show no significant effect in either context.
     Only 107 coast-to-coast playoff games exist across 43 seasons
     (5,806 regular-season) — too sparse for reliable playoff inference.

   Playoff rest controlling for team quality (N = 2,956 games):
   quality_diff = home RS win% − away RS win% (same season).
   Predictor                     log-odds     ≈pp         p     
   ────────────────────────────  ────────  ──────  ────────  ───
   rest_diff (per day)             +0.068    +1.6     0.113     
   quality_diff (RS win% gap)      +4.778  +111.7    <0.001  ***

─── LEAGUE-WIDE 3-POINT SHOOTING AND HOME COURT ADVANTAGE ──────────────
   Does more 3-point shooting reduce home court advantage?
   Two angles: season-level correlation and game-level logistic regression.

   Regular season  (n = 43 seasons)
   Season-level Pearson r  = -0.902  (p = <0.001  ***)
   Season-level Spearman ρ = -0.890  (p = <0.001  ***)

   Era           Mean 3PA%    Home win%    n seasons
   ---------- ------------ ------------ ------------
   1984–94             6.8%         65.0%           11
   1995–01            18.1%         60.1%            7
   2002–04            18.3%         61.1%            3
   2005–17            23.8%         59.5%           13
   2018–22            37.5%         56.2%            5
   2023–26            40.5%         55.6%            4

   Game-level bivariate logistic  (N = 49,106 games)
   coef = -0.0110 log-odds per pp of 3PA rate
   ≈ -2.64 pp per 10 pp rise in 3PA rate  95% CI [-3.07, -2.20]
   p = <0.001  ***

   Controlling for era (within-era game-level effect):
   coef = -0.0095  (≈ -2.27 pp per 10 pp 3PA)  95% CI [-3.08, -1.45]  p = <0.001  ***
   (If this is small and insignificant, 3PA effect is fully explained
    by the secular trend — higher 3PA and lower HCA happen at the same
    time but 3PA does not predict outcomes within any given era.)

   Playoffs  (n = 42 seasons)
   Season-level Pearson r  = -0.499  (p = <0.001  ***)
   Season-level Spearman ρ = -0.422  (p = 0.005  **)

   Era           Mean 3PA%    Home win%    n seasons
   ---------- ------------ ------------ ------------
   1984–94             8.7%         67.7%           11
   1995–01            20.9%         64.1%            7
   2002–04            20.8%         64.2%            3
   2005–17            25.8%         64.3%           13
   2018–22            38.6%         60.8%            4
   2023–26            40.1%         57.6%            4

   Game-level bivariate logistic  (N = 3,292 games)
   coef = -0.0123 log-odds per pp of 3PA rate
   ≈ -2.84 pp per 10 pp rise in 3PA rate  95% CI [-4.01, -1.66]
   p = <0.001  ***

   Controlling for era (within-era game-level effect):
   coef = -0.0136  (≈ -3.12 pp per 10 pp 3PA)  95% CI [-5.89, -0.36]  p = 0.027  *
   (If this is small and insignificant, 3PA effect is fully explained
    by the secular trend — higher 3PA and lower HCA happen at the same
    time but 3PA does not predict outcomes within any given era.)

   ─ Cointegration check: is the 3PA-HCA correlation genuine or spurious? ─
   ADF unit-root tests  (H0: unit root; p ≥ 0.05 → I(1) / nonstationary):
   3PA rate (regular season)           ADF = -0.304  p = 0.925  → I(1) nonstationary
   Home win %                          ADF = -1.184  p = 0.680  → I(1) nonstationary

   Engle-Granger cointegration  (H0: no long-run relationship):
   t = -1.486  p = 0.766  
   ► Both I(1) but NOT cointegrated — r = -0.902 is likely
     spurious; within-era game-level controls are the reliable evidence.

   ─ Partial correlation: detrend both series, then correlate residuals ─
   Remove the year trend from both 3PA rate and home win %;
   if the residual r collapses, the raw r = -0.90 is a trend artifact.

   Raw Pearson r (season level):        r = -0.902
   Partial r (year-detrended residuals): r = -0.526  p = <0.001  ***
   ► Residual r shrinks but remains significant (raw: -0.902 → partial:
     -0.526; 42% of raw r explained by shared trend).
     The 3PA-HCA relationship has a genuine component, but the shared
     40-year secular trend accounts for a large fraction of the raw r.

   ─ Rolling 10-season Pearson r: stability of the 3PA-HCA relationship ─
   Stable r → genuine relationship; large swings or sign flips → spurious.

   10-season rolling r range: [-0.874, -0.194]  sign flips: 0
   Most negative r = -0.874 centered on season ending 1997
   ► Rolling r varies widely (-0.87 to -0.19) — moderate
     instability suggests the relationship is partly trend-driven.


─── GRANGER CAUSALITY — DOES 3PA RATE LEAD HOME COURT ADVANTAGE? ───────
   Granger causality: does 3PA rate in year t-1 improve forecasts of HCA in
   year t, beyond what past HCA values predict on their own?
   H0: 3PA lags add no predictive power for HCA (F-test via VAR).
   Both series differenced when I(1) to satisfy stationarity. Max 2 lags.

   Testing in first-differenced (both I(1))  (N = 42 observations)

   3PA rate → HCA (does 3PA lead the decline?)
    Lag    F-stat     p-value                       Verdict
   ────  ────────  ──────────  ────────────────────────────
      1     1.487       0.230             no Granger effect  
      2     1.369       0.268             no Granger effect  

   HCA → 3PA rate (reverse: does HCA drive 3PA adoption?)
    Lag    F-stat     p-value                       Verdict
   ────  ────────  ──────────  ────────────────────────────
      1     0.663       0.421             no Granger effect  
      2     0.299       0.743             no Granger effect  


─── REBOUNDING DECOMPOSITION — WHY THE HOME EDGE FADED  (home minus away) 
   OREB/DREB diff = home minus away offensive/defensive rebounds per game.
   Share edge = home share of available offensive boards minus away share
   (percentage points) — a pace- and volume-free measure of the edge.
   Trend = slope of trend line (change per season year).

   reg: reb-share-edge trend/yr = -0.052  95% CI [-0.060, -0.044]  (p = <0.001)
   po: reb-share-edge trend/yr = -0.046  95% CI [-0.076, -0.015]  (p = 0.004)
   Regular season  (N = 49,107 games)

   Era                OREB diff       DREB diff        REB diff Share edge (pp)
   ────────────────────────────────────────────────────────────────────────────
   1984–94                +0.61           +1.64           +2.24           +2.14
   1995–01                +0.62           +1.18           +1.79           +1.83
   2002–04                +0.43           +1.31           +1.74           +1.59
   2005–17                +0.33           +0.97           +1.29           +1.15
   2018–22                +0.20           +0.85           +1.05           +0.79
   2023–26                -0.05           +0.59           +0.54           +0.21
   ────────────────────────────────────────────────────────────────────────────
   Trend/yr           -0.018***       -0.027***       -0.044***       -0.052***

   Playoffs  (N = 3,292 games)

   Era                OREB diff       DREB diff        REB diff Share edge (pp)
   ────────────────────────────────────────────────────────────────────────────
   1984–94                +0.89           +1.72           +2.61           +2.74
   1995–01                +0.66           +1.18           +1.84           +1.79
   2002–04                -0.15           +0.87           +0.72           +0.32
   2005–17                +0.55           +1.22           +1.77           +1.71
   2018–22                +0.50           +0.85           +1.34           +1.24
   2023–26                +0.05           +1.09           +1.14           +0.70
   ────────────────────────────────────────────────────────────────────────────
   Trend/yr           -0.015          -0.023  *       -0.037 **       -0.046 **

   Does the home edge track the league's retreat from the offensive glass?
   Season-level Pearson r (share edge vs league OREB rate) = +0.824  (p = <0.001  ***,  N = 43 seasons)
   League OREB rate: 32.9% → 25.9%   |   Home share edge: +2.74pp → -0.34pp
   ► The home rebounding edge fades in lockstep with the league-wide
     decline in offensive rebounding — the effort-driven offensive boards
     where a home edge could form have largely disappeared.

   ─ Cointegration check: is the OREB-HCA correlation genuine or spurious? ─
   ADF unit-root tests  (H0: unit root; p ≥ 0.05 → I(1) / nonstationary):
   League OREB rate                    ADF = -1.275  p = 0.641  → I(1) nonstationary
   Home rebound share edge             ADF = -0.133  p = 0.946  → I(1) nonstationary

   Engle-Granger cointegration  (H0: no long-run relationship):
   t = -2.791  p = 0.168  
   ► Both I(1) but NOT cointegrated — r = +0.824 is likely
     spurious; within-era game-level controls are the reliable evidence.


─── PLAYER-TRACKING REBOUNDING MECHANISM  (home minus road, tracking era) 
   Confirms how the home rebounding edge expresses itself in the tracking
   data: offensive-rebound conversion, box-outs, and second-chance points.
   Window is short (~2014 on; box-outs ~2016 on) — corroborates the modern
   mechanism, not the 40-year decline.

   Metric                          N seasons      Mean    Trend/yr        p
   ────────────────────────────────────────────────────────────────────────
   OREB conversion edge (pp)              13    +0.709   -0.086  *    0.024
   Box-out edge (per game)                11    -0.000   -0.005       0.775
   2nd-chance pts edge (per game)         13    +0.289   -0.016       0.304

   ► The home edge is small and flat-to-declining across the tracking era —
     consistent with the offensive-glass advantage having largely collapsed
     before high-resolution tracking even began.


─── OUT-OF-SAMPLE FORECAST — DO THE CHANNELS PREDICT THE LATER DECLINE? 
   Freeze the four-channel win model (eFG%, fouls, turnovers, rebounds)
   on the training seasons, then predict each later season's home win %
   from that season's box-score edges. A frozen early mapping that tracks
   the held-out decline means the mechanism is stable, not fitted to
   hindsight. Baselines: extrapolating the training trend line, and a flat
   training-mean forecast. Lower RMSE on the held-out seasons is better.

   Regular season  (train 1984–2013, test 2014–2026)

    Season    Actual   Channel pred   Trend pred
   ───────  ────────  ─────────────  ───────────
      2014     58.0%          58.4%        58.3%
      2015     57.5%          58.0%        58.1%
      2016     58.9%          58.7%        57.8%
      2017     58.4%          59.9%        57.6%
      2018     57.9%          57.3%        57.4%
      2019     59.3%          57.8%        57.1%
      2020     55.1%          56.7%        56.9%
      2021     54.4%          53.4%        56.6%
      2022     54.4%          55.2%        56.4%
      2023     58.0%          57.3%        56.2%
      2024     54.3%          55.6%        55.9%
      2025     54.4%          54.5%        55.7%
      2026     55.4%          54.9%        55.5%

   Held-out RMSE:  channel = 0.95 pp   trend = 1.45 pp   flat mean = 5.48 pp
   ► The frozen early channel model reconstructs the 2014–2026 decline
     it never saw and beats a naive extension of the early trend line — the box-score mechanism is stable across the
     split, not an artifact of fitting on the full history.

   Playoffs  (train 1984–2013, test 2014–2026)

    Season    Actual   Channel pred   Trend pred
   ───────  ────────  ─────────────  ───────────
      2014     56.2%          59.8%        65.5%
      2015     59.3%          59.2%        65.4%
      2016     67.4%          71.9%        65.4%
      2017     57.0%          56.1%        65.3%
      2018     70.7%          66.5%        65.3%
      2019     56.1%          60.6%        65.2%
      2021     56.5%          60.2%        65.1%
      2022     59.8%          63.2%        65.1%
      2023     59.5%          63.1%        65.0%
      2024     58.5%          63.0%        65.0%
      2025     57.1%          63.8%        64.9%
      2026     55.3%          57.5%        64.9%

   Held-out RMSE:  channel = 3.87 pp   trend = 7.30 pp   flat mean = 8.11 pp
   ► The frozen early channel model reconstructs the 2014–2026 decline
     it never saw and beats a naive extension of the early trend line — the box-score mechanism is stable across the
     split, not an artifact of fitting on the full history.


─── NON-PARAMETRIC CHANNEL DECOMPOSITION — GRADIENT BOOSTING + SHAP ────
   Robustness check on the linear mediation. A gradient-boosted win
   model learns home_win from the four box-score edges (eFG%, fouls,
   turnovers, rebounds) with no straight-line assumption and with
   interactions. SHAP splits each game's predicted win probability into
   additive channel contributions; averaged within an era they sum to
   that era's gap from the overall home win rate, so the early-minus-late
   difference per channel sums to the actual decline. Agreement with the
   linear breakdown means that breakdown does not hinge on linearity.

   Regular season  (N = 49,104 games, model accuracy 0.933,
   1984–94 → 2023–26: home win % 60.1 overall)

   Decline decomposition  (signed SHAP, 1984–94 minus 2023–26)
   Channel        Early pp   Late pp   Contribution  % of decline
   ────────────  ─────────  ────────  ─────────────  ────────────
   Shooting          +0.3     -3.0         +3.3 pp           35%
   Fouls             +1.5     +0.1         +1.4 pp           14%
   Turnovers         +4.2     +2.1         +2.2 pp           23%
   Rebounding        +2.0     -0.6         +2.6 pp           28%
   ────────────  ─────────  ────────  ─────────────  ────────────
   SHAP total                                +9.4 pp  (actual decline +9.3 pp)


   Playoffs  (N = 3,292 games, model accuracy 0.950,
   1984–94 → 2023–26: home win % 64.1 overall)

   Decline decomposition  (signed SHAP, 1984–94 minus 2023–26)
   Channel        Early pp   Late pp   Contribution  % of decline
   ────────────  ─────────  ────────  ─────────────  ────────────
   Shooting          -2.8     -6.3         +3.5 pp           38%
   Fouls             +0.5     -0.8         +1.3 pp           14%
   Turnovers         -1.8     -3.0         +1.2 pp           13%
   Rebounding        +1.6     -1.6         +3.3 pp           35%
   ────────────  ─────────  ────────  ─────────────  ────────────
   SHAP total                                +9.3 pp  (actual decline +10.3 pp)



─── RULE-CHANGE ERAS — DO THE ERA BREAKS MATTER BEYOND THE YEAR TREND? ─
   Home win % by rule-change era; pairwise tests between consecutive eras.
   Trend-controlled model: home_win ~ year + C(era).
   LR test: do era dummies jointly add explanatory power beyond the year trend?
   (If not, the decline is a smooth drift; if yes, specific rules caused jumps.)

   Regular season  (N = 49,107 games)

   Era            N games   Home win %
   ────────────  ────────  ───────────
   1984–94         11,275        64.9%
   1995–01          7,777        59.9%
   2002–04          3,567        61.1%
   2005–17         15,749        59.5%
   2018–22          5,829        56.3%
   2023–26          4,910        55.6%

   Consecutive eras — two-proportion z-tests:
    1984–94 → 1995–01    -4.9 pp   (z = +6.95, p = <0.001  ***)
    1995–01 → 2002–04    +1.2 pp   (z = -1.21, p = 0.227  )
    2002–04 → 2005–17    -1.6 pp   (z = +1.79, p = 0.074  )
    2005–17 → 2018–22    -3.2 pp   (z = +4.24, p = <0.001  ***)
    2018–22 → 2023–26    -0.7 pp   (z = +0.76, p = 0.449  )

   Trend-controlled logistic: home_win ~ year + C(era)
   (reference era = 1984–94)

   Predictor                     log-odds     ≈pp         p     
   ────────────────────────────  ────────  ──────  ────────  ───
   era: 1995–01                    -0.108    -2.6     0.010   **
   → 1994-95 (1995–01) level shift: -2.6 pp  95% CI [-4.6, -0.6] pp  (drop magnitude [0.6, 4.6])
   era: 2002–04                    +0.001    +0.0     0.988     
   era: 2005–17                    +0.027    +0.6     0.722     
   era: 2018–22                    +0.001    +0.0     0.990     
   era: 2023–26                    +0.025    +0.6     0.836     
   year trend (per yr)             -0.012    -0.3    <0.001  ***

   LR test — era dummies jointly vs. year-only model: χ²(5) = 20.68,  p = <0.001  ***

   ► Era dummies are jointly significant beyond the year trend —
     specific rule-change periods show a level shift above or below
     what the underlying trend alone would predict.

   Playoffs  (N = 3,292 games)

   Era            N games   Home win %
   ────────────  ────────  ───────────
   1984–94            794        67.9%
   1995–01            496        64.1%
   2002–04            241        64.3%
   2005–17          1,090        64.3%
   2018–22            336        60.7%
   2023–26            335        57.6%

   Consecutive eras — two-proportion z-tests:
    1984–94 → 1995–01    -3.8 pp   (z = +1.40, p = 0.163  )
    1995–01 → 2002–04    +0.2 pp   (z = -0.05, p = 0.957  )
    2002–04 → 2005–17    -0.0 pp   (z = +0.00, p = 0.999  )
    2005–17 → 2018–22    -3.6 pp   (z = +1.20, p = 0.231  )
    2018–22 → 2023–26    -3.1 pp   (z = +0.82, p = 0.414  )

   Trend-controlled logistic: home_win ~ year + C(era)
   (reference era = 1984–94)

   Predictor                     log-odds     ≈pp         p     
   ────────────────────────────  ────────  ──────  ────────  ───
   era: 1995–01                    -0.090    -2.1     0.589     
   era: 2002–04                    -0.037    -0.9     0.876     
   era: 2005–17                    +0.032    +0.7     0.914     
   era: 2018–22                    -0.042    -1.0     0.920     
   era: 2023–26                    -0.132    -3.0     0.781     
   year trend (per yr)             -0.009    -0.2     0.496     

   LR test — era dummies jointly vs. year-only model: χ²(5) = 2.24,  p = 0.815  

   ► Era dummies do not add significant explanatory power beyond
     the year trend (p = 0.815) — the decline is well-described
     as a continuous drift without discrete era-level jumps.


─── ITS (INTERRUPTED TIME SERIES) — 1994-95 BOUNDARY ───────────────────
   Model: home_pct ~ year + post95 + time_since_break  (season-level WLS)
   post95      = 1 for seasons from 1994-95 onward (immediate level shift)
   time_since  = (year − 1994) × post95           (slope change post-break)
   Weights: game counts per season.

   Regular season  (N = 43 seasons)  R² = 0.779
   Parameter                   Coef        p   Sig
   ──────────────────────  ────────  ───────  ────
   Pre-break trend/yr        -0.522    0.004    **
   Level shift (1994-95)     -0.622    0.597      
   Slope change/yr           +0.341    0.060      

   Implied slopes: pre-break = -0.522 pp/yr, post-break = -0.181 pp/yr
   ► Borderline slope change (p=0.060): rate of HCA decline appears
     to slow after 1994-95 (-0.52 → -0.18 pp/yr),
     but no discrete immediate jump (level p=0.597). Consistent with
     the QLR break at 1999 — change accumulated gradually over seasons.

   Playoffs  (N = 42 seasons)  R² = 0.225
   Parameter                   Coef        p   Sig
   ──────────────────────  ────────  ───────  ────
   Pre-break trend/yr        +0.249    0.651      
   Level shift (1994-95)     -2.308    0.551      
   Slope change/yr           -0.485    0.390      

   Implied slopes: pre-break = +0.249 pp/yr, post-break = -0.235 pp/yr
   ► Neither level nor slope significant at 1994-95.
     Overall HCA trend drove this context — 1994-95 not a sharp break.


─── PLACEBO TESTS — IS 1994-95 UNIQUELY SIGNIFICANT? ───────────────────
   For each year t in 1987–2010: OLS on season home win%,
   model pct ~ year + step_t  (step_t = 1 if season >= t).
   A significant NEGATIVE step = discrete drop at that boundary.
   If 1994-95 uniquely stands out, it strengthens the causal claim.

   Regular season  (N = 43 seasons)

     Year   Step coef (pp)     p-value   Sig
   ──────  ───────────────  ──────────  ────
     1987           -0.61       0.650     
     1988           -1.13       0.356     
     1989           -2.03       0.071     
     1990           -2.88       0.006  ** 
     1991           -2.81       0.005  ** 
     1992           -3.33      <0.001  ***
     1993           -3.15      <0.001  ***
     1994           -2.51       0.010  ** 
     1995           -2.00       0.043  *   ← 1994-95
     1996           -1.16       0.253     
     1997           -0.51       0.618     
     1998           +1.01       0.333     
     1999           +1.88       0.072     
     2000           +1.80       0.089     
     2001           +2.02       0.059     
     2002           +2.61       0.014  *  
     2003           +3.38       0.001  ** 
     2004           +2.68       0.014  *  
     2005           +2.39       0.030  *  
     2006           +2.32       0.035  *  
     2007           +2.21       0.044  *  
     2008           +2.45       0.023  *  
     2009           +2.22       0.039  *  
     2010           +1.63       0.130     

   Significant negative steps (p<0.05): years 1990–1995
   ► 1994-95 (year=1995) IS in the significant window — consistent
     with a break in the decline period. Note: years before 1995 also
     appear significant because any boundary before the 1994-95 drop
     places the decline in the 'post' window; this is expected when
     a real break exists. The RULE-CHANGE ERAS test isolates 1994-95
     SPECIFICALLY after partialling out the year trend.
   Significant positive steps (p<0.05): years 2002–2009
   ► Positive dummies after ~2002 reflect the slope moderation
     (§1b QLR): post-1999 HCA is 'too high' vs. the pre-1999 trend.

   Playoffs  (N = 42 seasons)

     Year   Step coef (pp)     p-value   Sig
   ──────  ───────────────  ──────────  ────
     1987           +2.91       0.453     
     1988           +1.11       0.755     
     1989           -0.19       0.955     
     1990           +3.18       0.318     
     1991           +0.90       0.774     
     1992           +1.95       0.526     
     1993           +0.78       0.799     
     1994           +1.10       0.719     
     1995           -0.30       0.922      ← 1994-95
     1996           +3.03       0.326     
     1997           +2.71       0.386     
     1998           +1.76       0.579     
     1999           +1.68       0.602     
     2000           +3.14       0.334     
     2001           +0.99       0.766     
     2002           +3.37       0.309     
     2003           +5.28       0.110     
     2004           +6.67       0.043  *  
     2005           +3.81       0.255     
     2006           +6.99       0.033  *  
     2007           +5.51       0.094     
     2008           +4.68       0.154     
     2009           +0.46       0.889     
     2010           -0.91       0.777     
   Significant positive steps (p<0.05): years 2004–2006
   ► Positive dummies after ~2004 reflect the slope moderation
     (§1b QLR): post-1999 HCA is 'too high' vs. the pre-1999 trend.


─── CHANNEL EVENT STUDY — WHICH CHANGED FIRST AT 1994-95? ──────────────
   ITS model per channel: diff ~ year + post95 + (year-1994)×post95
   β_level = immediate shift at 1995; β_slope = change in per-year rate.
   If hand-checking is the mechanism, FOUL diff should show the
   strongest IMMEDIATE response; others should be smaller or delayed.

   Regular season  (N = 43 seasons)

   Channel              Pre slope/yr   Level shift   Slope chg/yr     Lev p     Slp p
   ──────────────────  ─────────────  ────────────  ─────────────  ────────  ────────
   Foul diff                  +0.002        +0.436         +0.011     0.007     0.636  **/
        level-shift 95% CI [+0.13, +0.74]
   eFG% diff (pp)             +0.012        -0.200         -0.025     0.327     0.392  /
        level-shift 95% CI [-0.61, +0.21]
   TOV diff                   +0.039        +0.170         -0.028     0.181     0.130  /
        level-shift 95% CI [-0.08, +0.42]
   REB diff                   -0.051        +0.036         +0.007     0.845     0.795  /
        level-shift 95% CI [-0.34, +0.41]

   Playoffs  (N = 42 seasons)

   Channel              Pre slope/yr   Level shift   Slope chg/yr     Lev p     Slp p
   ──────────────────  ─────────────  ────────────  ─────────────  ────────  ────────
   Foul diff                  -0.073        +0.395         +0.097     0.315     0.092  /
        level-shift 95% CI [-0.39, +1.18]
   eFG% diff (pp)             -0.031        +0.435         +0.013     0.524     0.898  /
        level-shift 95% CI [-0.93, +1.80]
   TOV diff                   +0.020        +0.379         -0.026     0.376     0.674  /
        level-shift 95% CI [-0.48, +1.23]
   REB diff                   +0.051        -0.937         -0.073     0.220     0.507  /
        level-shift 95% CI [-2.46, +0.58]

   Note: foul_diff = PF_home − PF_away. Negative values mean away teams
   get MORE fouls called (home court foul advantage). A positive level shift
   means the home foul advantage SHRANK immediately (foul_diff moved toward 0).
   The expected signature of the hand-checking rule change:
   • Foul diff: significant POSITIVE level shift (home foul edge shrinks IMMEDIATELY)
   • Other channels: no significant immediate shift (teams adapt over seasons)


─── TRAVEL DISTANCE — HOME WIN % BY AWAY TEAM FLIGHT MILES ─────────────
   Distance = haversine miles from away team's home arena to game arena.
   Does longer travel reduce the visiting team's winning odds?

   Regular season  (N = 49,107, baseline home win % = 60.1%)

         Bucket         N   Home win %   vs. baseline
   ────────────  ────────  ───────────  ─────────────
          0–500    11,238        60.4%          +0.2 pp
       500–1000    15,696        60.9%          +0.8 pp
      1000–1500     9,873        59.2%          -0.9 pp
          1500+    12,300        59.6%          -0.5 pp

   Bivariate logistic: coef = -0.00003 log-odds/mi  (≈-0.07 pp per 100 mi,  95% CI [-0.13, -0.02]),  p = 0.010  *

   Playoffs  (N = 3,292, baseline home win % = 64.1%)

         Bucket         N   Home win %   vs. baseline
   ────────────  ────────  ───────────  ─────────────
          0–500       923        62.3%          -1.8 pp
       500–1000     1,250        65.8%          +1.7 pp
      1000–1500       733        63.4%          -0.7 pp
          1500+       386        64.0%          -0.1 pp

   Bivariate logistic: coef = +0.00001 log-odds/mi  (≈+0.02 pp per 100 mi,  95% CI [-0.23, +0.27]),  p = 0.888  


─── BACK-TO-BACKS — DID FEWER TIRED VISITORS DRIVE THE DECLINE? ────────
   A back-to-back (B2B) is a game on zero days' rest. The 'load
   management' story: visitor B2Bs have grown rarer, so home teams
   face fewer tired opponents. Regular season only (B2Bs are rare
   in the playoffs). Games without a known prior game are excluded.

   Visitor and home B2B frequency by era:
   Era                 N  Visitor B2B   Home B2B   Home win %
   ────────────  ───────  ───────────  ─────────  ───────────
   1984–94        11,123        35.0%      19.2%        64.9%
   1995–01         7,669        34.6%      16.6%        60.0%
   2002–04         3,516        34.0%      16.3%        61.0%
   2005–17        15,520        32.7%      15.5%        59.5%
   2018–22         5,749        21.0%      14.2%        56.2%
   2023–26         4,847        18.8%      16.5%        55.6%

   Home win % by rest situation (all seasons pooled):
   Situation          N games   Home win %
   ────────────────  ────────  ───────────
   Neither on B2B      29,553        59.1%
   Visitor B2B only    10,866        64.7%
   Home B2B only        3,936        54.6%
   Both on B2B          4,069        60.8%

   Shift-share decomposition of the home win % change, 1984–94 → 2023–26:
   Home win %: 64.9% → 55.6%   (total change -9.29 pp)
   Frequency component (schedule: fewer B2Bs)        -0.71 pp  (   8% of change)
   Win-rate component (per-situation edge fading)    -8.59 pp
   Interaction                                       +0.02 pp

   ► Visitor B2Bs have grown much rarer, which does nudge home court
     downward — but the win-rate gap between rested and tired matchups is
     small, so the schedule shift explains only ~8% of the decline.
     The other ~92% is the home edge within each rest situation
     fading — not a scheduling story.


─── PACE AND HOME COURT ADVANTAGE ──────────────────────────────────────
   Does faster-paced play (more possessions per game) reduce home court advantage?
   Season-level correlation plus game-level logistic regression.

   Regular season  (n = 43 seasons)
   Season-level Pearson r  = +0.241  (p = 0.120  )
   Season-level Spearman ρ = +0.116  (p = 0.458  )

   Era           Mean pace    Home win%    n seasons
   ---------- ------------ ------------ ------------
   1984–94           102.4          65.0%           11
   1995–01            93.9          60.1%            7
   2002–04            93.2          61.1%            3
   2005–17            95.3          59.5%           13
   2018–22           101.4          56.2%            5
   2023–26           101.4          55.6%            4

   Game-level bivariate logistic  (N = 49,104 games)
   coef = +0.0095 log-odds per possession
   ≈ +2.28 pp per 10 extra possessions  95% CI [+1.10, +3.47]
   p = <0.001  ***

   Controlling for era (within-era game-level effect):
   coef = +0.0107  (≈ +2.57 pp per 10 possessions)  95% CI [+1.67, +3.48]  p = <0.001  ***

   Expected pace (LOO)  (N = 48,866 games)
   Bivariate: coef = +0.0064  (≈ +1.54 pp per 10 poss)  p = 0.227  
   Within-era: coef = +0.0086  (≈ +2.06 pp per 10 poss)  p = 0.063  

   Playoffs  (n = 42 seasons)
   Season-level Pearson r  = -0.142  (p = 0.370  )
   Season-level Spearman ρ = -0.257  (p = 0.100  )

   Era           Mean pace    Home win%    n seasons
   ---------- ------------ ------------ ------------
   1984–94            98.5          67.7%           11
   1995–01            89.9          64.1%            7
   2002–04            92.5          64.2%            3
   2005–17            92.8          64.3%           13
   2018–22            98.4          60.8%            4
   2023–26            97.4          57.6%            4

   Game-level bivariate logistic  (N = 3,292 games)
   coef = -0.0041 log-odds per possession
   ≈ -0.94 pp per 10 extra possessions  95% CI [-2.97, +1.09]
   p = 0.363  

   Controlling for era (within-era game-level effect):
   coef = -0.0053  (≈ -1.23 pp per 10 possessions)  95% CI [-3.49, +1.03]  p = 0.285  

   Expected pace (LOO)  (N = 3,292 games)
   Bivariate: coef = -0.0056  (≈ -1.29 pp per 10 poss)  p = 0.367  
   Within-era: coef = -0.0100  (≈ -2.31 pp per 10 poss)  p = 0.154  


─── COMPETITIVE BALANCE AND HOME COURT ADVANTAGE ───────────────────────
   Hypothesis: more parity (lower team win% std dev) → lower home court advantage.
   Parity = std dev of all-team win percentages for the season.

   N = 43 seasons
   Pearson r  = -0.092  (p = 0.556  )
   Spearman ρ = -0.051  (p = 0.743  )

   Trend line: home_win_pct ~ parity_std_dev
   Slope: -21.250 pp per unit std dev  (p = 0.556  )
   R² = 0.0085

   Era-bucketed averages (disparity ↓ = more parity, home win % ↓ = less advantage):

   Era             Win% std dev    Home win %
   ────────────  ──────────────  ────────────
   1984–94               0.1551         65.0%
   1995–01               0.1700         60.1%
   2002–04               0.1393         61.1%
   2005–17               0.1559         59.5%
   2018–22               0.1461         56.2%
   2023–26               0.1544         55.6%

   ► Near-zero, non-significant correlation — parity (team win% disparity)
     does not independently predict home court advantage across seasons.
     The era-bucketed pattern is mixed: disparity peaked in 1995–01 while
     home win % was already declining, and fell in 2002–04 while home win %
     ticked back up. The two series do not move in lockstep.

   ─ Cointegration check: is the parity-HCA correlation genuine or spurious? ─
   ADF unit-root tests  (H0: unit root; p ≥ 0.05 → I(1) / nonstationary):
   League parity (win% std dev)        ADF = -3.153  p = 0.023  → I(0) stationary
   Home win %                          ADF = -1.975  p = 0.298  → I(1) nonstationary
   ► At least one series is I(0) stationary; cointegration does not apply.
     Standard correlation is interpretable without spurious-trend concern.


   Detrended checks (both series share a downward trend — remove it first):
   First-differenced (Δparity vs. Δhome-win%):
   Pearson r = -0.330  (p = 0.033  *)  N = 42 year-pairs
   Residual-on-year (detrended parity vs. detrended home-win%):
   Pearson r = -0.345  (p = 0.023  *)  N = 43 seasons

   ► At least one detrended test is significant — some association
     remains after removing the common trend. Interpret with caution
     (N is small and first-differences amplify measurement noise).

─── ARENA ATTENDANCE AND HOME COURT ADVANTAGE ──────────────────────────
   Source: Basketball-Reference per-game attendance (~2000 onward).
   Part A: does league attendance track home win % across seasons?
   Part B: 2020-21 dose-response — crowd size varied by local rule.

   N = 27 seasons (avg crowd 4,600–18,384/game)
   Pearson r  = +0.248  (p = 0.212  )
   Spearman ρ = -0.492  (p = 0.009  **)

   Detrended (remove shared drift):
   First-differenced  r = +0.073  (p = 0.724  )  N = 26 year-pairs
   Residual-on-year   r = +0.331  (p = 0.091  )  N = 27 seasons

   ─ Cointegration check: is the attendance-HCA correlation genuine? ─
   ADF unit-root tests  (H0: unit root; p ≥ 0.05 → I(1) / nonstationary):
   League avg attendance               ADF = -3.654  p = 0.005  → I(0) stationary
   Home win %                          ADF = -1.762  p = 0.400  → I(1) nonstationary
   ► At least one series is I(0) stationary; cointegration does not apply.
     Standard correlation is interpretable without spurious-trend concern.


   ► Crowd *size* does not track home court advantage. Attendance has
     held near arena capacity for 25 years while HCA fell — the level is
     flat where the advantage is not. Crowd size is not behind the decline.

   2020-21 home win %:  empty arena 51.0% (n=573)  vs.  fans present 58.5% (n=591, median attendance 3280)
   Logit home_win ~ attendance (per 1,000 fans):
   Effect: +0.51 pp per 1,000 fans  [95% CI -0.24, +1.25]  (p = 0.184  )

   ► No significant within-season attendance effect detected.

─── WHAT EXPLAINS THE REGULAR-SEASON DECLINE?  (N = 48,424 games) ──────
   Outcome: home_win. Baseline home win %: 60.1%.
   McFadden R² is analogous to a linear-regression R² but typical values are much smaller;
   the ΔR² column shows how much each block adds over the previous model.
   '≈pp' = approximate marginal effect in percentage points (at mean p).
   p-values and CIs use cluster-robust SEs (clusters = season-year).

   Model                                R²       ΔR²   % of fit
   ──────────────────────────────  ───────  ────────  ─────────
   Era only                         0.0029   +0.0029      57.9%
   + Rest differential              0.0037   +0.0008      16.3%
   + Altitude (DEN/UTA)             0.0049   +0.0011      22.9%
   + Time zone diff                 0.0050   +0.0001       2.0%
   + COVID flag                     0.0050   +0.0000       1.0%

   Full model coefficients  (reference era = 1984–94):

   Predictor                                     log-odds     ≈pp     95% CI (pp)         p     
   ────────────────────────────────────────────  ────────  ──────  ──────────────  ────────  ───
   era: 1995–01                                    -0.209    -5.0  [ -6.8, -3.3]    <0.001  ***
   era: 2002–04                                    -0.167    -4.0  [ -6.4, -1.6]    <0.001  ***
   era: 2005–17                                    -0.230    -5.5  [ -7.1, -3.9]    <0.001  ***
   era: 2018–22                                    -0.318    -7.6  [-10.4, -4.9]    <0.001  ***
   era: 2023–26                                    -0.375    -9.0  [-11.0, -7.0]    <0.001  ***
   rest diff (per day)                             +0.062    +1.5  [ +1.1, +1.9]    <0.001  ***
   altitude home (DEN/UTA)                         +0.326    +7.8  [ +4.5,+11.2]    <0.001  ***
   time zone diff (per zone)                       -0.023    -0.6  [ -0.9, -0.2]     0.005   **
   COVID seasons                                   -0.097    -2.3  [ -4.6, -0.1]     0.045    *

   ► Era dummies imply a net decline of -9.0 pp from 1984–94 → 2023–26.

   Shapley R² decomposition  (2⁵ = 32 logits, same N = 48,424 games):
   Each block's average marginal R² over all 5! orderings.
   Compare to sequential (order-dependent, era entered first).

   Block                          Shapley   Sequential
   ────────────────────────────  ────────  ───────────
   Era (structural decline)         52.6%        57.9%
   Rest differential                17.9%        16.3%
   Altitude (DEN/UTA)               23.7%        22.9%
   Time zone diff                    1.4%         2.0%
   COVID flag                        4.5%         1.0%

   ► Era Shapley share: 53%  (sequential: 58% — sequential inflated because era is entered first).
   ► Rest + altitude + tz + COVID (Shapley): 47%.

─── PRE/POST-2014 COEFFICIENT STABILITY  (regular season only) ─────────
   Do rest, altitude, and time zone effects change after the 2014 Finals format shift?
   Stable coefficients → those factors didn't drive the post-2014 change.

   Predictor                              Pre-2014   Post-2014     Shift
                                          log-odds    log-odds          
   ───────────────────────────────────  ──────────  ──────────  ────────
   rest diff (per day)                      +0.053      +0.081    +0.028
   altitude home (DEN/UTA)                  +0.389      +0.209    -0.180
   time zone diff (per zone)                -0.022      -0.024    -0.002
   ───────────────────────────────────  ──────────  ──────────  ────────
   Intercept (overall home adv. level)      +0.463      +0.267    -0.196

   N pre-2014:  32,975 games  (home win %: 61.8%)
   N post-2014: 15,449 games  (home win %: 56.6%)

   ► The intercept dropped by 4.7 pp after 2014, confirming the overall decline.
   ► Rest, altitude, and tz coefficients show some change — those factors' effects on winning are largely stable.

   Formal interaction test — pooled logit with post2014 × factor interactions:
   H0: coefficients unchanged before and after 2014.

   Interaction term                log-odds     ≈pp         p     
   ──────────────────────────────  ────────  ──────  ────────  ───
   rest_diff × post2014              +0.028    +0.7     0.142     
   altitude_home × post2014          -0.180    -4.3     0.026    *
   tz_diff × post2014                -0.002    -0.0     0.917     
   ──────────────────────────────  ────────  ──────  ────────  ───
   post2014 (level shift)            -0.196    -4.7    <0.001  ***

─── PLAYOFF SERIES STRUCTURE — HOME WIN % BY GAME NUMBER ───────────────
   Does home court advantage vary by game number within a series (G1–G7)?
   G1/G2 at higher seed, G3/G4 at lower seed, then alternates (2-2-1-1-1 format).

     Game   N games   Home win %    vs. G1
   ──────  ────────  ───────────  ────────
       G1       509        69.4%         —
       G2       512        71.9%   +2.5 pp
       G3       509        55.0%  -14.3 pp
       G4       501        55.3%  -14.1 pp
       G5       423        74.5%   +5.1 pp
       G6       321        55.5%  -13.9 pp
       G7       188        63.8%   -5.5 pp

   Chi-square test (H0: home win % uniform across all game numbers):
   χ²(6) = 84.54,  p = <0.001  ***

   Weighted trend line across game numbers: -1.07 pp/game  (p = 0.553  )
   (Positive = home win % rises as the series goes deeper)

   ► G7 home win % = 63.8%  (vs. G1 = 69.4%, diff = -5.5 pp)
     G7 n = 188 games (series that went to 7)

─── PLAYOFF HOME WIN % BY ERA — HIGHER SEED vs LOWER SEED AT HOME ──────
   In 2-2-1-1-1 format: G1,G2,G5,G7 = higher seed at home; G3,G4,G6 = lower seed at home.
   (Pre-2014 Finals used 2-3-2; Finals ≈ 1/15 of games — minor effect on pooled figures.)

   Era             Higher seed at home (G1,2,5,7)   Lower seed at home (G3,4,6)     Gap
   ────────────  ────────────────────────────────  ────────────────────────────  ──────
   1984–94         71.0%  ( 345 games)                  65.4%  ( 260 games)        +5.6 pp
   1995–01         60.1%  ( 198 games)                  65.8%  ( 158 games)        -5.7 pp
   2002–04         74.2%  ( 132 games)                  52.3%  ( 109 games)       +21.9 pp
   2005–17         75.2%  ( 589 games)                  51.5%  ( 501 games)       +23.7 pp
   2018–22         71.7%  ( 184 games)                  47.4%  ( 152 games)       +24.4 pp
   2023–26         64.7%  ( 184 games)                  49.0%  ( 151 games)       +15.7 pp
   ────────────  ────────────────────────────────  ────────────────────────────  ──────
   All eras        70.8%  (1632 games)                  55.2%  (1331 games)       +15.6 pp

   ► In the early eras (1984–94, 1995–01) the lower-seeded team won ~65–66% at home,
     nearly matching the higher seed's own home win rate. Home court was a genuine
     equalizer. From 2002 onward the lower-seed home win rate collapsed to ~47–52%,
     while the higher seed's remained at 65–75%. What faded is the boost home court
     gave to the team that needed it most.

─── PLAYOFF SERIES SIMULATION — DOES THE PER-GAME EDGE SURVIVE A BEST-OF-7? 
   Monte Carlo: 200,000 simulated 2-2-1-1-1 series between two
   otherwise-equal teams, home-court team hosting games 1,2,5,6,7. Input is
   the observed single-game home win % per era.

   Era         RS /game  RS series   PO /game  PO series
   ─────────────────────────────────────────────────────
   1984–94        64.9%      54.9%      67.9%      56.0%
   1995–01        59.9%      53.3%      64.1%      54.6%
   2002–04        61.1%      53.6%      64.3%      54.7%
   2005–17        59.5%      53.2%      64.3%      54.7%
   2018–22        56.3%      52.1%      60.7%      53.5%
   2023–26        55.6%      51.9%      57.6%      52.5%

   ► Regular season: per-game home edge fell 9.3 pp across eras,
     but the series edge fell only 3.0 pp (now 51.9%).
   ► Playoffs: per-game edge fell 10.3 pp, series edge fell 3.4 pp (now 52.5%).

   Caveats: the playoff per-game % conflates home court with seeding (better
   teams host more), so the regular-season row is the cleaner pure-venue
   input. The sim assumes games are independent given the per-game edge, so
   it illustrates the format's leverage rather than forecasting a series.


─── PLAYOFF HCA — SEEDING QUALITY DECOMPOSITION ────────────────────────
   Does the playoff HCA decline reflect true home-court weakening, or do
   better seeds simply fail to dominate lower seeds as they once did?
   quality_diff = home RS win% − away RS win% (same season).
   N = 3,292 playoff games with complete quality data.

   Model comparison — year trend before and after quality control:

   Model                            year (pp/yr)         p   McF. R²
   ──────────────────────────────  ─────────────  ────────  ────────
   Year only                              -0.225    <0.001    0.0025
   Quality only                                —         —    0.0649
   Year + quality_diff                    -0.229     0.001    0.0673

   quality_diff (bivariate):  +111.92 pp per unit  (p = <0.001  ***)
   quality_diff (full model): +112.16 pp per unit  (p = <0.001  ***)
   Year trend retained after quality control: 102%
   Absorbed by quality_diff: -2%

   Has the seed-quality gap itself trended over time?
   Trend in mean quality_diff per season: -0.00026 per yr  (p = <0.001  ***,  R² = 0.3569)

   Era breakdown — mean quality_diff and playoff home win %:
   Era                N   Mean quality_diff   Home win %
   ────────────  ──────  ──────────────────  ───────────
   1984–94          794             +0.0172        67.9%
   1995–01          496             +0.0146        64.1%
   2002–04          241             +0.0076        64.3%
   2005–17        1,090             +0.0084        64.3%
   2018–22          336             +0.0090        60.7%
   2023–26          335             +0.0108        57.6%

   Lower-seed-at-home check (G3+G4 where quality_diff < 0):
   N = 827 games  Home win % = 51.5%
   ► Even when the objectively weaker team is at home, they win 52% — pure venue effect.

   ► Quality control barely moves the year coefficient (102% retained) —
     the playoff decline is primarily genuine home-court weakening, not seed compression.

─── REGULAR SEASON — QUALITY-TIER HOME WIN % BY ERA ────────────────────
   Does the playoff pattern above (a weaker home team collapsing against a
   stronger visitor) also show up in the regular season?
   quality_diff_prior = home minus away *prior*-season win% (same-season
   win% would be circular here, unlike in the playoff test above).
   N = 46,612 regular-season games with a same-name prior season for both teams.

   Home team at least 10 points better/worse than the visitor last season:
   Era            Stronger team at home   Weaker team at home     Gap
   ────────────  ──────────────────────  ────────────────────  ──────
   1984–94         81.6%  (3,202 games)           46.7%  (3,198 games)       +34.9 pp
   1995–01         78.0%  (2,593 games)           40.8%  (2,587 games)       +37.2 pp
   2002–04         76.0%  (1,053 games)           48.6%  (1,049 games)       +27.4 pp
   2005–17         74.7%  (4,973 games)           44.9%  (4,969 games)       +29.8 pp
   2018–22         68.4%  (1,898 games)           43.8%  (1,904 games)       +24.6 pp
   2023–26         69.5%  (1,522 games)           41.3%  (1,520 games)       +28.2 pp

   quality_diff_prior × era interaction (LR test, all 46,612 games):
   χ²(5) = 64.68,  p = <0.001  ***

   Direction: does quality's effect on who wins at home grow or shrink with each year?
   quality_diff_prior × year (continuous): -0.02810 per yr  (p = <0.001  ***)

   ► The regular season moves the OPPOSITE way from the playoffs. Quality's effect on
     who wins at home is real (p < 0.001 both ways) but has been shrinking, not growing,
     across 40 years: the stronger-vs-weaker-home win % gap in the table above is a few
     points narrower now than in the 1980s, while the playoff seeding gap widened sharply.
     A single playoff game can amplify a quality gap in a way 82 games of regular-season
     noise apparently damps down instead.

─── TEAM QUALITY ROBUSTNESS — ERA EFFECT WITH HOME/AWAY TEAM FIXED EFFECTS 
   Does the era decline survive adding home- and away-team fixed effects?
   Franchise indicators remove systematic differences in home win rates
   across teams, so the era slope is not confounded by which franchises
   happen to host more games in different periods.

   Era coefficients (pp relative to 1984-94 baseline):

   Era               Baseline    With team FE     Shift
   ────────────  ────────────  ──────────────  ────────
   1995–01            -5.0 pp         -4.6 pp   +0.4 pp
   2002–04            -4.0 pp         -3.8 pp   +0.2 pp
   2005–17            -5.5 pp         -5.4 pp   +0.2 pp
   2018–22            -7.6 pp         -7.2 pp   +0.5 pp
   2023–26            -9.0 pp         -8.6 pp   +0.4 pp

   McFadden R²: baseline = 0.0050  →  with team FE = 0.0271  (Δ = +0.0220)
   Max era coefficient shift across eras: 0.5 pp
   ► Era coefficients are stable under team FE — the decline is
     not explained by which franchises host games.


─── PLAYOFF FORMAT PERIODS — DID THE SCHEDULING CHANGES MATTER? ────────
   Playoff home win % by format period (1985, 2003, 2014 changes).
   Pairwise tests compare consecutive periods; the trend-controlled model
   asks whether format adds a level shift beyond the secular year trend.

   Period       N games   Home win %
   ──────────  ────────  ───────────
   1984              79        64.6%
   1985–02        1,282        66.1%
   2003–13          925        66.3%
   2014–26        1,006        59.4%

   Consecutive periods — two-proportion z-tests:
       1984 → 1985–02    +1.6 pp   (z = -0.29, p = 0.772  )
    1985–02 → 2003–13    +0.1 pp   (z = -0.06, p = 0.952  )
    2003–13 → 2014–26    -6.8 pp   (z = +3.10, p = 0.002  **)

   Trend-controlled logistic: home_win ~ year + format_period
   (reference period = 2003–13)

   Predictor                     log-odds     ≈pp         p     
   ────────────────────────────  ────────  ──────  ────────  ───
   format: 1984                    -0.369    -8.5     0.251     
   format: 1985–02                 -0.182    -4.2     0.239     
   format: 2014–26                 -0.146    -3.4     0.298     
   year trend (per yr)             -0.012    -0.3     0.157     

   LR test — format dummies jointly vs. year-only model: χ²(3) = 4.68,  p = 0.197  

   ► After controlling for the year trend, the 2014–26 dummy is not significant
     (p = 0.298) — the post-2014 drop is consistent with the secular
     decline passing through, not a distinct format-change effect.

─── FRANCHISE HOME COURT ADVANTAGE — HOME VS. ROAD WIN % ───────────────
   Which franchises benefit most from playing at home?
   HCA = home win% − road win% (controls for overall team quality).

   Regular season  (39 franchises with ≥50 home games)
   Sorted by EB-shrunken HCA.
   CI ± = 95% half-width (binomial SE).

   Franchise                      n_h   home%     n_r   road%     HCA    CI ±  Shrunken
   ────────────────────────── ─────── ─────── ─────── ─────── ─────── ─────── ─────────
   Denver Nuggets               1,730    64.7%   1,729    36.8%   +27.9 ±    3.2     +26.8 pp
   Utah Jazz                    1,728    69.6%   1,730    43.1%   +26.6 ±    3.2     +25.7 pp
   Washington Bullets             574    54.2%     574    27.7%   +26.5 ±    5.5     +24.5 pp
   Seattle SuperSonics          1,009    67.0%   1,009    41.4%   +25.6 ±    4.2     +24.4 pp
   Kansas City Kings               82    59.8%      82    24.4%   +35.4 ±   14.1     +23.8 pp
   New Jersey Nets              1,165    53.9%   1,165    29.7%   +24.2 ±    3.9     +23.4 pp
   Indiana Pacers               1,728    62.8%   1,730    38.9%   +23.9 ±    3.2     +23.4 pp
   Atlanta Hawks                1,726    61.5%   1,727    38.2%   +23.3 ±    3.2     +22.8 pp
   Cleveland Cavaliers          1,729    62.0%   1,722    38.9%   +23.2 ±    3.2     +22.8 pp
   Portland Trail Blazers       1,729    65.8%   1,731    42.7%   +23.0 ±    3.2     +22.6 pp
   Los Angeles Clippers         1,247    50.2%   1,247    27.7%   +22.5 ±    3.7     +22.1 pp
   Milwaukee Bucks              1,729    61.0%   1,730    39.3%   +21.7 ±    3.3     +21.5 pp
   San Antonio Spurs            1,725    70.4%   1,732    49.0%   +21.5 ±    3.2     +21.3 pp
   Sacramento Kings             1,646    53.4%   1,648    31.9%   +21.5 ±    3.3     +21.3 pp
   Charlotte Bobcats              402    47.5%     402    25.4%   +22.1 ±    6.5     +21.3 pp
   Golden State Warriors        1,727    58.5%   1,724    37.2%   +21.2 ±    3.3     +21.0 pp
   New Orleans/Oklahoma City       82    58.5%      82    35.4%   +23.2 ±   14.9     +20.7 pp
   Phoenix Suns                 1,732    64.4%   1,727    43.8%   +20.7 ±    3.2     +20.6 pp
   Houston Rockets              1,729    65.4%   1,729    45.1%   +20.3 ±    3.2     +20.3 pp
   Orlando Magic                1,481    57.3%   1,486    37.2%   +20.0 ±    3.5     +20.0 pp
   Detroit Pistons              1,724    60.4%   1,728    40.9%   +19.5 ±    3.3     +19.6 pp
   New York Knicks              1,725    57.7%   1,727    38.6%   +19.1 ±    3.3     +19.2 pp
   Chicago Bulls                1,727    61.0%   1,724    42.3%   +18.7 ±    3.3     +18.9 pp
   Boston Celtics               1,728    66.6%   1,729    48.4%   +18.2 ±    3.2     +18.5 pp
   New Orleans Hornets            361    56.0%     361    38.8%   +17.2 ±    7.2     +18.4 pp
   Miami Heat                   1,524    61.5%   1,525    43.5%   +17.9 ±    3.5     +18.2 pp
   Memphis Grizzlies            1,007    56.9%   1,008    39.4%   +17.5 ±    4.3     +18.1 pp
   Washington Wizards           1,154    49.0%   1,156    31.5%   +17.5 ±    3.9     +18.0 pp
   Los Angeles Lakers           1,729    68.4%   1,728    50.8%   +17.6 ±    3.2     +17.9 pp
   Dallas Mavericks             1,730    60.0%   1,731    42.9%   +17.1 ±    3.3     +17.5 pp
   Philadelphia 76ers           1,728    56.2%   1,731    39.3%   +16.9 ±    3.3     +17.3 pp
   Minnesota Timberwolves       1,479    50.0%   1,479    34.1%   +15.9 ±    3.5     +16.6 pp
   Vancouver Grizzlies            230    28.7%     230    15.2%   +13.5 ±    7.5     +16.5 pp
   New Orleans Pelicans           522    51.0%     524    36.8%   +14.1 ±    6.0     +16.2 pp
   Charlotte Hornets            1,035    53.0%   1,038    38.1%   +15.0 ±    4.2     +16.1 pp
   Toronto Raptors              1,237    54.9%   1,237    39.9%   +15.0 ±    3.9     +15.9 pp
   Oklahoma City Thunder          721    66.6%     719    52.4%   +14.1 ±    5.0     +15.7 pp
   LA Clippers                    441    64.6%     441    53.1%   +11.6 ±    6.5     +14.9 pp
   Brooklyn Nets                  564    48.4%     564    38.8%    +9.6 ±    5.8     +13.1 pp

   League mean HCA = +20.0 pp  (raw range: +9.6 to +35.4 pp)
   Variance decomposition: observed SD = 4.9 pp, sampling noise = 30%, true between-franchise SD ≈ 4.1 pp
   ► Denver Nuggets: raw +27.9 pp, shrunken +26.8 pp  (rank #1/39 by shrunken)
   ► Utah Jazz: raw +26.6 pp, shrunken +25.7 pp  (rank #2/39 by shrunken)

   Playoffs  (32 franchises with ≥20 home games)
   Sorted by raw HCA (EB shrinkage collapses all to league mean — see variance decomp below).
   CI ± = 95% half-width (binomial SE).

   Franchise                      n_h   home%     n_r   road%     HCA    CI ±  Shrunken
   ────────────────────────── ─────── ─────── ─────── ─────── ─────── ─────── ─────────
   Utah Jazz                      144    66.0%     141    26.2%   +39.7 ±   10.6     +26.9 pp
   Portland Trail Blazers         115    60.9%     118    22.9%   +38.0 ±   11.7     +26.9 pp
   Seattle SuperSonics             69    66.7%      69    29.0%   +37.7 ±   15.4     +26.9 pp
   Atlanta Hawks                  108    57.4%     114    24.6%   +32.8 ±   12.2     +26.9 pp
   Los Angeles Clippers            33    60.6%      36    27.8%   +32.8 ±   22.2     +26.9 pp
   Toronto Raptors                 59    61.0%      60    28.3%   +32.7 ±   16.9     +26.9 pp
   Brooklyn Nets                   25    52.0%      25    20.0%   +32.0 ±   25.1     +26.9 pp
   Los Angeles Lakers             225    74.2%     206    43.2%   +31.0 ±    8.9     +26.9 pp
   Orlando Magic                   72    59.7%      75    29.3%   +30.4 ±   15.3     +26.9 pp
   Denver Nuggets                 103    59.2%     107    29.0%   +30.3 ±   12.8     +26.9 pp
   Milwaukee Bucks                102    59.8%     107    29.9%   +29.9 ±   12.9     +26.9 pp
   Charlotte Hornets               24    58.3%      31    29.0%   +29.3 ±   25.4     +26.9 pp
   Boston Celtics                 221    68.8%     196    39.8%   +29.0 ±    9.2     +26.9 pp
   Oklahoma City Thunder           80    70.0%      75    41.3%   +28.7 ±   15.0     +26.9 pp
   Detroit Pistons                149    68.5%     138    39.9%   +28.6 ±   11.1     +26.9 pp
   Houston Rockets                135    63.7%     129    35.7%   +28.0 ±   11.6     +26.9 pp
   Indiana Pacers                 133    64.7%     142    36.6%   +28.0 ±   11.3     +26.9 pp
   Miami Heat                     143    67.1%     135    39.3%   +27.9 ±   11.3     +26.9 pp
   New York Knicks                128    65.6%     133    38.3%   +27.3 ±   11.7     +26.9 pp
   Golden State Warriors          107    73.8%     109    47.7%   +26.1 ±   12.5     +26.9 pp
   Chicago Bulls                  146    70.5%     139    44.6%   +25.9 ±   11.1     +26.9 pp
   Sacramento Kings                41    58.5%      42    33.3%   +25.2 ±   20.8     +26.9 pp
   Memphis Grizzlies               50    50.0%      52    25.0%   +25.0 ±   18.2     +26.9 pp
   Dallas Mavericks               115    60.9%     128    35.9%   +24.9 ±   12.2     +26.9 pp
   Cleveland Cavaliers            127    66.1%     128    41.4%   +24.7 ±   11.9     +26.9 pp
   San Antonio Spurs              187    69.0%     187    44.4%   +24.6 ±    9.7     +26.9 pp
   Philadelphia 76ers             109    57.8%     114    36.8%   +21.0 ±   12.8     +26.9 pp
   Washington Wizards              34    52.9%      37    32.4%   +20.5 ±   22.6     +26.9 pp
   Minnesota Timberwolves          51    52.9%      55    32.7%   +20.2 ±   18.5     +26.9 pp
   Phoenix Suns                   132    59.1%     128    39.8%   +19.2 ±   11.9     +26.9 pp
   New Jersey Nets                 53    52.8%      58    41.4%   +11.5 ±   18.5     +26.9 pp
   LA Clippers                     28    39.3%      28    42.9%    -3.6 ±   25.8     +26.9 pp

   League mean HCA = +26.9 pp  (raw range: -3.6 to +39.7 pp)
   Variance decomposition: observed SD = 8.0 pp, sampling noise = 101%, true between-franchise SD ≈ 0.0 pp
   ► Utah Jazz: raw +39.7 pp, shrunken +26.9 pp  (rank #1/32 by shrunken)
   ► Denver Nuggets: raw +30.3 pp, shrunken +26.9 pp  (rank #10/32 by shrunken)


─── FRANCHISE HCA — ERA COMPARISON (split at 2001–02) ──────────────────
   Regular season only. Franchise name changes merged: Bullets→Wizards, LA Clippers→Los Angeles Clippers.
   Min 400 home games in each era required.

   N = 26 franchises with ≥400 home games in both eras
   League avg HCA — 1984–2001: 25.6 pp  |  2002–26: 17.0 pp  |  change: -8.6 pp

   Franchise                       1984–2001   2002–26   Change  N early
   ──────────────────────────────  ─────────  ────────  ───────  ───────
   Sacramento Kings                    +31.6     +15.2    -16.4      640
   Phoenix Suns                        +29.5     +14.3    -15.2      722
   New York Knicks                     +26.7     +13.6    -13.1      722
   Denver Nuggets                      +35.5     +22.5    -13.0      722
   Charlotte Hornets                   +21.3      +8.7    -12.6      517
   Boston Celtics                      +24.9     +13.4    -11.5      722
   Orlando Magic                       +27.5     +16.5    -11.0      476
   Detroit Pistons                     +25.3     +15.3    -10.0      722
   Cleveland Cavaliers                 +28.9     +19.0     -9.9      722
   Houston Rockets                     +26.0     +16.2     -9.8      722
   San Antonio Spurs                   +26.6     +17.8     -8.8      722
   Utah Jazz                           +31.6     +22.9     -8.7      722
   Chicago Bulls                       +23.8     +15.1     -8.7      722
   Indiana Pacers                      +28.7     +20.5     -8.2      722
   Philadelphia 76ers                  +21.3     +13.7     -7.6      722
   Portland Trail Blazers              +27.3     +19.9     -7.4      722
   New Jersey Nets                     +26.9     +19.9     -7.0      722
   Atlanta Hawks                       +27.3     +20.5     -6.8      722
   Washington Wizards                  +24.4     +17.7     -6.7      722
   Los Angeles Clippers                +23.3     +17.2     -6.1      681
   Milwaukee Bucks                     +24.9     +19.4     -5.5      722
   Minnesota Timberwolves              +19.5     +14.2     -5.3      476
   Miami Heat                          +21.3     +16.2     -5.1      517
   Golden State Warriors               +24.1     +19.2     -4.9      722
   Dallas Mavericks                    +19.4     +15.5     -3.9      722
   Los Angeles Lakers                  +18.0     +17.2     -0.8      722

   ► Every franchise declined: 26/26 with a negative change.
   ► Biggest declines: Sacramento Kings (-16.4 pp), Phoenix Suns (-15.2 pp), New York Knicks (-13.1 pp)
   ► Smallest declines (least negative): Los Angeles Lakers (-0.8 pp), Dallas Mavericks (-3.9 pp), Golden State Warriors (-4.9 pp)


─── FRANCHISE HCA — REGULAR SEASON VS. PLAYOFFS CONSISTENCY ────────────
   Do franchises that protect home court in the regular season also do
   so in the playoffs? Correlation across franchises with both figures.

   N = 32 franchises with both regular-season and playoff HCA
   Raw HCA:
   Pearson r  = +0.362  (p = 0.042  *)
   Spearman ρ = +0.275  (p = 0.128  )

   Shrunken HCA: true between-franchise variance ≈ 0 in at least one context
   (observed spread across franchises is entirely sampling noise).
   Shrinkage collapses all values to the league mean — shrunken correlation undefined.
   This confirms that franchise-level playoff HCA differences are not reliably
   distinguishable from random variation given typical playoff sample sizes.

   Mean regular-season HCA (shared franchises): +19.6 pp
   Mean playoff HCA (shared franchises):        +26.9 pp
   Mean playoff − regular-season gap:           +7.2 pp (SD 7.4)

   ► Raw correlation positive and significant (r = +0.362) —
     franchises that protect home court in the regular season tend to do so
     in the playoffs too, though playoff sample sizes are too small for
     franchise-level shrinkage to improve on raw estimates.

─── WIN MARGIN TRENDS  (home team point differential per game) ─────────
   Positive = home team winning by more.
   Trend = slope of trend line (change per season year).

   Regular season  (N = 35,536 games)

   Era             All games    Home wins  Home losses
   ───────────────────────────────────────────────────
   1984–94                 —            —            —
   1995–01             +3.05       +11.60        -9.71
   2002–04             +3.62       +11.66        -9.00
   2005–17             +3.00       +11.70        -9.78
   2018–22             +1.95       +12.16       -11.20
   2023–26             +2.02       +13.01       -11.73
   ───────────────────────────────────────────────────
   Trend/yr        -0.057***    +0.048***    -0.095***

   Playoffs  (N = 2,357 games)

   Era             All games    Home wins  Home losses
   ───────────────────────────────────────────────────
   1984–94                 —            —            —
   1995–01             +3.87       +10.92        -9.42
   2002–04             +4.43       +11.38        -8.10
   2005–17             +4.48       +12.43        -9.85
   2018–22             +4.30       +13.90       -10.55
   2023–26             +3.87       +14.86       -11.06
   ───────────────────────────────────────────────────
   Trend/yr        -0.017       +0.149***    -0.101 **

   ► Overall reg-season mean margin: +2.76 pts.
   ► Overall playoff mean margin:    +4.27 pts.

─── WIN MARGIN POLARIZATION — UNCONDITIONAL QUANTILE REGRESSION  (checks blowout claim in other findings) 
   home margin ~ year at q = 0.10, 0.25, 0.50, 0.75, 0.90.
   Margin > 0 = home winning. Q10 = big home losses; Q90 = big home wins.
   All quantiles parallel → pure level effect (conditional divergence is artifact).
   Q10↓ with Q90↑ → genuine polarization.

   Regular season  (N = 35,536 games, 1997–2026)

   Quantile   Slope pts/yr                95% CI         p     
   ────────  ─────────────  ────────────────────  ────────  ───
        Q10         -0.167  [-0.197, -0.137]    <0.001  ***
        Q25         -0.099  [-0.118, -0.080]    <0.001  ***
        Q50         -0.053  [-0.072, -0.033]    <0.001  ***
        Q75         +0.000  [-0.019, +0.019]     1.000     
        Q90         +0.050  [+0.020, +0.080]     0.001   **

   IQR change rate (Q90 − Q10 slope diff): +0.217 pts/yr
   ► Q90 rises / Q10 falls — genuine variance widening (polarization confirmed).
     The conditional-on-outcome divergence in §6 reflects a real change in
     distribution shape, not just a composition effect.

   Playoffs  (N = 2,357 games, 1997–2026)

   Quantile   Slope pts/yr                95% CI         p     
   ────────  ─────────────  ────────────────────  ────────  ───
        Q10         -0.104  [-0.213, +0.005]     0.062     
        Q25         -0.110  [-0.193, -0.028]     0.009   **
        Q50         -0.000  [-0.080, +0.080]     1.000     
        Q75         +0.091  [+0.014, +0.168]     0.020    *
        Q90         +0.222  [+0.113, +0.331]    <0.001  ***

   IQR change rate (Q90 − Q10 slope diff): +0.326 pts/yr
   ► Q90 rises / Q10 falls — genuine variance widening (polarization confirmed).
     The conditional-on-outcome divergence in §6 reflects a real change in
     distribution shape, not just a composition effect.


─── NET RATING SPLIT BY VENUE  (home team pts per 100 possessions) ─────
   Net rating = (home pts − away pts) / avg possessions × 100.
   Positive = home team outscored visitors per 100 possessions.
   Requires pace data; seasons without TOV/OREB data are excluded.

   Regular season  (N = 35,536 games with pace data)

   Era           Net rating (pts/100)
   ──────────────────────────────────
   1984–94                          —
   1995–01                      +3.22
   2002–04                      +3.87
   2005–17                      +3.13
   2018–22                      +1.93
   2023–26                      +1.97
   ──────────────────────────────────
   Trend/yr                 -0.067***

   Playoffs  (N = 2,357 games with pace data)

   Era           Net rating (pts/100)
   ──────────────────────────────────
   1984–94                          —
   1995–01                      +4.31
   2002–04                      +4.89
   2005–17                      +4.86
   2018–22                      +4.36
   2023–26                      +3.93
   ──────────────────────────────────
   Trend/yr                 -0.036   

   ► Overall reg-season mean net rating: +2.86 pts/100 poss.
   ► Overall playoff mean net rating:    +4.58 pts/100 poss.

─── MULTIPLE COMPARISONS — BH FDR CORRECTION ACROSS PRIMARY TESTS ──────
   BH correction at q = 0.05; threshold for rank i (ascending p): (i/m) × 0.05.
   Tests re-run here on the same data to form a self-contained table.

   m = 14 primary tests.  BH threshold for rank i: (i/14) × 0.05.

   Rank  Test                                         p-value   BH thresh  Survives
   ────  ────────────────────────────────────────  ──────────  ──────────  ────────
      1  RS HCA year trend                             <0.001      0.0036       YES
      2  RS rest differential                          <0.001      0.0071       YES
      3  RS OREB rate vs rebound share edge            <0.001      0.0107       YES
      4  RS 3PA within-era effect                      <0.001      0.0143       YES
      5  RS altitude (DEN/UTA)                         <0.001      0.0179       YES
      6  PO HCA year trend                             <0.001      0.0214       YES
      7  RS era dummies beyond year trend               0.002      0.0250       YES
      8  RS travel distance                             0.010      0.0286       YES
      9  PO rest differential                           0.020      0.0321       YES
     10  PO 3PA within-era effect                       0.027      0.0357       YES
     11  RS parity vs HCA (first-diff)                  0.033      0.0393       YES
     12  RS time zone effect                            0.051      0.0429        no
     13  RS pace LOO within-era                         0.063      0.0464        no
     14  PO era dummies beyond year trend               0.640      0.0500        no

   BH result: 11 / 14 tests survive (q = 0.05).
   Does NOT survive BH: RS time zone effect, RS pace LOO within-era, PO era dummies beyond year trend
   ► Core findings (HCA trends, rest, altitude, era shift, 3PA) survive.
     Marginal factors (travel, parity, time zone) may not — treat as exploratory.


════════════════════════════════════════════════════════════════════════