NBA Home Court Advantage — Regression Results
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NBA HOME COURT ADVANTAGE — REGRESSION ANALYSIS
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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.
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