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How the Luck Adjustment Works

A detailed breakdown using the PHI @ MIN game from 2026-02-22

Actual Score: PHI 135 - MIN 108
Adjusted Score: PHI 113.6 - MIN 114.2
Luck Swing: +27.6 points (Home team benefited)

The Process

1 Get Every 3-Point Attempt

We fetch play-by-play data and extract each 3-point shot with its context:

This game had 70 total 3-point attempts.

2 Calculate Each Player's Expected 3P%

Using Bayesian estimation with a sliding prior, adjusted for shot difficulty. Player stats are weighted with exponential decay (recent shots matter more):

Player Expected 3P% = (Weighted Makes + κ × Adjusted Prior) / (Weighted Attempts + κ) Where: - Base prior (μ) scales from 32% (low volume) to 36% (1000+ weighted 3PA) - Shot mix adjustment: Prior adjusted based on career assisted vs unassisted 3PA: • Pull-up (unassisted) shooters: prior ×1.12 — harder shots depress career % • Catch-and-shoot (assisted) shooters: prior ×0.95 — easier shots inflate career % - Prior strength (κ) scales from 200 (low volume) to 300 (high volume) - Weighted stats use exponential decay so recent performance matters more

Worked Examples: Veteran vs Rookie

Player Weighted 3PA Weighted 3PM Career % Shot Mix Adjusted Prior (μ) Prior Strength (κ) Expected 3P%
T. Maxey (veteran) 2405.3 911.9 37.9% 45% ast / 55% unast 37.6% 300 37.8%
V. Edgecombe (rookie) 562.5 203.4 36.2% no data (×1.0) 34.2% 256 35.6%
T. Maxey: (55% unassisted — creates his own shots) Scale = min(2405.3 / 1000, 1.0) = 1.000 Base μ = 32% + (36% - 32%) × 1.000 = 36.0% Shot mix multiplier = 0.45 × 0.95 + 0.55 × 1.12 = 1.043 Adjusted μ = 36.0% × 1.043 = 37.6% κ = 200 + (300 - 200) × 1.000 = 300 Expected = (911.9 + 300 × 0.376) / (2405.3 + 300) = 1024.7 / 2705.3 = 37.8% V. Edgecombe: (rookie — no shot mix data, uses ×1.0) Scale = min(562.5 / 1000, 1.0) = 0.562 μ = 32% + (36% - 32%) × 0.562 = 34.2% (no adjustment) κ = 200 + (300 - 200) × 0.562 = 256 Expected = (203.4 + 256 × 0.342) / (562.5 + 256) = 291.2 / 818.7 = 35.6%
3 Apply Shot Difficulty Multiplier

Each shot type has a difficulty multiplier based on league-average make rates:

Final Expected % = Player Expected % × Shot Difficulty Multiplier Multipliers (relative to league avg {LEAGUE_AVG_3P*100:.1f}%): Corner + Catch-and-shoot: 1.12× (easiest) Above-break + Catch-and-shoot: 1.04× Corner + Pullup: 1.01× Above-break + Pullup: 0.93× Above-break + Stepback: 0.90× Running shots: ~0.88× (hardest)
4 Sum Expected Makes & Calculate Adjustment

Sum up expected make probabilities for each team, compare to actual makes:

Luck = Actual Makes - Expected Makes Point Adjustment = 3 × Luck - (ORB Rate × PPP × Luck) ≈ 2.7 points per make above/below expectation

{home_team} Shot-by-Shot Breakdown

Each 3-point attempt by {home_team} with the full calculation:

Player Result Location Shot Type Weighted 3P Prior (μ, κ) Player Exp% Multiplier Final Exp%
J. Randle ✗ Miss Above Break Catch Shoot 937.7/2826.2 (33.2%) (36.0%, 300) 33.5% 1.041 34.8%
A. Edwards ✓ Made Corner Catch Shoot 1256.8/3376.4 (37.2%) (36.0%, 300) 37.1% 1.123 41.7%
A. Edwards ✗ Miss Above Break Pullup 1256.8/3376.4 (37.2%) (36.0%, 300) 37.1% 0.932 34.6%
T. Shannon Jr. ✗ Miss Corner Catch Shoot 40.6/105.9 (38.3%) (32.4%, 211) 34.4% 1.123 38.6%
D. DiVincenzo ✓ Made Corner Catch Shoot 1161.0/3060.7 (37.9%) (36.0%, 300) 37.8% 1.123 42.4%
J. McDaniels ✗ Miss Above Break Pullup 576.5/1558.9 (37.0%) (36.0%, 300) 36.8% 0.932 34.3%
A. Dosunmu ✓ Made Corner Catch Shoot 555.8/1401.4 (39.7%) (36.0%, 300) 39.0% 1.123 43.8%
A. Edwards ✗ Miss Corner Stepback 1256.8/3376.4 (37.2%) (36.0%, 300) 37.1% 0.986 36.6%
J. McDaniels ✗ Miss Corner Catch Shoot 576.5/1558.9 (37.0%) (36.0%, 300) 36.8% 1.123 41.4%
B. Hyland ✗ Miss Above Break Stepback 570.5/1538.9 (37.1%) (36.0%, 300) 36.9% 0.904 33.4%
B. Hyland ✗ Miss Above Break Catch Shoot 570.5/1538.9 (37.1%) (36.0%, 300) 36.9% 1.041 38.4%
J. Randle ✓ Made Corner Catch Shoot 937.7/2826.2 (33.2%) (36.0%, 300) 33.5% 1.123 37.6%
D. DiVincenzo ✗ Miss Corner Stepback 1161.0/3060.7 (37.9%) (36.0%, 300) 37.8% 0.986 37.2%
J. Randle ✗ Miss Above Break Pullup 937.7/2826.2 (33.2%) (36.0%, 300) 33.5% 0.932 31.2%
J. Clark ✗ Miss Corner Running 62.7/192.1 (32.6%) (32.8%, 219) 32.7% 0.932 30.5%
A. Edwards ✓ Made Above Break Stepback 1256.8/3376.4 (37.2%) (36.0%, 300) 37.1% 0.904 33.6%
A. Edwards ✓ Made Above Break Running 1256.8/3376.4 (37.2%) (36.0%, 300) 37.1% 0.877 32.5%
A. Edwards ✗ Miss Above Break Catch Shoot 1256.8/3376.4 (37.2%) (36.0%, 300) 37.1% 1.041 38.6%
M. Conley ✗ Miss Above Break Catch Shoot 2053.0/5335.5 (38.5%) (36.0%, 300) 38.3% 1.041 39.9%
D. DiVincenzo ✓ Made Above Break Catch Shoot 1161.0/3060.7 (37.9%) (36.0%, 300) 37.8% 1.041 39.3%
D. DiVincenzo ✓ Made Above Break Catch Shoot 1161.0/3060.7 (37.9%) (36.0%, 300) 37.8% 1.041 39.3%
A. Dosunmu ✗ Miss Corner Catch Shoot 555.8/1401.4 (39.7%) (36.0%, 300) 39.0% 1.123 43.8%
J. Randle ✗ Miss Above Break Catch Shoot 937.7/2826.2 (33.2%) (36.0%, 300) 33.5% 1.041 34.8%
A. Edwards ✗ Miss Above Break Stepback 1256.8/3376.4 (37.2%) (36.0%, 300) 37.1% 0.904 33.6%
D. DiVincenzo ✗ Miss Corner Catch Shoot 1161.0/3060.7 (37.9%) (36.0%, 300) 37.8% 1.123 42.4%
J. McDaniels ✗ Miss Corner Catch Shoot 576.5/1558.9 (37.0%) (36.0%, 300) 36.8% 1.123 41.4%
J. McDaniels ✗ Miss Above Break Stepback 576.5/1558.9 (37.0%) (36.0%, 300) 36.8% 0.904 33.3%
A. Edwards ✗ Miss Above Break Pullup 1256.8/3376.4 (37.2%) (36.0%, 300) 37.1% 0.932 34.6%
B. Hyland ✓ Made Above Break Running 570.5/1538.9 (37.1%) (36.0%, 300) 36.9% 0.877 32.3%
M. Conley ✗ Miss Corner Catch Shoot 2053.0/5335.5 (38.5%) (36.0%, 300) 38.3% 1.123 43.1%
J. Randle ✗ Miss Above Break Catch Shoot 937.7/2826.2 (33.2%) (36.0%, 300) 33.5% 1.041 34.8%
B. Hyland ✗ Miss Above Break Catch Shoot 570.5/1538.9 (37.1%) (36.0%, 300) 36.9% 1.041 38.4%
A. Dosunmu ✓ Made Corner Running 555.8/1401.4 (39.7%) (36.0%, 300) 39.0% 0.932 36.3%
TOTALS 12.3 exp
Actual: 10 made -2.3 luck

MIN Player Summary

Player Shots Made Expected Makes Luck Point Impact
D. DiVincenzo 5 3 2.01 +0.99 +2.7
A. Dosunmu 3 2 1.24 +0.76 +2.1
A. Edwards 8 3 2.86 +0.14 +0.4
J. Clark 1 0 0.30 -0.30 -0.8
T. Shannon Jr. 1 0 0.39 -0.39 -1.0
B. Hyland 4 1 1.43 -0.43 -1.1
J. Randle 5 1 1.73 -0.73 -2.0
M. Conley 2 0 0.83 -0.83 -2.2
J. McDaniels 4 0 1.50 -1.50 -4.1
TOTAL 33 10 12.29 -2.29 -6.2

PHI Shot-by-Shot Breakdown

Each 3-point attempt by PHI with the full calculation:

Player Result Location Shot Type Weighted 3P Prior (μ, κ) Player Exp% Multiplier Final Exp%
K. Oubre Jr. ✓ Made Above Break Catch Shoot 1149.0/3502.0 (32.8%) (36.0%, 300) 33.1% 1.041 34.4%
T. Maxey ✓ Made Above Break Catch Shoot 911.9/2405.3 (37.9%) (36.0%, 300) 37.7% 1.041 39.2%
D. Barlow ✗ Miss Corner Running 45.2/166.0 (27.2%) (32.7%, 217) 30.3% 0.932 28.2%
V. Edgecombe ✓ Made Above Break Catch Shoot 203.4/562.5 (36.2%) (34.2%, 256) 35.6% 1.041 37.0%
T. Maxey ✗ Miss Above Break Pullup 911.9/2405.3 (37.9%) (36.0%, 300) 37.7% 0.932 35.1%
V. Edgecombe ✗ Miss Above Break Stepback 203.4/562.5 (36.2%) (34.2%, 256) 35.6% 0.904 32.2%
Q. Grimes ✓ Made Above Break Catch Shoot 829.0/2255.1 (36.8%) (36.0%, 300) 36.7% 1.041 38.2%
V. Edgecombe ✓ Made Corner Catch Shoot 203.4/562.5 (36.2%) (34.2%, 256) 35.6% 1.123 39.9%
Q. Grimes ✓ Made Above Break Catch Shoot 829.0/2255.1 (36.8%) (36.0%, 300) 36.7% 1.041 38.2%
Q. Grimes ✗ Miss Above Break Stepback 829.0/2255.1 (36.8%) (36.0%, 300) 36.7% 0.904 33.2%
T. Maxey ✗ Miss Above Break Stepback 911.9/2405.3 (37.9%) (36.0%, 300) 37.7% 0.904 34.1%
T. Maxey ✓ Made Above Break Pullup 911.9/2405.3 (37.9%) (36.0%, 300) 37.7% 0.932 35.1%
Q. Grimes ✗ Miss Corner Catch Shoot 829.0/2255.1 (36.8%) (36.0%, 300) 36.7% 1.123 41.2%
C. Payne ✓ Made Above Break Pullup 704.1/1939.0 (36.3%) (36.0%, 300) 36.3% 0.932 33.8%
K. Oubre Jr. ✗ Miss Corner Catch Shoot 1149.0/3502.0 (32.8%) (36.0%, 300) 33.1% 1.123 37.1%
K. Oubre Jr. ✓ Made Corner Catch Shoot 1149.0/3502.0 (32.8%) (36.0%, 300) 33.1% 1.123 37.1%
C. Payne ✗ Miss Above Break Pullup 704.1/1939.0 (36.3%) (36.0%, 300) 36.3% 0.932 33.8%
T. Maxey ✗ Miss Above Break Stepback 911.9/2405.3 (37.9%) (36.0%, 300) 37.7% 0.904 34.1%
V. Edgecombe ✓ Made Above Break Catch Shoot 203.4/562.5 (36.2%) (34.2%, 256) 35.6% 1.041 37.0%
V. Edgecombe ✓ Made Above Break Catch Shoot 203.4/562.5 (36.2%) (34.2%, 256) 35.6% 1.041 37.0%
K. Oubre Jr. ✗ Miss Above Break Catch Shoot 1149.0/3502.0 (32.8%) (36.0%, 300) 33.1% 1.041 34.4%
K. Oubre Jr. ✗ Miss Above Break Catch Shoot 1149.0/3502.0 (32.8%) (36.0%, 300) 33.1% 1.041 34.4%
Q. Grimes ✓ Made Corner Catch Shoot 829.0/2255.1 (36.8%) (36.0%, 300) 36.7% 1.123 41.2%
V. Edgecombe ✓ Made Above Break Pullup 203.4/562.5 (36.2%) (34.2%, 256) 35.6% 0.932 33.1%
J. Walker ✗ Miss Above Break Catch Shoot 122.3/396.3 (30.9%) (33.6%, 240) 31.9% 1.041 33.2%
Q. Grimes ✗ Miss Above Break Stepback 829.0/2255.1 (36.8%) (36.0%, 300) 36.7% 0.904 33.2%
C. Payne ✗ Miss Above Break Pullup 704.1/1939.0 (36.3%) (36.0%, 300) 36.3% 0.932 33.8%
T. Maxey ✓ Made Above Break Pullup 911.9/2405.3 (37.9%) (36.0%, 300) 37.7% 0.932 35.1%
V. Edgecombe ✓ Made Above Break Stepback 203.4/562.5 (36.2%) (34.2%, 256) 35.6% 0.904 32.2%
Q. Grimes ✓ Made Above Break Catch Shoot 829.0/2255.1 (36.8%) (36.0%, 300) 36.7% 1.041 38.2%
K. Oubre Jr. ✗ Miss Corner Catch Shoot 1149.0/3502.0 (32.8%) (36.0%, 300) 33.1% 1.123 37.1%
K. Oubre Jr. ✓ Made Corner Catch Shoot 1149.0/3502.0 (32.8%) (36.0%, 300) 33.1% 1.123 37.1%
T. Maxey ✓ Made Above Break Pullup 911.9/2405.3 (37.9%) (36.0%, 300) 37.7% 0.932 35.1%
Q. Grimes ✓ Made Corner Catch Shoot 829.0/2255.1 (36.8%) (36.0%, 300) 36.7% 1.123 41.2%
J. Edwards ✓ Made Above Break Catch Shoot 140.2/400.4 (35.0%) (33.6%, 240) 34.5% 1.041 35.9%
J. Edwards ✗ Miss Above Break Running 140.2/400.4 (35.0%) (33.6%, 240) 34.5% 0.877 30.2%
D. Terry ✓ Made Above Break Pullup 119.2/343.7 (34.7%) (33.4%, 234) 34.2% 0.932 31.8%
TOTALS 13.1 exp
Actual: 21 made +7.9 luck

PHI Player Summary

Player Shots Made Expected Makes Luck Point Impact
V. Edgecombe 7 6 2.48 +3.52 +9.5
Q. Grimes 8 5 3.04 +1.96 +5.3
T. Maxey 7 4 2.48 +1.52 +4.1
D. Terry 1 1 0.32 +0.68 +1.8
K. Oubre Jr. 7 3 2.52 +0.48 +1.3
J. Edwards 2 1 0.66 +0.34 +0.9
C. Payne 3 1 1.01 -0.01 -0.0
D. Barlow 1 0 0.28 -0.28 -0.8
J. Walker 1 0 0.33 -0.33 -0.9
TOTAL 37 21 13.13 +7.87 +21.2

Final Calculation

MIN

PHI

ORB Adjustment Calculation

Each lucky make isn't worth a full 3 points because missed 3s generate offensive rebounds (~27% ORB rate) that lead to additional scoring (~1.1 points per possession). We subtract this "lost opportunity" value:

Point Adjustment = Raw 3PT Value − ORB Opportunity Cost = (3 × Luck) − (ORB Rate × PPP × |Luck|) = (3 × Luck) − (0.27 × 1.1 × |Luck|) ≈ 2.7 × Luck
Team Luck Raw 3PT Value ORB Adjustment Net Point Impact
MIN -2.29 -6.9 +0.7 -6.2
PHI +7.87 +23.6 -2.3 +21.2

Net Result

The luck differential of -10.2 makes in favor of PHI translates to 27.4 points of margin swing after ORB adjustment.

Actual margin: MIN -27

Adjusted margin: MIN +0.6

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Generated 2026-02-23 17:29 | View on GitHub