ANSWER

How Shots Spread

Strategy & Shot

Strokes Gained–based dispersion parameters for physics engines and strategy models.

Dispersion parameters by distance drive the accuracy of any physics engine.

Dispersion model overview

This tool generates distance-based dispersion parameters for physics engines, based on Mark Broadie's "Every Shot Counts" and related statistical models.

Adjust player skill level (handicap) below; the simulation and engine-ready data table update in real time. Use the output as reference points for linear interpolation.

Main logic

  • Dispersion scale: Dispersion scale: Error grows linearly with distance (y = ax + b).
  • Elliptical: Elliptical distribution: Distance error and direction error are independent.
  • Short bias: Short bias: Amateurs tend to land short of the target.

Model parameters

5%

Higher = more spread left/right

4%

Higher = more distance variance

0%

How much to shift mean landing short of target

150y

Dispersion simulation (top view)

Center (0,0) = Pin

Distribution for 100 shots with current parameters (95% confidence ellipse).

Distance vs dispersion (linear model)

Carry : run ratio model

Engine data table

Interpolation data for current settings. Load as CSV or array into your program.

Distance (y)Lateral (±y)Long (±y)Bias (y)Carry:Run
50y± 3.5y± 3.0y-0.0y98 : 2
100y± 6.0y± 5.0y-0.0y95 : 5
125y± 7.3y± 6.0y-0.0y95 : 5
150y± 8.5y± 7.0y-0.0y92 : 8
175y± 9.8y± 8.0y-0.0y92 : 8
200y± 11.0y± 9.0y-0.0y88 : 12
225y± 12.3y± 10.0y-0.0y88 : 12
250y± 13.5y± 11.0y-0.0y85 : 15
275y± 14.8y± 12.0y-0.0y85 : 15
300y± 16.0y± 13.0y-0.0y85 : 15

Implementation note

Lateral = (coefA * Distance) + base
Long = (coefB * Distance) + base
(x, y) = ( random_normal() * lateral, Distance - bias + random_normal() * long )

References & data sources

  • Mark Broadie"Every Shot Counts: Using the Revolutionary Strokes Gained Approach to Improve Your Golf Performance and Strategy" (2014) - ストローク・ゲインドの基礎理論および分散データの主要ソース。
  • Thomas Kielen"Statistical Analysis of Golf Dispersion" (関連文献) - アマチュアおよびプロゴルファーのショット分散に関する統計的研究。
  • PGA TOUR ShotLink公式ショットデータ - 各距離・ライごとのプロ平均着弾誤差データ。