Par-Equivalent Tees: Matching Skill to Course Length

This note defines a player's par-equivalent tee as the course length at which that player profile's expected gross score equals par. The idea is not that a shorter course is always "fair," nor that tee selection can replace the World Handicap System. Rather, tee selection is treated as an ex ante instrument for removing mean-score differences before the round begins. Using a shot-level golf simulator with expected-score-minimizing shot targets and minimum-mean strategy selection, I scale two synthetic par-72 courses--one smooth and one hazard-intensive--and solve for the length that makes Tour, scratch, HCP10, and HCP20 profiles average 72. The resulting yardages are strongly ordered by skill, but not proportional to driver distance: the HCP20 profile averages par only at extremely short lengths, about 2,275 yards on the smooth course and 1,778 yards on the hazard course. Once player-specific tees equalize expected gross score, centered head-to-head gross matches are essentially balanced, suggesting that variance and tail risk become the next objects of competition design.