Same Axis, Different Place: How Middlegame Style Shifts Across the Expertise Gradient

Abstract

A companion study found that elite male and female titled chess players differ in multivariate middlegame style, but it could not test how style changes with skill. Open FIDE titles are rare below 2000 Elo, so the skill-by-sex interaction was underpowered. This paper isolates the skill effect in a single-sex sample of 2,216 female titled players (176,620 rated online games; Elo 1013 to 2894), where sex cannot confound the comparison. Ten engine-independent style indicators were reduced by principal-component analysis and examined across rating bands. Two results hold. First, the attacking-positional dimension that organizes style is structurally invariant across skill. Its loading pattern is near-identical between adjacent coarse rating bands (Tucker's congruence >= .979). Second, players shift along that dimension as skill rises, moving near- monotonically (band-mean Spearman ρ = -.97) away from the forcing, exchange-heavy, reactive pole toward tension-holding, mobility, and central control. Most of the shift is concentrated early: a segmented regression locates a breakpoint near 1800 Elo, below which style changes roughly three to four times faster than above it. A third apparent result did not survive scrutiny. Within-band dispersion of style scores falls with rating (r = -.74 across bands), which would suggest that experts converge stylistically. But games played per player rises with rating, and sampling noise accounts for 25 to 52 percent of within-band variance with a steep gradient. Once games played is controlled, the player-level association between rating and dispersion is zero. I report the artifact in full because it is a general hazard for any study that summarizes style from game averages. The design is cross-sectional, so these are differences between players at different ratings, not trajectories within players.