Adjust for snapshot ply to preserve causal interpretation

Ascertain whether additional adjustments are required for the ply at which positions are snapshotted to preserve the causal interpretation of logistic-regression estimates of material value and skill effects, and, if needed, develop appropriate corrections for early versus late snapshots reflecting changing causal pathways as games progress.

Background

The authors sample positions at different plies and observe that the effect of rating difference diminishes later in games and that early snapshots may exhibit different causal pathways between skill, position, and outcomes.

They explicitly state uncertainty about whether ply-based adjustments are needed to maintain causal interpretation and suggest that this issue is distinct from lopsided positions.