Characterizing Amplitude-Dominated Performance: A Refinement of Fitts' Law for Target Acquisition on Large-Format Touchscreens

Large-format touchscreens have become commonplace in classrooms and meeting rooms, yet little is known about how their scale affects input behavior. Operating these displays engages more upper-limb joints—especially the shoulder—thereby altering movement dynamics. In a 65-inch touchscreen study, we found that conventional Fitts' law explains ≤ 80% of the variance in movement time, as performance is primarily driven by amplitude. To address the modeling bias resulting from this amplitude dominance, we refine the index of difficulty as IDx = log_2(A/(W + c) + 1). Rather than treating c as a mere fitting parameter, we interpret it as an intrinsic property of pointing dynamics: it quantifies the systematic deviation from the canonical speed-accuracy tradeoff implied by the "as quickly and accurately as possible" instruction. By calibrating c with the proposed anti-overfitting criteria, we improve model fits for both finger and pen input, raising R² to above 0.97. We present the calibration rules, interpret c across contexts, validate IDx robustness via leave-one-out cross-validation, and demonstrate its generalizability on data from prior studies—including a large tabletop experiment. Finally, we translate the findings into practical guidelines for UI and experimental design.