🤖 AI Summary
This study addresses the conflation of environmental difficulty and individual skill in traditional assessments of outdoor activity suitability, which typically rely on a single expert-derived curve. The authors introduce continuous item response theory to this domain for the first time, jointly modeling rider ability and trail difficulty using rider performance, terrain conditions, and binary outcomes. Success probability is characterized via a sigmoidal function, with a physics-informed expert curve serving as a prior for difficulty. Parameters are estimated through marginal maximum likelihood using Gaussian–Hermite quadrature, and graph connectivity constraints ensure identifiability. Experiments demonstrate that the model achieves a skill recovery correlation of 0.96 on synthetic data, locates minimum difficulty with an error under three units, and improves Brier skill scores by 0.33 over the expert-curve baseline, effectively disentangling and quantifying intrinsic difficulty from individual capability.
📝 Abstract
Suitability scoring for outdoor activities (kitesurfing, paragliding, ski touring) maps environmental conditions to a go/no-go verdict via expert-defined curves. These curves conflate two distinct quantities: the intrinsic difficulty of a condition and the skill of the person facing it. We introduce Inverse Suitability, a continuous-item Item Response Theory (IRT) model that identifies both from behavioural outcomes alone. Each outcome is a triple (rider r, condition metric x at site s, binary outcome y); we model P(y=1) = sigma(a (theta_r - delta(x, s))), where theta_r is latent rider skill, delta(x, s) is a latent difficulty function anchored to a physics-derived expert curve as its prior, and a is a discrimination parameter. The formulation is strictly more general than a single suitability curve, which it recovers exactly when skill is integrated out under the population distribution. Parameters are estimated by marginal maximum likelihood with Gauss-Hermite quadrature; identification holds when the rider-by-condition incidence graph is connected, with a documented single-curve fallback otherwise. We validate via synthetic recovery: on a reference cohort (80 riders times 30 outcomes) the model recovers latent skill at r = 0.96, locates the difficulty minimum within 3 units of ground truth, and improves held-out Brier Skill Score by +0.33 over the expert-curve baseline. The recovered difficulty function defines a measurable, site-level construct, an intrinsic difficulty atlas, that existing meteorological observation networks do not capture. All results reproduce from a single command on synthetic data, requiring no proprietary observations.