WEIGHTED HETEROGENEOUS SCORING MODEL: RECONSTRUCTION AND MATHEMATICAL VALIDATION OF THE FUNCTIONAL MOVEMENT SCREEN SCORING SYSTEM

Abstract

The total score of the Functional Movement Screen (FMS) is obtained by taking the average of the scores of the seven component tests, the assumption being that every component test has the same influence on injury risk implicitly. Nonetheless, the factor analyses have proven that the seven FMS tests are not unidimensional and their relationship with injury risk is quite different; deep squat (OR = 3.47) and hurdle step (OR = 2.26) have much higher predictive ability than other items. Not only does it lack biomechanical support but it also contradicts the basic measurement theory, which says that heterogeneous items cannot be summed using equal weights. To address the inadequacies of the equal-weight scoring, this paper suggests a Weighted Heterogenous Scoring (WHS) model which allocates varying weights depending on the specific contribution of each test to injury risk. We verified the theoretical benefits of the WHS over the conventional equal-weight total score approach in three aspects: information retention rate, stability in extreme scenarios, and cross-scenario consistency, using mathematical enumeration of all the 16,384 possible score combinations. It was found that the traditional equal-weight algorithm would only be able to identify 22 different score values (0 - 21) out of the total possible combinations, and had an information redundancy of 99.87%. With the introduction of different weighting, the effective discrimination of the WHS went up to 58 - 87 different score values, a 164 - 295% increase in information retention. In extreme settings (k = 3, three painful items), there was complete failure of the traditional equal-weight method (no combination reached the ≥ 14 threshold), whereas the WHS had consistent risk ranking performance. Equal-weight summation leads to information loss and dilution of predictive power in the FMS, which is mathematically resolved by the WHS to give an operational theoretical pathway to reconstruct the FMS scoring system.