Endpoint credibility and terminal acceleration in endurance cycling

Abstract

Distance feedback can change the final increase in cycling power without producing a corresponding change in completion time. Accurate information, source trust and uncertainty about the finish therefore require separate treatment. To determine the mathematical conditions under which credibility-weighted distance beliefs make a higher output acceptable until completion. Remaining distance is represented by a subjective probability distribution. A linear pool combines the pre-cue belief with the cue-implied distribution; perceived sustainable distance is calculated separately from expected speed and tolerable duration. Acceleration is acceptable when the upper distance quantile at a specified acceptance probability lies within that sustainable distance. For a pre-cue belief spanning 1.8--2.6 km, a cue spanning 1.5--1.7 km and an acceptance probability of 0.90, cue weights of 0.20 and 0.80 yield upper quantiles of 2.50 and 2.20 km. At a sustainable distance of 2.30 km, the criterion holds only for the larger weight. These values are analytical inputs, not participant observations. Disagreement between cues contributes directly to belief variance, so a nearer mean estimate need not remove the distant upper tail. Five predictions separate credibility, bias direction, interval width, cue-restoration timing and redundant position information. A prospective six-condition cycling experiment and a distance-based acceleration analysis specify tests of the decision criterion. The article contains theoretical derivations and cited endurance evidence; it makes no claim of a newly measured performance effect.