During motor adaptation the nervous system constantly uses error information to improve future movements. Today's mainstream models simply assume that the nervous system adapts linearly and proportionally to errors. However, not all movement errors are relevant to our own action. The environment may transiently disturb the movement production, for example, a gust of wind blows the tennis ball away from its intended trajectory. Apparently the nervous system should not adapt its motor plan in the subsequent tennis strokes based on this irrelevant movement error. We hypothesize that the nervous system estimates the relevance of each observed error and only adapts strongly to relevant errors. Here we present a Bayesian treatment of this problem. The model calculates how likely an error is relevant to the motor plant and derives an ideal adaptation strategy that leads to the most precise movements. This model predicts that adaptation should be a non-linear function of the size of an error. In reaching experiments we found strong evidence for the predicted non-linear strategy. The model also explains published data on saccadic gain adaptation, adaptation to visuomotor rotations and force perturbations. Our study suggests that the nervous system constantly and effortlessly estimates the relevance of observed movement errors for successful motor adaptation.