Falling is a significant health problem. Fall detection, to alert for medical attention, has been gaining increasing attention. Still, most of the existing studies use falls simulated in a laboratory environment to test the obtained performance. We analyzed the acceleration signals recorded by an inertial sensor on the lower back during 143 real-world falls (the most extensive collection to date) from the FARSEEING repository. Such data were obtained from continuous real-world monitoring of subjects with a moderate-to-high risk of falling. We designed and tested fall detection algorithms using features inspired by a multiphase fall model and a machine learning approach. The obtained results suggest that algorithms can learn effectively from features extracted from a multiphase fall model, consistently overperforming more conventional features. The most promising method (support vector machines and features from the multiphase fall model) obtained a sensitivity higher than 80%, a false alarm rate per hour of 0.56, and an F-measure of 64.6%. The reported results and methodologies represent an advancement of knowledge on real-world fall detection and suggest useful metrics for characterizing fall detection systems for real-world use.