The premier record of long-term solar activity is the sunspot count. After developing a theoretical model of sunspot visibility, this model is tested against observations, and recommendations are made for improved calculation of sunspot counts. The theoretical model's result is a predicted threshold size for sunspot visibility with the unaided (but filtered) eye, direct vision through a telescope, pinhole camera, and telescope projection. Also reported are over 3250 days of sunspot observations from six observers, 38 yr of daily observations by an experienced observer, 1837 days of observations from a network with over 50 experienced observers, observations from 30 inexperienced observers, as well as summaries of results from 102 AAVSO solar observers. The comparison of the observed thresholds with the predicted thresholds reveals agreement to within the uncertainties, so that the model is validated by observation.