The present study investigated the effect of different levels of fat, protein, and casein on (1) traditional milk coagulation properties, and (2) curd firming over time parameters of 1,272 goat milk samples. Relationships between fat, protein, and casein and some indicators of udder health status (lactose, pH, somatic cells, bacterial count, and NaCl) were also investigated. Traditional milk coagulation properties and modeled curd-firming parameters were analyzed using a mixed model that considered the effect of days in milk, parity, farm, breed, the pendulum of the instrument, and different levels of fat, protein, and casein. Fat, protein, and casein were also tested with the same model but one at a time. Information provided by this model demonstrated the effect of one component alone, without contemporarily considering that of the others. The results allowed us to clarify the effect of the major milk nutrients on coagulation, curd firming, and syneresis ability of goat milk. In particular, milk rich in fat was associated with better coagulation properties, whereas milk rich in protein was associated with delayed coagulation. The high correlation of fat with protein and casein contents suggests that the effect of fat on the cheese-making process is also attributable to the effects of protein and casein. When only protein or only casein was included in the statistical model, the pattern of coagulation, curd firming, and syneresis was almost indistinguishable. The contemporary inclusion of protein and casein in the statistical model did not generate computing problems and allowed us to better characterize the role of protein and casein. Consequently, given their strong association, we also tested the effect of casein-to-protein ratio (i.e., casein number). Higher values of casein number led to a general improvement in the coagulation ability of milk, suggesting that casein-to-protein ratio, not just protein or casein, should be considered when milk is destined for cheese making. These results are especially useful for dairy farmers who want to increase their profits by improving the technological quality of the milk produced.