Ingots of the bulk metallic glass (BMG), Zr64.13Cu15.75Ni10.12Al10 in atomic percent (at. %), are compressed at slow strain rates. The deformation behavior is characterized by discrete, jerky stress-drop bursts (serrations). Here we present a quantitative theory for the serration behavior of BMGs, which is a critical issue for the understanding of the deformation characteristics of BMGs. The mean-field interaction model predicts the scaling behavior of the distribution, D(S), of avalanche sizes, S, in the experiments. D(S) follows a power law multiplied by an exponentially-decaying scaling function. The size of the largest observed avalanche depends on experimental tuning-parameters, such as either imposed strain rate or stress. Similar to crystalline materials, the plasticity of BMGs reflects tuned criticality showing remarkable quantitative agreement with the slip statistics of slowly-compressed nanocrystals. The results imply that material-evaluation methods based on slip statistics apply to both crystalline and BMG materials.