The statistical geometry of the electrochemically active triple-phase boundary in solid oxide fuel cell (SOFC) anodes with oxygen-ion-conducting (zyrconya type) electrolyte is analyzed by means of an 'effective-medium' theory and verified by Monte Carlo simulations. Variation of the triple-phase boundary with time due to spontaneous sintering of metal particles is described by kinetic effective-medium equations. Their solution reveals possible degradation scenarios, as well as the factors that impede degradation, or even cause a rise of the active triple-phase boundary in the course of SOFC operation. The cermet composition, i.e. the relative portion of electrolyte, metal and pores, is among these factors, It is shown that the 'best' composition before degradation may not be the one that provides the best performance after degradation. The latter depends on the probability of pore opening in sintering of two metal grains. Rough estimates of this probability (and determination of the 'optimum' composition) would be possible from a comparison of the calculated porosity before and after degradation with experimental data, which are not available so far.