A statistic to measure the level of connectedness achieved among flocks would help producers to assess the risk of comparing EBV of animals from different flocks. The objectives of this research were to evaluate the pattern of change over time in selected connectedness measures and to determine how effectively these measures quantify the level of risk due to potential bias in EBV comparisons across production units. Connectedness was evaluated using simulated sheep populations, with connections established using sire referencing schemes (SRS). Pedigree and performance data for a single trait with a within-flock heritability of 0.25 were simulated (50 replications) for 15 flocks with 40 to 140 ewes per flock. Genetic means for each flock were sampled from a normal distribution with mean 0 and SD equal to the trait's genetic SD. After 10 yr of random mating, flocks had opportunity to join a SRS and selection began for the simulated trait. Yearling rams were chosen as reference sires randomly from the top one-sixth of the population ranked on BLUP EBV. Every year, in each flock, 3 reference sires were mated to 10 ewes each. Six sire referencing scenarios (including no SRS) and 2 sources of nonreference sires were simulated. Connectedness was measured in 2 ways: (i) as the average prediction error correlation (r(ij)) of the flock genetic means (flock r(ij)) or the EBV for the current crop of ram lambs (lamb r(ij)) or (ii) as the average scaled prediction error variance of differences (PEVD) in flock genetic means (flock PEVD) or in lamb EBV in the current crop of ram lambs (lamb PEVD). Flock r(ij) increased linearly in all scenarios while SRS was underway and leveled off if the flocks discontinued SRS. Lamb r(ij) increased rapidly as soon as SRS began but decreased substantially if the flocks discontinued SRS. Behavior of flock PEVD and lamb PEVD measures were similar but in the opposite direction (i.e., PEVD decreased with increasing r(ij)). Within scenarios, both flock r(ij) and flock PEVD had a nonlinear relationship with bias in comparing animals across flocks. However, only flock r(ij) exhibited a consistent relationship across simulation scenarios. When flock r(ij) reached 0.05 and 0.10, approximately 20 and 10%, respectively, of the bias due to initial differences in flock genetic means remained. These levels of flock r(ij) are suggested as benchmark levels for minimizing the risk of comparing animal EBV among units.