A much debated topic in recent studies of ultrafast exciton dynamics in molecular aggregates has been the precise definition of the exciton coherence domain in the B850 aggregate of photosynthetic purple bacteria. In this work we compare several measures of exciton delocalization and their variation with temperature, inhomogeneous broadening, and time. We find that the exciton wave packet prepared by a 40 fs pulse is initially delocalized over a substantial portion of the ring and contracts to a significantly smaller size on the time scale of a few hundreds of femtoseconds. Steady-state absorption and time-dependent pump-probe spectra of the B850 aggregate are simulated and compare well with previously reported experimental data. The calculated thermalized exciton wave packet size is in good agreement with previous experimental and theoretical estimates.