Dipolar fluids are known to exhibit complex self-assembly at low temperatures, yet a compact thermodynamic description of their aggregate statistics has remained elusive. Using molecular dynamics simulations of Stockmayer particles with a purely repulsive WCA core, we confirm that over broad regions of the ($\rho$, $T$) phase space the chain-size distribution follows an exponential decay with characteristic size $s_0$. Within this regime, we find that $s_0$ can be accurately described by an effective thermodynamic potential $\varphi$ that incorporates bonding energy, a crowding penalty, and translational entropy. Identifying deviations from this ideal scaling provides a further division of the phase space into four regions. Therefore, our results locate a regime of relatively simple chain statistics and offer an alternative regime-based perspective on dipolar self-assembly.