  Recently Bodeker has presented an effective infrared theory for the dynamics
of Yang-Mills theory, suitable for studying the rate of baryon number violation
in the early universe. We extend his theory to include Higgs fields, and study
how much the Higgs affects the baryon number violation rate in the symmetric
phase, at the phase coexistence temperature of a first order electroweak phase
transition. The rate is about 20% smaller than in pure Yang-Mills theory. We
also analyze the sphaleron rate in the analytic crossover regime. Our treatment
relies on the ergodicity conjecture for 3-D scalar $\phi^4$ theory.
