Rarity of Pareto-dominated fictitious-play orbits

Consider the space of $n\times n$ bimatrix games with entries in $[0,1]$. Restrict attention to games with a unique, completely mixed Nash equilibrium and to typical fictitious-play orbits; a game has Nash equilibrium Pareto dominating such orbits when the equilibrium payoff is at least as good for both players. Rarity conjecture. The set of such games has Lebesgue measure at most $0.01$. The claim is a quantitative formulation of the authors' numerical observation that games whose typical fictitious-play orbits are Pareto dominated by the Nash equilibrium appear to be rare. No proof or resolution is supplied here.