If there’s no UAPS, then:

– For n large, a lead of n+1 vs. n gives very little additional information about the teams’ relative abilities.

– Thus only the primitive effect of the lead is leftover. [I guess to complete the argument, I need a finite expected number of goals? I’m comfortable with that.]

However, under UAPS:

– The first bullet point above still applies, roughly.

– However, as we learn that the game is more high scoring, a lead takes on less meaning. If the professionals exhibit no UAPS and we have extensive UAPS about the 9-year-olds, then I think we can cook F(\infty) to be anything strictly less than 1.