I think there is a "best" p-value, and I don't think it's the "highest" p-value.

You don't want it too low, because then quality becomes meaningless. You do want to give good results to good teams. But there is also don't want it to be perfect - you want some unpredictability in sports. You don't want every match to be a foregone conclusion, and you want every supporter to be able to have some reasonable hope.

There is some data suggesting that one of the reasons that English football is popular is because it's low scoring. This increases the chance that random variation gives an "incorrect" result. In this hypothesis, unpredictability adds excitement and builds popularity.

The NFL achieves similar results a different way - various forms of consistency and negative feedback (salary cap, draft order, schedule) to keep teams very close in ability. This means that small differences like a game plan for a particular week can regularly affect results, and keeps predictability low.

> you want every supporter to be able to have some reasonable hope.

The England game a couple of nights ago. On paper England were better before hand, but Italy were winning until the last minute of injury time. Some England fans had already left the stadium, then in goes the goal, then extra time, then just as it looks like another horrendous penalty shootout there's a foul in the box and England take it, then the goalie stops it, but then it goes in.

Certainly a rollercoaster for both sets of fans.