The more air the higher it will bounce, the less air the lower it will bounce assuming the exact same amount of force is applied in each case. You do not want a ball that bounces too easily or one that is hard to make bounce. The reason it bounces higher with more air is because the outer cover is drawn tighter when more air is applied internally. The tighter the cover the higher it will bounce because it has more spring to it.
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Because when something is not inflated fully then it is partially flat. Which will affect its ability to bounce