• Home toilets use the bowl filling up to create a siphon through the drain trap. For that to work your toilet must first raise the water level above the top of the trap to create the pressure with its weight to start the siphon. I.e with the lid closed you are forcing more air to compress in a smaller volume generating a pressure difference outside the bowl and internally. Leave the lid open and that volume of air goes directly into the room without much resistance creating less pressure in the bowl compared to the surrounding air in the room. Hence with the lid open the distance, the spray travels is lower as it has a lower velocity.