That's a problem of aim, not spray formation, and thus beyond my expertise. The Rayleigh regimes produce large droplets (mainly diameters similar to the orifice) and not a finer spray that could go everywhere.

Also: Peeing into only the bowl won't necessarily minimize the mess. Air gets "entrained" into the water and that creates splatter. Best practice is to target the porcelain inside the bowl (just above the water line) and adjust the distance so that the stream has broken up less as droplets will create more splatter than a solid stream.

You could also sit down.

There are different reasons for this.

The biggest one is that many guys are just vile. Sad but true. They don't even try to aim, because someone else will clean it; and they don't even wash their hands after.

The next biggest is that sometimes where you point isn't where the stream goes, whether from a random pinch in the tube or a proprioception error.

And sometimes the stream is split, and it's not entirely predictable when that will happen.

Spray?? Never had an issue like that. Can't speak for everyone though.

To add to the other responses: sometimes it's splash-back from the bowl water itself. It's gotta be toilet bowl dependent, and I assume some people are just too lazy to clean theirs up.

I'm genuinely curious as to why this is, as someone who has never had trouble aiming or covered the seat in piss.