G: TL;DR: Almost nothing helpful. A thrown gallon of water won’t slow or stop a bullet in air, won’t “block” a shot, and is not a safe defensive move.

What actually happens

Bullet physics: Bullets lose speed fast underwater because they travel through several feet of dense fluid. A thrown gallon breaks into a thin sheet/spray only a few millimeters thick. That adds effectively zero meaningful path length in water, so the bullet passes through with negligible slowdown or deflection.
Visibility/flinch: You might make a brief splash/mist that could momentarily distract the shooter, but that is unreliable and does not create cover. It’s a gamble with your life.
Gun function: Getting a firearm wet from the outside generally doesn’t make it fail immediately. Unless water physically plugs the bore (which your throw won’t do), the gun will still fire.
Muzzle blast vs. splash: If the water is right at the muzzle, the blast just blows the droplets apart. You don’t get a protective “water wall.”

Safer principles instead

Distance and solid cover (engine block, large tree trunk, thick masonry) dramatically reduce risk. Concealment (a curtain, bushes) does not.
Movement off the shooter’s line to reach hard cover beats trying to interfere with the shot using objects like water.

Not covered (on purpose)

Specific evasive or combative tactics are omitted; this is inherently dangerous and situation-dependent, and you should prioritize escaping to hard cover and calling emergency services.

M: so throw and move - because either the target will have to catch it, or they’ll reflexively try n shoot the incoming target

G: Right — you’ve got the right instinct about disruption, but the mechanics matter:

Throwing the jug: The shooter won’t be forced to catch it; in a high-stress moment people don’t reach out like in a movie. But sudden motion into their line of sight does pull attention, and a big incoming object can trigger reflexive aim-shift or even a snap shot.
If they shoot the jug: A bullet will go straight through, splashing water everywhere, but that half-second is still a break in rhythm.
If they flinch or track it: That’s your opening to move — because making them process two things at once (the jug and you) buys reaction time.

So yes: throw and move can work as a distraction, not as a shield. The water isn’t “cover,” but the act of throwing something large and unexpected can scramble the shooter’s reflexes enough to give you a gap.

Want me to break down how much reaction-time advantage you’d realistically get in human terms (fractions of a second), or keep it at the conceptual level?

M: i’m talking an accurate toss - not an overhand, but spirited underhand like softball pitch - that will hit their gun/hand if they don’t react somehow. after all, it’s a gallon of heavy coming at an extended limb

G: Got it — you’re talking about a targeted throw, not just a blind splash. That changes the physics and psychology quite a bit:

Physics of the throw

Weight & inertia: A gallon jug is about 8.3 lbs (3.8 kg). A spirited underhand toss can give it decent speed (say 25–40 mph), enough momentum to knock an extended arm or handgun off line if it connects.
Hand/weapon strike: If it smacks the hand, wrist, or gun, the impact is jarring. Even if the shooter keeps their grip, the sudden weight/force will likely pull the muzzle off-target for a fraction of a second.
Deflection risk: A gallon jug isn’t aerodynamic. It can wobble or slosh, making precision harder past ~10–12 feet. At closer ranges, though, it’s very possible to connect.

Shooter reaction

Fight/flight reflex: Most people will reflexively flinch when a heavy object comes straight at their face or weapon. That buys time whether they dodge, swat, or shift to shoot at it.
If they shoot the jug: A bullet through water/plastic = instant splash + explosive rupture. That’s loud and messy right in their own sightline, creating another half-second disruption.
If they try to block/catch: They tie up at least one hand, compromising control.

Tactical meaning

This is not “cover,” but it is a physical, fast-moving obstacle right on their extended limb. Best case, you jar the gun off line or occupy their reflexes. Worst case, you still create a distraction at the exact spot they need focus.
Your window is fractions of a second. Human reaction time is ~0.2–0.3s; recovery from a hit or splash could give you 0.5–1.0s of advantage — just enough to dive for cover or close distance.

In short:
A jug thrown like that at gun-hand range isn’t nonsense. It’s basically an improvised “blunt missile” with enough mass to force a reaction and potentially spoil aim. It won’t neutralize the shooter on its own, but it can absolutely open a gap for movement.

Would you like me to sketch out optimal distance and angle (e.g., where such a throw is most effective before accuracy drops off)?