How much is a "splash"

I would measure a splash by the second - that is, holding the container (usually bottle) about a foot above the pan, and pour about a second or two's worth of liquid. Or to put it another way, stop pouring about when the stream of liquid hits the pan and consider that mid-air-stream a (medium) "splash".

I would usually get a couple tablespoons of liquid pouring this way. Of course, stronger liquids usually come in smaller mouthed bottles so less gets poured - for soy sauce, I'd get a few teaspoons, for water (from a cup) a few tablespoons, for something like liquid smoke - a few drops since the bottle's opening is very small.

More generally speaking, I've always considered "splash", "dash", "sprinkle" and other such measurements to be an equivalent for, like oft cited for salt and pepper, "to taste". Or perhaps "to texture", depending on the what-where-when that's being added. The recipe doesn't have a measurement because it isn't recipe-critical how much is actually added, it's just to the preference of whoever is cooking.

A splash is a small amount, definitely not 1/4 of a cup. This is obviously a subjective thing, but I'll try to put some numbers on it. Once I did a quick measurement of my soy sauce bottle to get an idea of how much I was using when I added a few shots (the bottle had a pin hole top and the soy came out in bursts when the bottle was shaken, I call that a shot). It turned out with that bottle about 6 shots was a teaspoon. If a recipe called for a splash of soy I'd have done 5 or 6 shots with that bottle, so I would call a splash of something about a teaspoon, aka 5ml, maybe up to 10ml. It's a non-specific amount so you don't need to be too worried about it.

Why don't recipes say to add a splash of something instead of an actual measurement? It could be laziness, the author didn't measure the amount used so adds subjective amount (I've been guilty of that once or twice), or rather than laziness the author didn't have time to grab a measuring spoon as the water was required quickly. It could also be the author's style choice, favoring a freestyle approach to cooking rather than specifying everything.

I'd have to do some testing to get firmer values for things, but they're still ranges, as it depends on what you're pouring it from. Here's what I typically use for imprecise measurements:

Liquids

• dash : a quick shake from a bottle with a restricted top. If it doesn't have one of those plastic things in the neck of the bottle, cover the opening partially with your thumb. (likely less than a teaspoon)
• splash : From a bottle with an unrestricted top, tip the bottle 'til the liquid starts flowing, then pull it back. (maybe a couple of tablespoons at most)
• glug : start pouring at a steep angle, stop when the bottle attempts to aspirate (air is sucked back into the bottle, making a 'glug' sound; very dependent on the size of the bottle opening and liquid's viscocity; might be a couple of tablespoons to a half cup)

Solid powders/granules

• dash : a shake or two from a container w/ a restricted top (eg, a shaker top on spices)
• pinch : what you can pick up between your thumb and one finger (note: dependent on what you're picking up; you can pick up more flaked salt than fine salt in a pinch)
• heavy pinch : what you can pick up between your thumb and two fingers

Misc

• smidge : very small, but I have no clue. I typically use a dash or a pinch.