How much is "a ladleful"?

Every sourdough starter has different characteristics, a ladleful of one will give a different result from the same amount of another. The recipe is right in that there's no way to say what result you are going to get, so why be exact.

The point I would make is that you want repeatibility, and the capability to adjust your amounts over time to suit your taste. So whatever you use to get it out (ladle, spoon, measuring cup, hand) I would weigh and record how much starter you use, you can add more or less and see how you get. As long as you keep using the same starter you can adjust to your taste.

Yes, ladles differ in capacity. My advice, just use whatever ladle you happen to have. If it were critical to the success or the edibility of the resulting food, the amount would hopefully have been specified a little better. Cooking is regarded by many common people as an art or practical activity, not an exact science (more like dancing than "coding"), so some recipes refer to imprecise quantities e.g. a handful, a few, a little bit of, a pinch (although I think I have heard of some folks trying to quantify that one), "to taste", or a "dusting". I have a hunch "ladleful" is one of those.

A typical US kitchen ladle hold 1/2 cup. I just measured mine to check my memory. It's not marked, and there are plenty of more or less fancy serving ladles that are likely to be different. So that gives you a ballpark.

If a recipe says 'a ladleful', it is sending you, I think, one of two messages. Either 'this is not an exact process (see answer by GdD for some reasons why in this case)', or 'this is not a very carefully written cookbook.'

There are people who produce repeatable results with sourdough. So, this suggests that either a carefully-maintained culture will produce a consistent result for a consistent quantity, or that there's more to learn about how to adjust.

I would suggest use your intuition and go by it. Since you have read the recipe and know it well and its ingredients, you know how much to use a particular ingredient. For ex, spices would have been definitely mentioned as a teaspoon and salt may be in a tablespoon etc. If it calls for water or stock, then ladleful may have been mentioned. And it's ok if its a little less or more. It will not affect the quality of the dish much. Analysis how much of a particular ingredient will suffice the dish. Try will little quantity and gradually increase in case you are not sure. It should turn out well. All the best.

Sourdough is a living organism, so the results of using it cannot be replicated by just specifying amount of starter, time and temperature. Moreover, if you use sourdough more often, you will use a small portion of the current dough as starter for the next one, so quality of the starter will not be constant. More important than measuring the amount is to judge the outcome: Did the dough raise enough? Has the surface the right feel? Texture is difficult to communicate, and the result you aim for depends on your taste, so the first time you use sourdough you should repeatedly touch the dough while raising, and note how the texture changes. This changing sensation is what you have to look for. Then you do a few experiments which tell you what texture gives the taste and fluffiness you are looking for, and then you can produce consistently good bread.

Both of my ladles measure 1/3 cup.