When increasing the amount of a single ingredient in bread, how do I calculate how much to increase the others?

Question

I have the bakers percentage formula from a recipe (Vienna bread from Bread Bakers Apprentice book). and the pre ferment came out a bit more than was indicated to be used in the recipe (19.3 oz instead of 13oz)

If the bakers percentages are as follows, how can I calculate how much to increase all the other ingredients to compensate for the extra pre ferment? (Note: I know a simple solution would be to just use 13oz of preferment by cutting away a portion of it, but I kind of just want to use it all up)

pre ferment 108% (13oz)

bread flour 100% (12oz)

sugar 4.2% (0.5oz)

malt powder 2.1% (0.25oz)

salt 2.1% (0.25oz)

yeast .92% (0.11oz)

egg 13.8% (1.65oz)

butter 4.2% (0.5oz)

water 54.2% (6 to 7 oz)

Answer 1

The key is that the percentages remain unchanged - they simply give the various ratios of the ingredients based on the flour weight.

What you need to adjust is the absolute weighs by the same factor you changed one ingredient, and that factor in your case is calculated by the (amount of preferment you intend to use)/(amount of preferment in the original recipe):

19.3 oz / 13 oz = 1,48

So you multiply all ingredients by 1,48 (or 1.5 if you are so inclined) and proceed as usual.

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Note that the same principle applies to scaling of all kinds of recipes that give weights or volumes for the ingredients, because the underlying principle of (ingredients are used in a certain ratio) is the same.