Can't tell you all how much I appreciate all the posts.  I've learned more in two years at the Fresh Loaf  than I learned in twenty years of buying and reading dozens of books on bread, not that I'm complaining about the books.  So many have been great.  I am quite indebted to Amy Glezer, Dan Leader, Joe Ortiz and, of course, the man they used to call Brother Juniper!  Also very grateful for the renegade Charles Van Over, wherever you are!

The following questions have been on my mind for some time.  Someone please help me to put this all to rest!  I have a three-part question regarding what I call "apparent hydration".

First part:

If I create a dough using 500g of AP flour, 300g water, 10g salt and a minimum of yeast, I produce a dough which I recognize as being 60% hydrated, both by look and feel.  I know how it should be kneaded, how it will shape and how it will develop in the oven.

What I don't know is this:  If I add 56g of butter to that same dough, whether at the beginning of mixing or even added to the dough after the gluten is well developed, how can/do I account for the changes the butter brings to the apparent hydration of the dough. If  I add 10% of the flour weight in butter to my 60% hydrated dough, the dough becomes much more sticky and appears significantly more slack.  I appreciate that average American butter has water content in it.  I don't know how much of the 56g is water.  But it seems to me that the "apparent hydrating effect" of the butter addition goes way beyond that little bit of water in the butter.  I am sure that I would find an even greater impact if I were to add 10% olive oil (by weight as a percentage of the flour weight) to a 60% hydrated dough, even though olive oil has, to my knowledge, no water in it at all.

So, does fat effectively contribute in some way to hydration, or at least to "apparent hydration"?  Or is the effect merely conditioning (for lack of a better word)?

Has anyone ever created a factor to account for the effect of fat on dough?  If I want a 60% hydrated dough, with a 10% butter content added or a 2% olive oil content added, to have more or less the same apparent hydration as the same dough without the fat, by how much do I adjust the water content down?  Is there a one to one ratio? Meaning that if I add 56g of butter to a dough but don't want it significantly more slack, should I reduce the water content by 56g?  I think I've tried that and the dough was too stiff.  Is it a 1.0g fat to 0.5g water ratio?  Or has this simply not been studied or quantified?

Have I made myself understandable?  Does Hamelman address this in "Bread"?

Second part:

If I take the same 500g AP flour, 300g water, 2% salt and minimal yeast dough and mix it as a straight dough, I get what I expect in terms of hydration, elasticity, extensibility, and so forth. However, if I mix half of the flour and half of the water as a pre-ferment along with a pinch of yeast, the final dough seems to me to be meaningfully more slack and extensible because of the addition of the biga or poolish..

Don't get me wrong. I don't at all dislike the effects of a pre-ferment on dough.  A poolish is one of the greatest inventions the Poles ever brought to Vienna!

But if I want to make a bagel dough at 60% hydration but decide to create a preferment with part of the ingredients, should I compensate for what seems to me to be the super-hydrative-effect from the preferment by reducing the final mix to something like 55% hydration?  Put another way, does the addition of a poolish allow me to reach an "apparent hydration" of 60% by using only 55% water?  Or is what I am experiencing merely another conditioning effect?

Third part:

Same lean dough but the addition is 10 to 15% white sugar?  I've always thought that adding 50g of white sugar to a formula for a sweet dough is the equivalent to adding 50g liquid to the final formula, even though sugar competes with flour for liquid.  But I've never actually seen this documented.  Again, is there a ratio of sorts to allow me to compensate for the effects that sugar bring to a dough?

So, in summary:

Should formulas adjust hydration to some extent for the addition of fat?

Should formulas do the same for pre-ferments?

Should formulas do the same for sugar?

Best, Bruce