I keep a 100% starter, but Reinhart wants 125%...
So, there it is. I keep a 100% hydration starter. For this multi-step San Fran sourdough recipe of his I've been following and liking, it takes me like, 3-4 days to do.. which is just long enough, I figure. So, i keep a 100% starter, because the math is easy. I have a variable amount of starter on hand at any time, from 10 grams to 90 grams at any time, depending on all sorts of things. Right now, I have 75 grams to spare, and I'm looking to build the 125% hydration starter right now, ferment it for 4 hours or so and then fridge it overnight like this recipe calls for.. but some times, I only have 30 grams, and need to build it up.. I do a 1.5lb loaf a t a time, so I need 172 grams of 125% starter here to kick off the process.. for this recipe. So, knowing I have 75 grams of 100% right now, and 172-75 = 97 grams of extra stuff I need, how do I best convert this to 125-ish percent hydration? This math should be easy, but I can't find the answer anywhere here on the site or in any of my books.. and I'm not smart enough to figure it out on my own. I know if I just split the 97/2 I'll keep it at 100% hydration, and I know I *could* just sorta wing it and add a bit more water.. and I know the 100% hydration of such a large percentage of the starter I plan to add this 97grams of material into is going to throw off the books a lot anyway, but.. really, how do I do it? :)
If you need a total of 172g starter at 125% hydration, divide 172 by 225 (100 'units' of flour and 125 of water). You get 0.764g - that's the weight of each unit in the starter.
Now multiply this weight by the number of units of flour and water that will constitute the starter:
0.764 x 100 = 76.4g total weight of flour that you need.
0.764 x 125 = 95.5g total weight of water that you need.
At the moment you have 37.5g each of flour and water. From here it's simple: 76.4 - 37.5 = 38.9; 95.5 - 37.5 = 58.
So add 39g flour and 58g water to your 75g starter to get 172g at 125% hydration.
You are my newest hero. I will sing your name in praise during the remainder of my starter mixing adventures for the day, and perhaps even for tomorrows, as well. Thank you!
No problem! There's a really good explanation of this at the Wild Yeast blog if you want to reference it in the future: http://www.wildyeastblog.com/2008/04/13/bakers-percentage-3/
but i always think of it as 5 to 4 - 5 parts water, 4 parts flour. I maintain my starter, but whenever i need to convert it to 125%, i just mix a teaspoon of starter with 50g water and 40g flour, a couple of feedings, and there you go
Like HokeyPokey, I think of 125% hydration as a 5:4 ratio (5 ÷ 4 = 125%) and use 9 (= 5 + 4) as my water/flour base part.
Taking 172g and dividing by 9, gives a part factor of 19.111...
So 172g at 125% hydration is:
5 x 19.111... = 95.555... grams of water
4 x 19.111... = 76.444... grams of flour
Converting from 100% hydration is then very simple. Since 100% hydration is 1/2 flour and 1/2 water, take the smaller number (76.444g of flour) and double it to give 152.888... of your 100% starter, which now represents:
4 x 19.111... parts water = 76.444...
4 x 19.111... parts flour = 76.444...
Now just add one part of 19.111... grams of water to create the 5:4 ratio.
Of course, depending on the resolution of your scale, you will have to round a couple of those numbers off.
I usually convert the hydration of a starter a recipe calls during the elaboration feeding prior to mixing.
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For your example, I might do the following ~6-8 hours before I would be mixing the dough:
As a general guide, I like to double the starter in the elaboration phase, so I would divide the final starter amount by 2 to get 86g. I now want to change that number to the nearest one divisible by 9 to arrive at my feeding amount. Just so happens that 90g is close and very easy to work with.
90 ÷ 9 = 10 (part factor)
90g of 125% starter =
5 x 10 = 50g grams of water
4 x 10 = 40g grams of flour
Hopefully the following makes sense:
172g (final starter amount) - 90g (elaboration feeding amount) = 82g (beginning starter amount)
82g ÷ 9 = 9.111... (part factor)
5 x 9.111... = 45.5 (water in 82g of 125% starter)
4 x 9.111... = 36.5 (flour in 82g of 125% starter)
2 x 36.5 = 73g (amount of 100% starter)
73g (100% starter) + 9g of water = 82g (125% starter)
82g (125% starter) + 50g (water) + 40g (flour) = 172g (final amount of 125% starter)
So my elaboration/conversion feeding would consist of 73g (100% starter) + 59g (50 + 9 water) + 40g (flour)
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The fun part of that all that is if you needed to convert to 172g of starter at 80% hydration, which is a ratio of 4:5 (4 ÷ 5 = 80%). So you could just swap the words 'water' and 'flour' and substitute '80%' for '125%' and the calculations would be the same.
I keep several starters, my San Fran and WW at 80% (4:5 ratio) and my Rye at 125% (5:4 ratio). I have become quite adept at multiplying and dividing by 9.