Baker's Math (2009)
thefreshloaf.comCommercial baker here. One place where this kind of math gets really weird is when the recipe uses multiple kinds of flours. We make a loaf that uses three kinds of flour, so this means a recipe will have flour percentages that are less than 100%, but that sum to 100% so the hydration percentage works.
For example, the recipe might say: Bread Flour 80%, Whole Wheat Flour 15%, and Rye Flour 5%. Personally I prefer just treating all ingredients as relative weights, and only convert to bakers math if needed. That is in large part because I wrote the software that is used on the production floor which spits out ingredient weights in grams, and no bakers math needed. It also keeps it simple for the employees, so they don’t have to learn how these ratios work.
I’ll also mention that the absolute best book on bread ever is the Modernist Bread set [0]. It’s pricey, but there are extremely well explained reasons behind certain methods, and debunking a lot of long held beliefs such as the efficacy of the autolyse.
Neat! Im curious - were you in tech before becoming a baker at all, or did you pick up the programming skills to help your baking career?
I ask because I'm always interested in hearing how non-programmers end up programming. I've long held the opinion that we (tech that is) should try to make things more programmable by users (e.g. game scripting, excel, the "citizen developer" world of sharepoint), etc and like to hear how non-tech folks use programming to solve problems.
Oh, I do software by trade. The bakery is because it started as a family business that I helped get off the ground. My background is in B2B payments and construction software. Even though the bakery doesn’t make as much money as software, there’s a whole other world of experience to be gained by running a blue collar business that runs 20 hours a day, 7 days a week. Very very different that a software shop.
But to your point, most ERP planning software for bakeries sucks badly, like really badly. One of the prominent ones you can purchase today runs off a JET database from the 90s, with the “cloud” version just being Citrix access to a VM. but they all seem to universally require you to print out paper every day for every shift, so a ton of people just fall back on Excel (using bakers math) to pan production, daily. My software runs on an iPad that is kept at each station for kind of shift, and it spits out packing sheets and invoices from Quickbooks, and integrates with our delivery route planner. It would be a full time job to be calculating everything from mix quantities to how to pack the final product, without mistakes, 7 days a week.
There definitely needs to be better tools for the lay-person though. None of my staff can make changes to our custom software, but also it is basically impossible to recreate it with low/no-code tools. Hence Excel…
I'm in a basically identical situation to you, except it's my partner's cafe-bakery and I'm probably a few years behind you.
I've chosen to use Odoo rather than roll my own. It's highly customizable and open source. I'm self hosting it and I've written a couple of small plugins so far. I'm finding it pretty hackable. It's built from comfortably boring tech (Python + PostgreSQL backend, Bootstrap + JS frontend). Not perfect by any means (for example there's an annoying split between the paid and free versions, although there are plugins to extend the free version to do nearly everything the paid one can, at least for my needs), but from what I can see it's way ahead of most other similar offerings and there's a big community of developers behind it and tutorials for nearly everything.
It's a decent ERP for a restaurant. I will need to build some bakery specific stuff on top but it's already reducing our workload a lot. Previously my partner was doing the low tech excel sheets and paper receipts method and we're gonna do a slow transition to Odoo over the next 6 months or so.
Besides that, we are trialling Rocket.Chat for Slack style messaging and Outline wiki (Notion clone minus database views) for knowledge management, both free and self hosted.
Odoo is somewhat technical to learn, unavoidably (as with any ERP software). But it's been a good test of the other two to see whether non-technical baking staff can use them. Some of them are very non-technical, internet = Facebook level.
Besides a few teething problems, so far so good. It's a learning experience for me, for sure. I'm staying out of the kitchen mostly but I am studying the coffee side of the business which is lovely change of pace from coding.
I’m always super interested to hear about industries seemingly “neglected” by software. There are so many software product opportunities off the beaten path.
Would you mind sharing the name of that 90s software?
What makes it impossible to recreate with low/no-code tools? It sounds like a relatively standard interface over some calculations which sounds like it should fit.
Amateur baker here. Perhaps the best insight into baker's math is that it depends on a lot of factors: the humidity, the type of flour, how coarse/fine it is ground, protein content, etc. And then it also depends on your technique and skill creating strength and structure. Handling high hydration dough requires a lot of skill and not doing it properly means you end up with a flat bread rather than a loaf of bread. If it doesn't hold it's shape, either your technique is lacking or your hydration is too high (or both). Or you bought the wrong flour. Seriously, look for decent bread flour on Amazon or wherever. Chances are your local super market does not actually sell any flour a baker would be happy to use.
The main point of baker's math is not to have recipes that you can share on the internet which people can then blindly follow but to have a repeatable process that works for the flour you use and whatever level of technique/skill you have.
Say you bake bread with a certain type of flour at a 75% hydration and you had a hard time shaping the dough; next time using the same flour drop the percentage to 70% and you might have an easier time and if you are happy with the bread you stick with that hydration. Or work on your technique. Or both. If you switch flour brand or type, you'll have to figure out the optimum hydration level again. But being systematic about weighing out your ingredients means you can at least repeat it once you get to the optimal ratios.
It’s a small world. One of my friends worked on those books. We enjoyed a few years eating test bread every time we saw them.
Nice, I’d love to have participated in their testing processes. They obviously treated it like a science and questioned a ton of institutional wisdom, and the results were fantastic.
This, at $500, stretches even my credulity, even as a collector of books, lover of bread, and owner of books about bread.
Yeah, it was an investment for sure. But it has allowed us to save a ton of time every day (e.g. save 30 minute on the autolyse), make tweaks to our recipes to match our processes, change our starters (use stiff levain instead of poolish for certain breads), and a bunch of other details. Not needed for the lay-person. For sourdough I’d opt for the Tartine books.
Autolyse probably is not the best example. I have several bread-making books and I don't think a single one advocates for autolyse. Not Tartine, not Forkish's, not Reinhart's. Lots of youtubers and bloggers love it though, no idea why.
Maybe not, but they do look at that one because a bunch of books are totally in favor, and a bunch are either against it or ignore it, so coming up with a definitive answer was a reasonable thing to do. Other examples of time savers would be when to add fats and salts in a dough, and proofing and punching times.
I’d need to double check, but I could have sworn that Tartine did have an autolyse where they have you wait a half hour before adding the salt and last bit of water. I don’t have the book handy at the moment though…
You are correct about the Tartine method. Skipping that step was one of the first customizations I made to their process, and I haven’t noticed any difference.
My bad, Tartine does have a 20 min "rest" step before adding salt.
For normal bread a rest time may be not useful, but there are special purposes when it may be needed.
For example, I make for myself at home a bread that is highly enriched in proteins, by washing the dough before baking, to remove a large part of the starch, up to 75% of it, so that the dough is enriched in gluten (the wheat flour used has a gluten to starch ratio around 1:6, while the bread made thus has a gluten to starch ratio around 2:3).
If a rest time of at least 20 minutes is not inserted between kneading the dough and washing it, the dough is not cohesive enough and the washing detaches not only the starch grains but also gluten fragments, causing a loss of the proteins that are intended to remain in the bread.
It is possible that with a much longer time of kneading the rest time could be omitted, but when the kneading is done manually and you make just one bread for yourself, it is certainly preferable to knead for only a short time, followed by a rest time during which you are free to do other activities.
Maybe you’ve already watched it, but Ragusea has a good 15m video on the topic, which goes over the chemistry and some pros and cons. Basically, it’s a trade off of less work (kneading) in exchange for more waiting. I imagine in an industrial context, it’s more efficient to just toss the dough into a machine.
The Tartine Bread book (as of 2018) explicitly recommends the autolyse/rest period (page 52, with more explanation on page 73).
Read Calvel on autolyse. He's the person who developed the process. While I can't compare his work (The Taste of Bread) to Modernist Bread (not having read those books), he comes at it from a scientific angle, not just as a baker.
Forkish explicitly calls for an autolyze period in most of the bread recipes he presents in “Flour Water Salt Yeast.”
Funny how we will easily spend that on something ephemeral like a phone or vacation but question it for something that will last forever.
Is there a "Modernist Bread Essentials" that summarizes it and is a bit more affordable?
> the Modernist Bread set. It’s pricey...
$625 is not "pricey", it's ridiculuously expensive.
I'm not so sure, I had the same reaction to your comment, but then clicked through; it's a set of five thick books, essentially a history book, two textbooks, and two recipe books, at $125ea. Pricey, definitely, but phrased like that I think not so ridiculous.
Even for 5 books it comes out to $125 per book and you must get all of them.
This doesn't really qualify as pricey.
It compares more favorably with collage textbooks which you could use these as.
Niche books can justifiably command higher prices.
For five books? Have you shopped for textbooks recently (in the last 30 years)?
$625 is a goddamned bargain.
Depends 100% on what you're going to get out of it/them.
Slightly related and maybe useful to someone: I built a "declarative" (sourdough) calculator which simplifies these calculations, or at least reverses the question so you just fill in what properties of the loaf you want. Link: https://breadfriend.com.
In the first sentence on the start page, there's an unnecessary apostrophe in the word "recipes". It's a plural form, not a possessive. Not everyone will agree or care, but this kind of thing can have an unfortunate effect when people come to the page for the first time and form an opinion about it.
Thanks, appreciate it. Fixed!
We call it here in Poland "baker's percentage" - how much ingradients are needed for 100 kg of summed flours.
Eg: recipe for "plain bread" can be:
- 60 - 70 kg wheat flour
- 40 - 30 kg rye flour
- 1.5 - 2 kg yeasts
- 1.8 - 1.5 kg of salt
- 0.x potato starch for keeping loafs unsticked, etc
No water in recipe: a) it's assumed 50% of flour weight (1 liter of water equals to 1kg); b) around 40 years ago cost of 50 l of water was less then 0.01 zł so it didn't show in price calculations.
Very often (in loafs with rye flour) there can be no rye flour addition at all - all rye flour is added as sourdough (water and rye flour, 50-50), amounts need to be adjusted.
Now, for ingradients for recipe in column one we have: 100 + 1.5 + 1.8 + 0.x + 50 (water) what gives 153.x kg of raw dough. But after baking and storing it some water evaporates so total weight of finished product is less then 153.x kg, maybe 135 kg, maybe 128 kg - depends on loaf weight - bigger loaf then less water evaporates. That number is called "efficiency" of the recipe, you can read it in industry standards books for given loaf weight or measure yourself by test baking. It is used to calculate product price/order or ingradients for given order.
That method is industry standard, we try to teach it to a journeymans. If only they didn't have problems with basic %'s... H_2O ? What's that ? NaCl ? Forget it. Seriously, what teachers in basic schools are doing ??
Confectioners do not use that method, they sum everything and substract wastes.
> That method is industry standard, we try to teach it to a journeymans. If only they didn't have problems with basic %'s... H_2O ? What's that ? NaCl ? Forget it. Seriously, what teachers in basic schools are doing ??
Teaching it in such uninteresting ways kids don't remember it. And I'm not surprised based on funding and wages...
I’m surprised how something so basic as learning that baking recipes are ratios of mass makes me feel more comfortable and inclined to try baking than anything ever has before. It’s such a simple concept, and much more approachable to me than I’d expected before I clicked the link.
> learning that baking recipes are ratios of mass makes me feel more comfortable [...] It’s such a simple concept
Yes. Almost all recipes get the presentation wrong by using a mix of units and fractions, e.g.:
1 cup flour, sifted 2/3 cup water 1 tsp salt 0.5 g yeast 1 large eggSame. I was pleasantly surprised by the simplicity of the math and the usefulness of it.
I've always thought of baking as a science and cooking as an art (although both are on a spectrum from art to science).
That’s basically how I thought of it too, but now I think I can kind of understand the science.
For example, let's take a typical formula for French bread:
Flour: 100%
Water: 66%
Salt: 2%
Instant yeast: 0.6%
Total: 170%My brain will not stop telling me that the total is 168.6%.
You get used to it. In practice it makes things very simple! Especially if you have a scale with a % option [0], but even without if you’re cooking with nice round metric weights.
I just chuck some flour on the scale, whack the % symbol, and use the set percentages for everything else.
> You get used to it.
You do. The single most important factor is "what does the dough feel like - how stiff and hard, or how loose and wet?"
The water % captures this in 1 number.
e.g. A 60% hydration pizza dough is much stiffer than a 80% hydration focaccia dough.
Just by seeing that one number, I get an idea of how the dough is going to be to work with.
Yeah, but what you're saying is essentially "I don't need the recipe anymore - I can do this by feel", which is awesome, but who then is the recipe for except people who are trying to learn? Maybe throw us a bone :)
> Yeah, but what you're saying is essentially "I don't need the recipe anymore - I can do this by feel"
I'm really not.
I don't do it "by feel", I measure everything in grams, including water. I hate recipes in "cups" since a cup of flour or salt is not a fixed quantity - it depends on grain size, how hard you pack it down, the weather etc. But 10g salt is a fixed amount.
I'm just saying that "500g flour, 60% hydration" tells me a lot about both how to measure it accurately (300g water), and how it will feel (fairly stiff). It's an accurate part of the recipe, expressed in the fewest numbers.
The % is scale-invariant.
If ambient humidity can affect moisture content of flour, then you have more unknowns than constraints and hydration % is not enough. Doing it by feel would seem to be required to get an end-to-end result.
Yes, though that isn't such a big deal for me, as I'm not in a desert or a rainforest, the ambient humidity here is middling and doesn't vary so much. Minor changes are not very important. Flour gets stored in sealed containers, and compensations for the changes during baking are minor. e.g. the cloth over the dough is moistened during summer. Ambient humidity maybe matters like a 1-2% difference here, not a 10% difference.
I do notice seasonal changes, but that's IMHO more due to changes in ambient room temperature than anything else.
Also, I would say that measuring in grams allows you to notice and more accurately quantify that "it's dryer than usual today for the same quantities - must be due to the ambient conditions that require an adjustment".
He/she is saying something slightly different, not “I like that I can do this by feel without percentages” but rather “I like how, by a quick glance at this percentage, I know something about how that will feel in the bowl.”
60% hydration: firmer, like Play-Doh without the crumbling
70% hydration: softer and maybe a little sticky
80% hydration: super sticky, still kneadable
Really high hydration requires a lot more care, both to stop it from getting everywhere and to get it kneaded enough that it actually rises (if that is even desired)
Exactly that.
it's a single, scale-invariant number that conveys important information. And can be used to weigh accurately.
> Maybe throw us a bone :)
I am often amused in forums like this one, where in one moment we will decry those who who do not learn their tech by fiddling with it, for fear of breaking it - and then in the next breath be afraid of putting a touch too much water in our flour.
The recipe is for yourself so you can remember how to do the same nice thing again.
I just use 80% hydration, it makes things easier and tastier.
Depends a lot of ambient humidity. When I lived in the North of Ireland (rainforest humidity) I always had to vastly reduce the humidity level of every recipe, sometimes by as much as half, otherwise I'd be drinking my baguettes.
So true, I just ruined a rye loaf by under-hydrating it at 65%, but I live in the desert. Lesson learned!
I find it also depends on your flour, even batch to batch (we buy 50 lb bags). Some have higher moisture content and one needs to adjust by a few % even in the same external conditions.
A bit messy though.
For me, anything over 65% usually requires stretch and fold technique, as opposed to a knead. It's not messy at all when done that way.
Think of it as a ratio(+) not percentages so
Flour 100 parts, water 66 parts and so on
(+) because that is what it is
> Think of it as a ratio(+) not percentages so
> Flour 100 parts, water 66 parts and so on
> (+) because that is what it is
It is! But it's a ratio to a standard 100 … and that's literally what a percentage is ("per centum" = "by the hundred").
Think of all the numbers as only having two significant figures
Yeah, the total is wrong. It's not a weird bakers' math total. It's a wrong total.
If you used the formula with a base of 1000 grams of flour, that's:
That adds to 1686g of dough.water: 660g salt: 20g yeast: 6gUsually, bakers allow for a reasonably large margin of error, and they'll also intentionally diverge from a formula based on circumstance or whim. Getting to 1700 from 1686 would take an intentional diversion.
Exactly this. It's this sort of thing that annoys me about recipes in general, but bread recipes in particular.
The article mentions "rounded to nearest gram" but clearly they also round to nearest percent...
If you're working with 500g or 1000g of flour, then to the nearest gram is easily precise enough.
If you're measuring 8g of salt, then yeah, maybe you want 8.0g - to the first decimal point.
If you're going beyond that, then where did you get your scale, how much did it cost, what are the benefits and how do you find using it? Do you tweezer salt grains, for instance?
Don't forget to multiply the result by 13/12
Is this a joke or an advice which could use some more explanation?
A “baker’s dozen” is 13. Presumably so that the baker gets one to himself.
This was a response to an old law where bakers were accused of "cheating" customers by overpricing undersized loaves or intentionally creating giant air pockets in their bread to minimize the amount of converted flour the customer would be getting.
one such source: https://www.britannica.com/story/why-is-a-bakers-dozen-13
That article doesn’t have any sources and I’m hesitant to take it as a primary source. A blog isn’t an encyclopedia, even with the same name.
Also doesn’t pass some cursory thinking. If the law is about loaves being too light or small, how does giving out an extra loaf to people who buy 12 help? Who is even buying 12 loaves of bread when restaurants are rare and refrigeration non-existent? Armies, but then they’re buying even way more.
I don’t know why this needs a backstory. A dozen is a common number for objects because it’s highly composite. Then buy X get 1 free promotions are one of the simplest ways to give discounts. No one has to be the first to do it. It could spread and people could come up with it on their own.
> If the law is about loaves being too light or small, how does giving out an extra loaf to people who buy 12 help?
If the baker gives you 13 and calls it 12, that makes it harder for a greedy baker narrative to stick. It doesn't have to be logical, it's about managing impressions.
> Who is even buying 12 loaves of bread when restaurants are rare and refrigeration non-existent?
The average family used to be the size of a small army. 12 loafs of bread could be eaten in 1 or 2 days if you've got 12 hungry kids and bread is a major component of their diet.
It doesn’t add up that it would just be about managing impressions or controlling a narrative. The fact that there was a law regulating the price of loaves of bread is well recorded. Anyone selling loaves too small but also selling baker’s dozen would be in violation.
I regret trying to say buying a dozen would be uncommon. It’s more that even if they sell a dozen, of course there’d frequently be orders smaller than that.
Bakers were under constant suspicion of cheating customers and the regulations. Adulterated flour was a big concern too, not just loafs too small or airy. To manage their reputations, I think bakers would rationally take any edge they can get.
> Bakers were under constant suspicion of cheating customers and the regulations.
I once found a book of old German jokes and basically every third one the joke's essence was some kind of slander against the town miller.
I totally agree that bakers would give an extra loaf to help their reputation. I seriously doubt this was done as a way to stay in line with the law as the linked article claims.
Loaves weren’t necessarily the same size as we have now. And smaller pastries have always existed.
I suspect part of it was make 13 so if one gets messed up you still have 12 - and usually you don’t lose one so an extra is available.
Kind of like how Denny’s started giving you the thing they mixed the milkshake in along with the shake.
Bread rolls perhaps, not loaves?
But don’t forget, people used to eat _way_ more bread in earlier times …
It's because in older days without modern packaging you could expect one egg to break on the way home.
It’s a reference to a bakers dozen - make 13 so you can taste one and be left with 12.
It’s a joke. A “baker’s dozen” is 13, not the standard 12.
This sounds like Shi’ite inheritance math.
This is also how it works in meat curing, etc world. If I'm making a pork sausage, for example, all ingredient amounts are listed in terms of the weight of the meat.
My Baking experience improved substantially for me when I moved to weighing my ingredients instead of measuring by volume. My voice assistant has also been super helpful in quick conversions from recipes.
I’ve never understood cooking by volume and will reject any recipe that uses it. Especially for ingredients that don’t have a fixed density.
1 cup of flour? I can easily get double the amount in my cup depending on how I scoop it.
1 cup chopped mint leaves… wtf?
1 large potato… kill me! At the farmers market potato’s can come in very different shapes and sizes.
I’m confident enough of a cook to know how much mint and potato I want, but it’s impossible for flour.
My rule of thumb is if the packet describes it in grams, then why should the recipe use volume??
Converting between volume and weight is also senseless for anything other than water.
I guess what you can take away from volume recipes is that the quantities aren't that critical. Usually your recipe will turn out quite delicious even if you get a small "large potato" or an oversized "large egg".
You're right though that you can definitely pack a measuring cup with flour and get more than you intended. Bread can be pretty persnickety too, which is why volume based recipes mention how to fill the measuring cup.
>I’ve never understood cooking by volume and will reject any recipe that uses it.
Here is the secret: recipes are not all that precise. There is no point getting a caliper out to measure the length of a cinnamon stick when the variation between individual people's tastes is already larger than the variation in the (admittedly humorous) "cup of chopped mint leaves." A recipe will come out fine for large variations in input ingredients, if that wasn't true do you think the standard measuring cup sizes would be 1/4, 1/3, 1/2 and 1?
While it’s impossible to know how much the cup of flour weighed at the time the recipe was written, you can start by looking up how much the flour you are using weighs per cup and try that much with the recipe. Then if you feel it needed more flour, make a notation.
> 1 large potato… kill me! At the farmers market potato’s can come in very different shapes and sizes.
Yeah—and what happens if you end up with a large potato the size of a small potato? Then you're completely hosed.
This is how concrete mixes are specified as well, all relative to the mass of cement.
For me the main reason to use bakers' percentage is to design recipes.
Once I have designed the recipe in bakers' percentage I use my handy spreadsheet to convert this to grams for the final recipe.
When you spend some time making bread you get the hang of how things work together. How much is 80, 90 or 100% of water, what kind of correction in % of water I need depending on flour composition, whether you want 2 or maybe 3% salt for this particular bread, how much sourdough starter you want, etc.
I also use large amounts of starter and of very varying composition (wet starters, stiff starters, etc.), so even if I want to repeat the same recipe I may need to adapt it to a different starter.
So this is making the design a very easy process when it would be kinda hard when looking at grams.
I tend to think of this as cocktail math. :)
That is actually the more inconvenient way to do it. Much better is to start with 1kg end product weight and then use percentages of that. Scaling is also easier.
From an outsider point of view, my gut agrees. I mean, wouldn't it be easier to start with the quantity of end product, and go from there (It is just arithmetic to convert anyway, but still, the amount of dough in the end is what you care about, right?).
But I'm sure there's a reason they do it this way instead, Surely we aren't the first ones to think of this obvious alternative. I believe historically flour was big economic concern for bakers, so maybe putting it in terms of the thing that makes the biggest dent in their budget was more convenient.
When you’re using a starter, things get more interesting because you need to account for the water and flour content in it.
It usually doesn’t complicate it too much because most starters are 100% hydration - ie equal mass of flour and water.
Just the other day my wife misread our bread roll recipe and added too much water to the flour. I'm glad, I know bakers math and I'm good at mental arithmetic, so the dough could be rescued easily.
Once when I was a kid I was attempting to make Croissants and I misread a recipe and added 3 Tablespoons of salt instead of 3 teaspoons (and for anyone who doesn’t know the math offhand, I put in 9 teaspoons of salt). Suffice to say, they did not turn out.
When did bakers first start using decimal? Was it always decimal? I'm surprised, since most things I've seen in the "real world" tend to be fractional.
More "baker's units" than "baker's math". It's regular math.
Little question, Why isn’t the total 100 percent?
When adding butter, throw away the formula.
When it comes to Pao Doce (a Portuguese sweet bread), butter is an absolutely necessary ingredient. And unquestionably delicious!
I think people who are downvoting must have misunderstood the joke. The joke is, add more butter. It's like estimating for an engineer, or adding the appropriate amount of salt and spice for a midwestern home cook. You can never ever go high enough. Whatever you were about to do with the butter, just multiply it by 3x and add 50% more on top again after.
(The one weird hack you wish you didn't know about your favorite restaurants' most flavorful dishes!)
Michelin star level mashed potatoes are like a third butter, not even exaggerating.
Similar for cocktails.
Should it not be Bakers' Math?
It certainly should be, as this guy explains https://www.youtube.com/watch?v=wMFGv6wd5Y8
That would be an insult to Mr. Baker.
It’s called abuse of notation as it’s useful in practice but not strictly a percentage.
It's a percentage of a base unit. i.e. the amount of flour used is 100% of the base unit amount.
Sounds like you want the total percentage which is just as easy to find. Given their example, the total is 170%. The proportion of flour to the total is 100%/170% = ~59%.
Think of it as a "separation of concerns". Using a base unit allows you to measure without regard for the other ingredients. Expressing it in percent allows you to scale a recipe without regard for the literal amounts. It's a good system.
Ever write CSS with "rem" units? It's the same idea.
Doesn't it all depend on the implied subject of the percentage? If you're thinking in percentage of total ingredients in the bread, then yes maybe it's an abuse of the notation. But I believe the intent in this case is to express each non-flour ingredient as a percentage of the weight of the flour. In that case it's a genuine percentage relationship.
What’s the abuse here? This seems like ‘math’ to me.
Abuse of notation is incredibly common in mathematics, there’s no conflict there.
The abuse would be if you think that percentages should always refer to portions of the whole. Not sure that’s correct, though.
I don't know that I'd use the term abuse, but the basic idea is that there are things called odds ratios (Bayes' theorem looks especially convenient with them!) as distinct from things called probabilities... The distinction is precisely this one, that probabilities are implicitly normalized to 100% total while odds you're supposed to sum everything together and divide.
And then the point is just that we typically condition people to treat percentages as probabilities rather than odds. So you would have said something like 50:33:1:0.3 in “odds speak” for flour:water:salt:yeast in the dough mixture discussed in OP. But bakers instead communicate “:66:2:0.6” with the first number always implicitly being 100 (great), and they then use the % symbol (slightly confusing).
Because they never say “flour: 100%” an unsuspecting novice might think that a 60% hydration dough is ~40% flour by mass, mix this together to form a 150%-hydration mixture, and wonder why the only thing that they can make with it is some sort of pancakes.
Probabilities? Why do you need to bring those in?
Percentages are just a way of writing rational numbers. Bread recipes are expressed effectively as 1 part flour to n parts of each ingredient. But since n in that formulation is usually a value less than 1, expressing that number as a percentage is convenient. Percentage notation seems completely appropriate for this usecase.
So 60% hydration means 1 part flour to 60% of 1 part water, i.e. to .6 parts water.
As in it goes against the designed usage (where total is 100%), but it still works.
The total ingredients being 170% can be found confusing initially. I'm glad the author provided more context and the example of a 500g flour recipe.
Why does the total have to be 100%?
Do all fractions have to add to 1?