Friday, January 25, 2013


When you've gone to the trouble of collecting hundreds of recipe ratios, it's ever so tempting to call the resulting average recipe ratio the ideal ratio. This would be a mistake and I'll illustrate why with an example. Here's the average ingredient ratio for Swedish Pancakes based on about 200 distinct recipe ratios: 1:3.5:1:0.16 (all purpose flour:milk:medium egg:butter). And here is an ingredient list for 450 grams of batter.


Swedish Pancakes (Pannkakor)

79g or 150ml all purpose flour
278g or 278ml milk
80g, 68ml or 2 eggs where each egg is ~53g
13g or 13ml unsalted butter
1/4 tsp salt

The above ingredient ratio comes with a high level of confidence, statistically speaking, in the sense that if I were to collect another 200 distinct recipe ratios, I would be quite likely to get the same ratio. If you're interested in the actual confidence intervals, feel free to download and run the code.

Even though the Swedish pancake ratio is very stable, it is still not the case that this is the ideal ratio. Take a look at this, very similar, recipe ratio: 1:3.2:1.3:0.3 (all purpose flour:milk:egg:butter).

Swedish Pancakes
78g or 148ml all purpose flour
249g or 249ml milk
103g, 87ml or 2 eggs where each egg is ~53g
20g or 20ml unsalted butter
1/4 tsp salt

Clearly these two ratios are different, and yet the second ratio is also the average of 200 distinct recipes. So what's going on?

The first ratio is the result of 200 recipes written in Swedish, whereas the second comes from 200 recipes for Swedish pancakes written in English. Maybe these differences are due to cultural preferences in taste or accompaniments, although it could just as easily be the influence of TV chefs. In fact the only thing that can be said with any certainty is that average recipe ratios can change depending on the source of the information. The ratios I present here are predominantly from online sources. Perhaps the results would be different if I had taken the ratios from cookbooks. And then again, there would likely be a difference between older and newer cookbooks.

When I first looked at average recipe ratios for crumble, for my own convenience I selected recipes based on weight measurements rather than volume. Although I didn't do a systematic study of the differences, it was clear just browsing through the recipes that both weight based and volume based recipes tended towards rounded figures. I would expect to see marked differences between recipe ratios collected using the two different measurement systems and, coming back to pancakes, this could account for the difference between the Swedish pancake recipe ratios given that most online recipes written in English include measurements in US cups, whereas Swedish recipes are generally given in deciliters.

Let's imagine there is some way to collect recipe ratios in a way that avoids introducing any bias of the kind mentioned above. Could we then obtain an ideal recipe ratio? The answer is still no! Here is an extract from user Athanasius' excellent review of Michael Ruhlman's book Ratio.
[...] That is really where the "ratio" argument falls apart. Cooking and baking are about ratios, but in a larger sense they're about FORMULAS. That is, you have a ratio of ingredients, but you combine things in certain ways (using different mixing techniques, timing, etc.), and then you prepare them by cooking them in certain ways (at certain temperatures, with certain timing, perhaps adding or changing things at various times, etc.). A ratio tells you very little if you know nothing about the rest of the formula and the techniques required to prepare a dish. If "ratio" was the only thing needed, recipes would only consist of lists of ingredients with no instructions.
Does this observation apply to a recipe as simple as pancakes? Indeed it does. On the Seasoned Advice Q&A site I answered a question about the differences between Swedish Pancakes and Crêpes. Here is the average Crêpes ratio: 1:1.97:0.75:0.17 (all purpose flour:milk:medium egg:butter). And again, as an ingredients list for 450 grams of batter,

Crêpes (French recipes)
116g or 219ml all purpose flour
228g or 228ml milk
86g, 73ml or 2 eggs where each egg is 53g
20g or 20ml unsalted butter
1/4 tsp salt

As I remarked in my answer, the Crêpes were a little tougher than Swedish pancakes. What I missed in my analysis is the fact that Crêpes and Swedish pancakes are traditionally cooked differently. Swedish pancakes are made by swirling batter around a frying pan whereas French Crêpes are made on a Crêpes maker where the batter is spread out with a specially designed utensil. It seems reasonable to suppose that Crêpes made using the traditional method would not be as tough as those I made.

Crepes maker
So comparing recipe ratios without reference to cooking technique can lead you astray. This argues in favour of maximising bias! An ideal recipe ratio, if there were such a thing, would be tightly coupled to a procedure for using the ratio. For a thorough investigation into the ideal Swedish Pancake we would differentiate between recipes that use cold butter or melted. And if melted, we would again differentiate between melted butter where the milk solids have been toasted or not. If this gives us an ideal ratio, it is ideal in a very narrow sense.

This last criticism applies equally to recipe ratios arrived at via experimentation or any other means. In conclusion: there is no such thing as an ideal or perfect recipe ratio. So why go to the trouble of finding average recipes at all? I'll answer that question in my next post.

Tuesday, January 1, 2013

Your Average Recipe

As I zapped through the channels a few months back, an infotainment program caught my attention. Members of the public had to guess how many jelly beans there were in a jar, as you might do for the chance of winning a prize.

They asked 1000 people, as I recall, and averaged out the guesses. The average guess was out by only a very few jelly beans. I was amazed, and frankly I still am. It makes sense once you've thought about it for a while, but still it's amazing.

Counting Jelly Beans
Getting back to recipes. There are countless times I've gone online to look up a recipe only to be overwhelmed and somewhat frustrated by the abundance and variety of different recipes available for the same dish. You can't tell just by looking at them which is the best, and you couldn't possibly try all of them to find out.

I wondered if instead of choosing any single recipe, maybe I could average out recipe ratios and converge on the perfect ratio. I set about trying to do this when I tried to answer a question I posted on the StackExchange cookery Q&A site.

This taught me that there is really no such thing as the 'perfect ratio'. It really depends on your expectations, what is traditional, what else you are serving and a bunch of other things. Nevertheless, averaging out the recipe ratio for crumble also produced a pretty damn good crumble, so I kept going and averaged out some more recipe ratios.

At this point it's worth pointing out that there are some difficulties to overcome before averaging recipe ratios. Some are easy to solve, like converting between different units of weight and normalising to a fixed yield. Some problems only have approximate solutions, like converting from liquid measures to units of weight. And then there's an amount of guess-work when, for example, you are confronted with recipes that specifies a number of eggs of unspecified size and you have to decide a weight for them.

I'll be talking more about the many and various problems in finding average recipe ratios, including the software tools I'm working on that help take some of the tedium out of gathering and crunching data.

So now you will understand why the Blueberry Muffin recipe in the previous post is very likely to work, even though I never tried it before posting. The recipe is the average of 23 distinct recipe ratios. I've tried it now and, as I expected, it was good. There are two parts to the recipe: the ingredient list and the preparation instructions. Obviously it is only possible to average the ingredient proportions. The method of preparation comes mostly from a muffin recipe from America's Test Kitchen. Cheating a bit, I know.

Thursday, November 15, 2012

Untried Recipes - Blueberry Muffins

If I were to tell you that I had a great recipe for Blueberry muffins but I hadn't tried it yet, you would have a right to be sceptical. What, then, if I told you that nobody, to my knowledge, had ever attempted it.

Here is a recipe for Blueberry muffins. You won't find it in any cookbook or anywhere except here on the internet. Nevertheless, it's a great recipe: better than most perhaps.  Although, to be perfectly honest, I don't believe anyone, including me, has ever tried it.

I'll explain later. First the recipe.

Untried Blueberry Muffins



  • 331g or 628ml all purpose flour
  • 111g or 110ml butter, melted and slightly cooled
  • 193g or 229ml granulated sugar
  • 106g, 89ml or 2 medium eggs where each egg is ~53g
  • 240g or 240ml milk
  • 10g or 10ml lemon juice
  • 13g or 14ml baking powder
  • 1g or 1ml baking soda
  • 3g or 2ml salt
  • 3g or 3ml vanilla extract
  • 256g or 410ml frozen blueberries


  1. Preheat the oven to 435ºF (218ºC) and prepare a standard muffin tin.
  2. In a small bowl mix the milk with the lemon juice and leave to stand for 20 minutes (no need to wait, you can continue through the steps).
  3. In a saucepan, over a medium-high heat, simmer half the blueberries (128g) together with two teaspoons of sugar until they are reduced to 51g or 54ml.
  4. Take the saucepan off the heat and add the remaining frozen blueberries. Stir them in gently to cool the mixture.
  5. In a large bowl whisk the flour, baking powder, baking soda and salt together.
  6. In a medium bowl whisk the remaining sugar and the eggs together.
  7. Add the melted butter to the medium bowl and whisk.
  8. When the 20 minutes have passed, add the milk that was left standing and the vanilla extract to the medium bowl and whisk.
  9. Add the contents of the saucepan (i.e. the blueberries) and the medium bowl to the dry ingredients and fold in, being careful not to overmix.
  10. Fill the muffin tin and bake for 18 minutes.