Idle Time

Converting to metric

First let’s get rid of all these messy cup-and-tablespoon measurements.

I’m going to use the US culinary definition of these units:

• 1 cup = 240 milliliters
• 1 tbsp = 15 milliliters

There are other definitions, even within the US (because of course there are), so don’t go running to your handiest conversion app or search engine or natural-language assistant gizmo. If you want to convert some number of tablespoons, multiply it by 15. If you want to convert some fraction of a cup, multiply it by 240.

That gives us our first revision of the table:

You shouldn’t use volume measurements for dry ingredients (particularly powders like baking mixes), but this helps us get a sense of the inconsistency within each ingredient.

To make twice as many cookies, we should use twice as much mix. For six cookies, we’re directed to use 1 cup (240 ml) of mix; arithmetic tells us that twice as much would be 2 cups (480 ml). But the tub tells us to use 1+³⁄₄ cups, which is 420 ml!

If we go all the way up to 24 cookies, the tub says to use 3 cups of mix, which is 720 ml. But we’re making four times as many cookies as when we were using 1 cup of mix. Shouldn’t we be using four cups?

Converting to grams (and tbsp)

As I mentioned, dry ingredients (especially powders) should use dry measurements, so here’s the same table given by weight. The nutrition label on the tub defines one serving as 2.5 tbsp or 25 grams, so I’m setting the conversion factor for the mix to 2.5×15 = 37.5 ml = 25 g.

As for the other conversion factors: A pound of butter contains 453.6 grams of butter* divided into four sticks. Each 8-tbsp stick is half a cup (1 cup = 16 tbsp), and 1 cup = 240 ml, so 120 ml = ^453.6⁄₄ g = 113.4 g. And water, famously, is 1 gram per milliliter.

That gives us the following table:

Having all the numbers in the same units lets us work out the ratios easily, and see that they are all over the place.

But realistically, I don’t measure butter in grams. I measure it in sticks, or eighths of a stick, which are also called tablespoons. It just so happens that 1 tablespoon (¹⁄₈ stick) of butter is 1 tablespoon (15 ml) in volume, but for butter-measuring purposes this is a coincidence that we can safely forget.

So here’s that version of the table:

Here we run into another problem, or perhaps symptom of the larger problem—the amount of butter for 12 cookies, ¹⁄₃ cup, isn’t a whole number of tbsp. For that matter, I don’t know of a good way to measure one-third of a cup of butter, except maybe to melt it. Another sign that the 12-count directions are particularly screwy.

Analyzing the ratios

Let’s start with a graph of the proportions within each recipe variant:

Those segments should all line up neatly.

The 4- and 8-count recipes have the least proportion of mix, while the 24-count recipe has the least proportion of butter. 6- and 12- have more mix and butter but less water (which isn’t necessarily a good thing, since the dry ingredients—particularly flour and leavener—need water to activate).

Note that this graph gives the proportions within the total mass of the ingredients. Put a pin in that.

My armchair analysis

My first approach is to simply take the 24-count recipe as definitive. The company gives all the amounts in cups and tablespoons, and scaling down with those units (particularly tablespoons) runs into precision issues where you end up with oddball fractions that you might not have a measuring spoon for. You’re not going to run into that as much when scaling up: 1 tbsp becomes 2 tbsp, or 3, or whatever.

Consider the water: The 6- and 12-count recipes use the same proportion of water as the 24-count recipe. The 12-count uses half as much water and the 6-count uses a quarter. But the 8-count recipe, which should call for 1+¹⁄₃ tbsp, settles for 1 tbsp. (Not even 1.5!) It’s certainly possible to measure 1+¹⁄₃ tbsp (it’s 1 tbsp + 1 tsp, or 50 ml), but perhaps they chose to fudge the measurement rather than explain that.

So we could assume that any fudging happened when they scaled down and ran into inconvenient units, and the 24-count recipe is definitive.

I get that they’re trying to make this “easy”, but baking is not a practice that rewards being loosey-goosey with measurements. I can’t tell you what the best proportions are without trying every combination, but I can at least try to reverse-engineer what the directions are supposed to be.

Anyway, here are the measurements based on the 24-count recipe, scaled down to each of the batch sizes from the original table.

Oops. We’re back at thirds of a tbsp of butter again. That won’t work. (We could round to 1 tbsp and 3 tbsp, but then we’re messing with the ratio again, just like Betty Crocker did.)

Another approach would be to analyze the variations between the different quantities and look for patterns to try to select a stable ratio.

Let’s start from the 24-count row for now. That makes the variation on that row zero by definition. For the rest, variation is defined as scaling the 24-count to the desired batch size, taking that as 100%, and dividing the measurement called for on the row by that scaled measurement. That is to say: How much more (or less) of each ingredient does the smaller recipe call for than what is proportionally expected based on the 24-count recipe?

Well then. Some pretty clear patterns do emerge:

• Most of the variants use one-third more mix than the naïvely-scaled amount from the 24-count recipe.
• The same variants that use one-third more mix also use one-half more butter.
• Two of them use 50% more water, while one (6-count) doesn’t adjust the water at all(!).
• Smaller variants aren’t as much smaller as you might expect—most of these add about one-third more total mass! (This is why these variations weren’t visible in the graph earlier, which was proportions of the total mass.)
• The 4- and 8-count variants win a majority vote, as they both agree on how much more mix, butter, and water to add.

With these findings, we can make an adjusted recipe based on the smaller variants, particularly 4- and 8-count. I will make one change: Increasing the water by ¹⁄₃ (matching the mix) rather than ¹⁄₂ or 0. So, increasing the mix and the water by ¹⁄₃ each, and the butter by ¹⁄₂.

Once again translating the box directions to metric:

• For regular muffins, “about” 45 ml ×12 = 540 ml
• For mini muffins, “about” 15 ml ×48 = 720 ml
• For jumbo muffins, “about” 80 ml ×6 = 480 ml

Notice how much easier it is to work out how much batter is used on each row when everything is in one unit? And now it’s immediately obvious that two of these can’t possibly be right!

We already know that the regular muffins’ dosage is wrong because I found that out the hard way. If we plug in the amount I ended up using, we get:

• For regular muffins, 60 ml ×12 = 720 ml

We already know that amount is right because it perfectly depleted my mixing bowl and produced well-sized regular muffins, so we can infer that the mini-muffins row is right as written.

80 ml (¹⁄₃ cup) for a jumbo muffin is not a whole lot more than what I used for a regular muffin. Moreover, I went and looked up a jumbo-muffin tin, plugged the listed dimensions for its wells into an online volume calculator, and came up with 231 ml for the interior volume of each well. If we assume that each of those wells should be half-full**, 80 ml is not nearly enough!

Working backwards from our total amount of batter, 720 ml ÷ 6 = 120 ml (half a cup, rather than one-third). That certainly crosses the halfway threshold on that jumbo-muffin tin, so that’s another reason to think that’s right.