Brioche Lab
What moves together in 217 brioche recipes
When a recipe uses more of one ingredient, does it tend to use more or less of another? For every pair of the 6 ingredient ratios (grams per 100 g of flour), this page ranks all 217 recipes on each and measures how closely the two rankings agree: Spearman's rho, from −1 (the more of one, always the less of the other) through 0 (unrelated) to 1 (always rise together).
15 pairs in all: 4 rise together at rho 0.20 or more, 5 move in opposite directions at −0.20 or less, and 3 are close to unrelated (between −0.10 and 0.10). This describes recipes as they are published; it does not say what changing one amount would do to a bake.
Every pair at once
Read a cell by its row and column. Caramel cells rise together, slate cells move in opposite directions, and the deeper the color the stronger the relationship. Pale cells with grey numbers are not distinguishable from no relationship with 217 recipes (p of 0.05 or more).
All 15 pairs as a table
| Pair | Rho | Strength | p |
|---|---|---|---|
| Butter and egg | 0.69 | strong | under 0.001 |
| Egg and milk or water | −0.64 | strong | under 0.001 |
| Butter and milk or water | −0.63 | strong | under 0.001 |
| Egg and salt | 0.34 | weak | under 0.001 |
| Butter and salt | 0.34 | weak | under 0.001 |
| Butter and sugar | −0.34 | weak | under 0.001 |
| Egg and sugar | −0.33 | weak | under 0.001 |
| Milk or water and salt | −0.23 | weak | under 0.001 |
| Sugar and milk or water | 0.21 | weak | 0.002 |
| Sugar and salt | −0.18 | very weak | 0.007 |
| Salt and yeast | −0.15 | very weak | 0.031 |
| Butter and yeast | 0.11 | very weak | 0.11 |
| Egg and yeast | 0.08 | negligible | 0.26 |
| Sugar and yeast | −0.07 | negligible | 0.34 |
| Milk or water and yeast | −0.02 | negligible | 0.81 |
The three clearest relationships
The strongest pairs that reach rho 0.20 either way with a p-value under 0.01. Each dot is a recipe; the line joins the median of the second ingredient within each fifth of recipes ranked by the first.
Recipes with more butter tend to use more egg
rho 0.69 across 217 recipes · strong · p under 0.001
The third of recipes with the most butter use a median of 57% egg; the third with the least butter, 24%.
Recipes with more egg tend to use less milk or water
rho −0.64 across 217 recipes · strong · p under 0.001
The third of recipes with the most egg use a median of 11% milk or water; the third with the least egg, 41%.
Recipes with more egg tend to use more salt
rho 0.34 across 217 recipes · weak · p under 0.001
The third of recipes with the most egg use a median of 1.8% salt; the third with the least egg, 0.6%.
Also strong, and left out above because both of its ingredients already appear: butter and milk or water (rho −0.63).
What moves on its own
- Yeast. Nearly independent of the rest: its strongest correlation with any other ingredient is −0.15, with salt. A recipe's amount of yeast says almost nothing about its other amounts.
The pairs closest to unrelated: milk or water and yeast (−0.02), sugar and yeast (−0.07) and egg and yeast (0.08).
How the numbers are made
Spearman's rho is the ordinary correlation of the two rankings, so it measures whether one amount tends to rise with the other, in a straight line or not, and a single extreme recipe moves it little. A recipe with none of an ingredient ranks lowest on it. An ingredient fewer than 12 recipes use is left out of the matrix.
The p-value is the chance of a rho at least this far from zero if the two amounts were unrelated. With 15 pairs tested, about 0.8 would pass 0.05 by chance alone even if no ingredient were related to another, which is why the relationships explained above must pass 0.01 and reach 0.20.
Every number is divided by the same flour weight, so a recipe light on flour reads high on every ingredient at once. That nudges every correlation toward positive: part of a positive rho can be flour, not the two ingredients. A negative one holds despite it.
A correlation describes the recipes as published. “Recipes with more butter tend to use…” is a statement about what bakers write down together, not a rule that adding one forces the other. Plot any two ingredients to see the recipes behind a number.