Probabilities and priors
How a maths theorem defines brand and product recognition

While on vacation, I finished reading the book ‘Everything Is Predictable – How Bayes’ Remarkable Theorem Explains the World’ by Tom Chivers. And yes, you may question my choices of books, but I have to admit it was a fascinating read! Especially since, by the end, it also explains how our brain interprets the world, including recognizing our favorite brands and products in the supermarket…

CONTENTS: False positives | Our lazy brain: predictive processing | The predictive processing of a Coca-Cola can | Studies on color: different prior! | Why is this important? 
Originally published: 16/08/2025 – Last update: 16/08/2025

Everything is predictable, it might sound like a firm statement, but adding just one more thing makes sense: everything is predictable, with a certain level of probability. Because that’s what it’s all about: probabilities. How likely is it? This is the famous p-value in scientific papers (how probable is it that the results found are random). That’s the ‘false positives’ when, e.g., doing a cancer test. And, guess what: we can handle the simple probabilities (when you’re going to toss a coin, it’s a 50/50 chance it will be heads up), but when it becomes a bit more complicated, we’re not that good at it… Even though our brain uses probabilities all the time, it’s how our brain processes information, it’s the basis of ‘predictive processing’. Which has a significant influence on how we deal with brand colors…

False positives
But let’s first look at an essential one where many go wrong: false positives when being tested for a particular disease. And getting this right can be life-changing. Testing positive will have a significant impact on someone’s life, necessitating more tests and possibly even therapy. It’s essential, especially since the math behind these false positives is often misunderstood…

Before doing the math, I should explain that the rate of ‘false positives’ is a ‘prior’ (prior knowledge) influencing the probability. It is information we know before assessing the probability. And that’s information we should take into account. A prior is also information that can change, based on new knowledge (e.g., I’ve seen the Kellogg’s ‘red’ change over the years, from vibrant red over magenta back to vibrant red). Now, false positives are something we are not good at. In a 1978 study at Harvard Medical School, they asked 60 medics a question involving false positives, only 11 (!) got it right…

So, back to the real math, and where many of us go.

If there is a disease that affects 1 in 1000 persons, and the tests have a 5% false-positive rate, what are the odds that you have the disease when your test turns out to be positive?

The shortcut our brain will make is: 5% false positive, so if I test positive, there is a 95% chance that I have the disease. But that shortcut is wrong, very wrong.

Let’s check it step by step.

• Out of 1 million people, 1000 will have the disease, 999.000 won’t.
• Of those 999.000 that do not have the disease, 5% will have a false positive result, that’s 49.950 persons testing positive.
• So we have 49.950 (false positive) + 1000 (real positive) = 50.950 people who tested positive, but only 1000 are real positives.

Meaning: if you tested positive, there is a close to 2% chance that you have the disease (1000 people who are positive / 50.950 who tested positive). Which is VERY different from what the 95% shortcut told our brain…

(BTW, if you want to read more about this, check out this blog post, and the calculation above didn’t take into account false negatives, which also exist)

Our lazy brain: predictive processing
As you can see from the example above, our brain initially takes shortcuts, the real calculation takes time, meaning it consumes more power. And as you may already know, our brain consumes a lot of energy… About 20% of the total energy consumption of our body while at rest, despite only representing about 2% of our body weight.

Over the ages, our brain has developed various tricks and shortcuts to keep its power consumption within reasonable limits. And one of those tricks is called ‘predictive processing’. Guess what: this is based on probabilities! The final chapter of the book was dedicated to how our brain uses probabilities to conserve energy.

To illustrate how this works, let’s examine how we process visual information, such as when shopping. You might think our brain acts like a camera, taking a ‘picture’ of the scene and then analyzing that complete picture. But that does not seem to be the case…

When shopping, we usually know upfront what we need: a can of Coca-Cola. That’s a prior. And in our brain, we have a mental image of what a can of Coca-Cola looks like. That mental image contains different elements that identify the product we want to buy. Which, of course, includes the color, but that’s not an Lab value, it’s a more rough description, like a color category. We know Coca-Cola should be red, but what exact red, people do not agree on. The most popular color in this test, was 4 dE00 from the real Coca-Cola red. The one that was 9 dE00 different was picked about the same number of times as the correct one.

If you need a very detailed description of a product, a logo, you will need a brand guide, like the one described by Project BBCG – A Better Brand Color Guide. But that kind of detailed description is not needed as mental image, not even the color description. Just think of the color of the shoes you are wearing at this moment, or your car: you will have a perfect mental image of those, but to what level of detail, within which dE00,  can you describe the color? 

So, when shopping, our brain uses a top-down approach: it takes that mental image of a can of Coca-Cola and then checks the visual information provided by our eyes to see if there is something in there that looks more or less like that mental image. When the processed information reaches a certain probability, our brain will say: “That’s it!”, and instruct our hands to grab it. A perfect example of this is my 10 dE00 mistake a few years ago, when buying breakfast cereals… The probability threshold was in that case likely too low, or the mental image was not detailed enough.

Color is of course an important part of that mental image, that prior. But to what extend? Is it color as in a specific Lab value? Or color as in a color category? Or in between? Some people selling color solutions might argue it’s an Lab value and only a 2 or 3 dE00 in print production should be tolerated, otherwise that will not reflect the mental image and therefore impact sales, negatively of course. However, after checking a lot of studies on the importance of color on brand recognition and sales, I still haven’t seen any study proving that point. The studies that are out there, talk about color in a more general way, like in color categories, not in Lab values and dE00 devations. For many years I have been asking people that are promoting that 2 dE00 tolerance to show me a study that proofs this, I still haven’t seen one. Also when talking to people from outside the printing industry, they say they don’t really care, as long as the quality of the product itself is OK. The perfect example is one of my colleagues, who often takes breakfast at the office. When he recently had bought a new box of cereals, I asked him if he had noticed something about that box. “I guess something with the color?”, he answered (yes, he knows me well). “It seems the color quality of the package isn’t the same as usual, but you know, I like these breakfast cereals a lot, so I did buy them.” And for the record: he is very picky about a lot of stuff, his home is minimalistic with every detail perfect in place. ‘Looking a bit different’ isn’t really a danger to brand loyalty, as this study with consumers already has shown.  And that famous quote that color enhances brand recognition by up to 80%? That’s on the use of color versus black and white, in newspapers. It’s not on color deviations.

Even though the absence of proof isn’t the proof of absence, I do see a lot of anecdotal evidence supporting the contrary. What I did see in real life, while shopping, is brand colors not being consistent to a 2 dE00 level. Not only due to printing errors, but also by design: Oreo, e.g., changed its brand color, with just over 10 dE00 between the old and new brand color. Even though both design were used side by side for some time nobody seemed to notice (no public outcry, only a very few articles on this change), nothing seemed to have happened? There is no mention of Oreo sales plumetting in that time frame in the public financial information, Oreo even showed a gain in market share in some regions during that period. And when I posted about this on LinkedIn, many comments showed that they didn’t care.

Below is an image from last week, do you know which brand that is? And what is the brand color of that breakfast cereal brand? 

Or what about the 11 dE00 difference in adjacent Dallmayr packages, where nobody called it a nightmare? If this difference would impact his sales in any way, would a shop owner put these next to eachother? Wouldn’t he just put them in different places in the shop instead of putting them side by side? And just look at the image below of the different Coca-Cola cans, some of them having – in Lab terms – a rather different color, but I still recognized it as Coca-Cola. Because from a more abstract point of view, it’s the same color category: vibrant red. 

While shopping, the mental image of a can of Coca-Cola is just one example of a prior that will play a role in the predictive processing. There are also others involved. For example, if you often go to a particular shop, it becomes a trusted place, that is prior knowledge. Based on that, your brain will conclude that there are only genuine products in that shop, lowering the probability threshold to state a product is the one you want to buy. Also, the aisle and the place on the shelf is prior knowledge: it’s usually the same spot, over and over again. Meaning: if that can of Coca-Cola is in the ‘right’ spot, your brain will be very fast concluding that the can you see, is a genuine one if it looks more or less like that mental image. One-tenth of a second, as studies with eye-tracking have shown. So, shopping is priors and predictive processing in action.

The predictive processing of a Coca-Cola can
Now let’s take a look at how that predictive processing seems to work in real life.

First, I asked several AI engines to create a sketch of a Coca-Cola can, as a representation of that mental image we have of such a can. This image above was, in my opinion, the best fit for my mental image. But your mental image might look a bit different.

To check how close a real can of Coca-Cola needs to be compared to that mental image, I took some samples from my collection of Coca-Cola cans. And as you will see, designs and colors can be quite different… Our brain doesn’t need a close to 100% match to that mental image to decide to buy it or not. As soon as the product in front of us is close enough to that mental image, our brain will say it’s OK to buy it. Just check the Coca-Cola cans below – all genuine ones – and guess how close they are to my, or your mental image…

To name a few differences between the real-life cans below:

• usually the name is horizontal, but in some cases, it is vertical
• the original can was only the logo, but over the years, there have been many different variations, adding extra text, extra images (e.g., a Santa in wintertime, which is BTW another prior: it’s winter, so it’s OK to have a Santa on a package)
• the Coca-Cola red can be different, sometimes it was closer to orange, some are even a tiny bit towards magenta, some are lighter, some are darker
• sometimes the ink is opaque, sometimes it’s transparent (depending on the material used), which delivers a very different visual impression, that transparent ink does not have the same intensity as the opaque one.
• the size of the cans: it switched from low/fat to high/sleek, plus most of the time it’s 33 cl, but sometimes also 25 cl, or even less (I did not include the smallest ones in the picture below)
• but what surprised me the most, is the ‘swirl’ (officially: ‘dynamic ribbon’). In my mental image, that’s part of the logo, so I was really surprised when I noticed that this was only shown on a few of the cans in my collection…

So, we don’t need a close to 100% match compared to the mental image we have of a product, a package. If the probability is high enough to think it’s genuine, we will buy it. If that were not the case, we wouldn’t have the ‘personalized’ bottles these days, with different names on them… And the same applies to the brand color. As shown in this study, we are pretty tolerant of what ‘Coca-Cola’ red should look like (a red that was 4 dE00 different from the real one, was trusted by almost everybody, even the 9 dE00 different red was trusted by 3 out of 4 participants). And look at the different colors in the picture above… BTW: that mental image is flexible and can change over time, based on new information, like, e.g., a slightly different design, or sligthly different color, like in the case of the Oreo redesign.

For the record: that image of Coca-Cola cans was taken with a Sony A7R III, using the ‘pixel shift’ option (which I reported on in this article). That option gives a better color rendering, which was necessary in this case.

Another example Dash, a P&G laundry detergent. Their signature color has always been blue, but since last year I guess, this is often shifting towards purple. The first time I noticed, I went to that same shop a few times that week. And the second time, there were less packages on the shelves, just like the third time. The fourth time, the shelves were again full with Dash packages. The only scenario where that is possible, is if consumer did buy those (purple) packages… The image below is one from last week, where both blue and purple packages were mixed. Both boxes under the orange arrow are the same variation of Dash, the only difference is the number of pods in the package. But the top one has a blue background, the bottom one a purple background. 

Studies on color: different prior!
The prior is where shopping differs significantly from studies on color perception I’ve seen.

In studies on color perception, both on Just Noticeable Difference (JND) and Just Acceptable Difference (JAD), people were asked if they noticed a difference, and with JAD, if that was acceptable or not. That was their prior: they needed to evaluate color differences, which means that the samples shown would probably have color differences. With that prior knowledge in mind, the brain started looking for color differences. This is very different from finding the product you want to buy in a shop full of color information. That’s why we need to go beyond JND and JAD when it comes to brand colors. We need studies on the Smallest Actionable Difference (SAD): from what color differences will consumers stop buying a product, in real-life settings and conditions.

A prior for people in the printing industry, for print buyers when doing a press check is brand consistency and print quality, which usually means color quality. That’s why they will take a very critical look at color, trying to find color differences. With print quality as a prior, that’s what the brain will focus on.

Why is this important?
Our brain is not a spectrophotometer that, when taking several measurements, will put exact numbers on a color. Our brain is probabilistic: while shopping, it will use probabilities to check if the product in front of us matches the mental image we have of that product. When the probability is high enough, we will grab it. And that time can be very short: one-tenth of a second in the case of Coca-Cola cans.

That’s also the game that some retailers play with their private brands: their competing products look quite similar to the real brands, trying to trick consumers that use a lower probability into buying their product. The lawsuit from Mondelez vs Aldi, which I reported on in this article, shows this. Based on the images provided in the lawsuit, the brand colors of competing products are for some products around 10 dE00. BTW, the Oreo trademark defines its brand color as ‘blue’.

But the most important conclusion is that the prior of consumers while shopping is very different from the prior when producing and checking the quality of a print job. In the first case, it’s the mental image of the product we need to find, in the second case, it’s the job of finding color differences. Consumers will view packaging and brand colors differently while shopping than print buyers do during a press check. We need to keep this in mind when setting quality requirements.

BTW, the book I’m reading at this moment is ‘Why We Remember’, by Charan Ranganath, a professor of psychology and neuroscience who studies the mechanisms in the brain that allow us to remember past events. This includes tests using fMRI scanning of people performing specific tasks. One of the things he discusses is how close memory and fantasy are in the human brain; that’s why it’s so easy to have false memories. And our brain does work with ‘frameworks’ to remember things, like that mental image of the Coca-Cola can.

Related posts:

And no one called it a brand’s worst nightmare…
(11 dE00 between adjacent packages) Brand colors IRL: the Coca-Cola case My color memory IRL (it’s embarrassing…)