The Losada Ratio, also known as the Critical Positivity Ratio or Losada Line, was a positive psychology concept originally proposed in 2005 in a paper published in the journal American psychologist by Marcial Losada of the Universidade Católica de Brasília and psychologist Barbara Frederickson of the University of Michigan.

This concept originally received support in the academic community with over 1000 citations (specifically, the positive psychology field) and was promoted in the popular media. Frederickson even wrote a book based on the concept titled "Positivity: Top-Notch Research Reveals the 3 to 1 Ratio That Will Change Your Life by Barbara Fredrickson" and Losada began a consulting business, Losada Line Consulting, as an offshoot. However, it was later subject to scrutiny, resulting in a retraction and general acceptance that it had been discredited.

### Overview of the Losada Ratio

The concept of the Losada Ratio grew out of the work of Losada and Frederickson and was based on the idea that it would be possible to determine a precise ratio of positive to negative emotions that determines people who will flourish versus those that will languish.

Losada and Frederickson used nonlinear dynamics modeling based on Lorenz systems to argue that the ideal positivity ratio fell in the range between 2.9013 and 11.6346.

Their data were based on observations of 60 management teams making strategic plans. They rated comments made by managers as positive or negative, and then related the ratio of positive to negative comments to profitability, customer satisfaction, etc.

In their paper, they described the proposed relation between positive information (P) and negative information (N) and plotted it onto a butterfly-shaped graph:

"The formula connecting P/N to emotional space is P/N = (E − i)b-1, where E is emotional space, i is the initial value of positivity/negativity (equal to 16), and b-1 is the Lorenz inverse constant (equal to 0.375). P/N = 1 when E = 18.66."

Overall, their findings were that there was an ideal amount of encouragement and reinforcement, and that this could be expressed as a positivity ratio. In other words, if a manager were to apply a ratio of roughly 3:1 positive versus negative feedback, an employee would flourish and enter a mindset for high performance.

However, if that ratio hit anything above roughly 11:1, then this would disrupt flourishing. This dividing line is where the term "Losada Line" comes from.

They also discussed how this concept could also apply to marriages and situations outside of organizations.

### Criticisms of the Losada Ratio

In 2011, Nicholas J. L. Brown, a 52-year-old part-time positivity psychology graduate student at the University of East London was assigned to read the paper by Losada and Frederickson. Brown was skeptical of the claims in the paper and felt that the mathematical claims were flawed.

Therefore, he enlisted the help of physicist Alan Sokal and psychologist Harris Friedman, and reanalyzed the data. These three researchers identified various conceptual and mathematical errors in the paper that would invalidate the claims of Losada and Frederickson. They felt that critical details had been left out, the experiments were poorly reported, there were errors in the use of differential equations, and that there was no justification for the interpretations made.

Together they wrote a rebuttal letter in which they raised the following concerns:

- The data used by Losada did not meet the criteria for use of differential equations.
- The parameters chosen were arbitrary, such that if different ones were chosen, this would had led to a different ratio.
- The butterfly graph was not a model of the data but the result of a computer simulation. In other words, the math was assembled to show the fit that was desired.
- The researchers did not understand the implications of nonlinear dynamic data and how windows of ratios would be more appropriate rather than a single ratio band.

In essence, Brown, Sokal, and Friedman argued that the positivity ratio was nonsensical and that there was no reasonable justification for using fluid dynamics (specifically, a model of convection in fluids) to describe human behavior.

### Outcome of Criticisms

Criticism of the Losada ratio contributed to the perception that the field of social psychology was lacking critical thinking and rigor, since nobody had thought to question the claims of the paper, including the journal's peer reviewers. This "romantic scientism," as it was sometimes called, was concerning in that it meant the foundation of positive psychology was being questioned.

For their part, Losada and Frederickson had different reactions to the critique.

Losada originally did not respond to the criticism saying that he was too busy with his consulting business, leaving Frederickson to fend for herself, who eventually distanced herself from Losada.

Frederickson acknowledged that the mathematical aspects of the paper were questionable and that she did not have the expertise to defend them on her own. However, she continued to assert that the empirical evidence was solid as was the notion of a higher ratio contributing to flourishing.

American Psychologist retracted the mathematical components of the paper, rendering the ratio invalid.

Eventually, Losada came forth with more formulas about asymmetric emotional fields and organization viscosity, but these claims were essentially, "too little too late."

### What We Can Learn From the Losada Ratio

What can be learned from this whole mess that is the Losada Ratio?

#### People Like to Reduce Things to Numbers

First, we learned that we like to reduce people to numbers. For instance, how often do you check your weight? Steps walked in a day? Have you ever checked your IQ? It was convenient to have a "3 to 1" ratio to work from, particularly in organizations.

However, this only truly works for the physical world. Human behavior is much more complex and is the result of multiple factors. If there is a critical positivity ratio, it's likely different for each person, because it depends on an individual's mindset, situation, challenges, and past experiences.

#### What Isn't Understood Isn't Questioned

Why wasn't the math behind the Losada Ratio questioned before Brown came along? Likely because the people reading the paper felt they had less knowledge than Losada when it came to understanding how the model was used. If you don't understand something, often the easiest route is to assume that you can trust someone who seems to know more than you.

#### Popular Culture Influences Perception

In the case of the Losada Ratio, it is likely that the popularity of the concept had something to do with why it took so long to be discredited. The concept took hold in organizations and among management; Losada even talked about how he discussed the concept with the president of MIT and vice president Al Gore.

#### A Word From Verywell

Overall, there seem to be two general takeaways when considering the Losada Ratio events. The first relates to where to go from here in terms of positivity/negativity when giving feedback to others, because that is what the Losada Ratio was all about. The second relates to how we can be critical of the information that we consume.

So first—what can we glean about positivity and negativity? If there were such a thing as a Losada Ratio, it's likely that it would differ for each person. This simply means that if you are a manager, you need to get to know your employees and figure out what ratio of positive versus negative feedback works to motivate each person. This could potentially be applied to other situations as well. If you're a parent, you probably know that each of your kids responds to feedback in different ways.

Next—when considering information, we like to think that we can check the source to determine if it's trustworthy. And while usually, this is true, it wasn't in the case of the Losada ratio. This study was published in an academic journal by university researchers and yet it did not have merit.

What this means is that you need to think critically about every piece of information that you consume.

If it's something that is not your area of expertise, don't assume that it's correct because you can't understand it. If something seems off, ask someone else you know is knows more about the topic than you.

While the situation of the Losada Ratio is somewhat of an anomaly in research circles, it highlights the need for continued questioning of what we assume to be true.