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The False Rejection Rate: The Importance of FRR & FAR Rates

The False Rejection Rate: What Do FRR & FAR Mean? — RecFaces

One of the main drivers for interaction between digital technologies and end-users is convenience. Yet, in many fields, such as business and government, security and the accuracy of identification and authentication are of equal importance.

Which indicators determine the convenience and safety of biometric security systems? Is there a factor that impacts them both? How can you upgrade your own security methods using biometric technology? Learn more in this article.

Table of Contents

What is the False Rejection Rate (FRR)?
What Is the False Acceptance Rate (FAR)?
How Do the FAR and FRR Impact Each Other?
Threshold FRR & FAR
Does the Biometric Reader Type Affect the FRR?
How FRR & FAR Affect Security Levels?
Is it Possible to Compare the FRR & FAR of Different Biometric Systems?
How do you calculate the false rejection rate?
What is the equal error rate?
What type of error is false acceptance?
What metric provides the best way to evaluate the performance of a biometric authentication system?
What is FRR in security?

What is the False Rejection Rate (FRR)?

One of the tasks of a security system is the recognition of unauthorized users trying to gain access. The flip side of this process is the likelihood of incorrectly identifying an authorized person as an impostor. When a security system fails to recognize an authorized user for who they are, false rejection occurs. The user receives a false negative outcome. In other words, a false negative is a false rejection. The less often this happens, the more convenient a security system is for a user.

The named indicator is reflected in the specification called the false rejection rate (FRR).

The rate is expressed as the percentage of attempts resulting in this outcome. For example, if the FRR is 0.02%, one in every 5,000 authorized users will not be recognized they try to gain access.

What Is the False Acceptance Rate (FAR)?

When the biometric security system recognizes an unauthorized person as a legitimate user, a false acceptance error occurs. In the binary system, this outcome is referred to as a false positive. That is, a false positive is a false acceptance. FAR, or the false acceptance rate, serves to indicate how prone the system to similar errors. It is measured by the number of false-positive recognitions divided by the total number of identification attempts.

How Do the FAR and FRR Impact Each Other?

The rates of false rejections and false acceptances have a single point of intersection. The coincidence of percentage indicators at this point indicates the equality of the rates. Such a point is named the equal error rate (EER). This algorithm predetermines the threshold values of the rates.

Ideally, the EER indicator should be zero, which means that FAR and FAR are also equal to zero. In practice, this is unattainable. Nevertheless, it is possible to achieve a compromise with contactless biometric smart cards.

Threshold FRR & FAR

A biometric recognition system can operate with two different models. The first, identification, requires the training of the system with the patterns of multiple individuals. When comparing pattern and template, the level of similarity is measured to compile the output of the need for rejection. The verification model suggests the reconciliation of biometric data with an individual's template.

This is where the level of similarity required for access to be granted is determined.

In both cases, there are certain thresholds that the system relies on. When evaluating the similarity, scores are used. In order for access to be granted, these identification or verification scores must exceed a certain threshold. However, this mechanism does not provide for one hundred percent reliability in practice, and errors occur.

Both the impostor's and the client's scores are distributed around a certain mean score.

If all impostor patterns are falsely accepted, the value of FAR is one, and if none of the impostor patterns are accepted, then FAR = 0.

The graphic on the left shows the FAR values for the score distribution for the varying threshold.

In turn, the FRR is also measured with a range between zero and one.

The choice of the threshold value becomes problematic if the distributions between the client and the impostor scores overlap.

Does the Biometric Reader Type Affect the FRR?

The characteristics of the biometric reader used can affect FRR levels. After connecting the reader and installing the software, an enrollment template is created for each individual, which the biometric system works from. It is desirable that the quality of this template be high enough to reduce the FRR problems associated with matching biometric scans with templates. There are other important considerations as well. For example, the results of a fingerprint scanner can be influenced by characteristics of different origins, from ethnicity to the cleanliness of a person's hands, which can lead to an increase in the FRR.

To create a biometric system template, a finger or palm vein scan can also be used. When using vascular biometric technology, identification accuracy increases, but it is also not ideal.

How FRR & FAR Affect Security Levels?

FAR and FRR are in a state of equilibrium. If you lower the FAR, the FRR level will rise, and vice versa. The false acceptance rate is responsible for security, while the false rejection rate is related to convenience for the end-user.

Ultimately, you will have to decide which is more important, usability or security.

The move to biometric security can be beneficial in many areas such as workforce management, POS, access control, and membership management. When choosing a suitable type of biometric reader, the following points should be analyzed:

  • Worker demographics;
  • Age range of persons who will use the reader;
  • Physical environment in which the biometric reader will be used;
  • Planned number of persons registered on the system.

With this data to hand, you can study the types of biometric readers available and their features to choose the one that will provide the optimal level of convenience and accuracy.

Is it Possible to Compare the FRR & FAR of Different Biometric Systems?

Long story short — no, there is no exact comparison. The bottom line is that even if you have FAR data from two different systems, they are not meaningful without specifying the FRR data of each biometric system. The system may have one rate at a very high level and another incredibly low. Moreover, even given the known data for both rates, it is impossible to decide that one system will perform better than the other.

At the moment, however, there are certain protocols and test sets, such as the FERET and the XM2VTS databases for face recognition evaluation. But even with this fact, which holds true for some biometric modalities, it is difficult to compare systems with different fundamentals like face scans or fingerprint scans.


Nowadays, decision-makers are increasingly concerned with the specifics of a new technology before they implement it in a company. The shift to biometric technology can benefit people in many ways.

Key points to bear in mind:

  1. A biometric security system is based on several rates and mechanisms, such as patterns obtained from the analysis of biometric data;
  2. If a certain level of similarity in a pattern that is being identified is not reached, the pattern is rejected by the system. And if, during verification, the data match the template, access is granted;
  3. In both cases, errors are possible, which is reflected in the FAR and FRR indicators;
  4. However, it is not enough to know just the practical value of one FAR indicator since it is inextricably linked with the FRR;
  5. There is no way to single out one superior biometric reader, but you can pick the one that best suits your organization;


How do you calculate the false rejection rate?

When the security system fails to recognize an authorized user for who they are, false rejection occurs. The FRR is expressed as a percentage of situations in which are user gets a false negative result. To calculate the FRR value, you need to divide the sum of genuine scores falling below the threshold by the total number of genuine scores.

What is the equal error rate?

The equal error rate is a biometric security system algorithm used to predetermine the threshold values for its FAR and FRR. When rates are the same, the common value is called EER. The lower the equal error rate value, the higher the accuracy of the biometric system.

What type of error is false acceptance?

Essentially, when a biometric security system identifies an unauthorized person as an authorized person.

What metric provides the best way to evaluate the performance of a biometric authentication system?

To assess the performance of biometric security systems, false rejection and false acceptance rates are used. The best assessment method also depends on the combination of these rates. However, there is no ideal security system.

What is FRR in security?

A biometric security system compares the available templates with the individual's data when they are trying to gain access. If a certain degree of similarity is not achieved, a rejection occurs. The false rejection rate can be described as the percentage of identification instances in which authorized users are incorrectly rejected.

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