The Matching Law in ABA Therapy explains how people tend to distribute their behavior among different choices based on the relative reinforcement available for each option. In simple terms, when two behaviors are available, the behavior that produces reinforcement more often may occur more frequently. Behavior analysts use this principle to better understand choice, reinforcement, appropriate behavior, and problem behavior.
What Is the Matching Law in ABA Therapy?
The Matching Law, associated with psychologist Richard Herrnstein, is a behavioral principle that explains how reinforcement can influence a person’s choices and behavior. It suggests that people tend to engage more often in behaviors that provide greater or more frequent reinforcement.
For example, if one activity consistently provides more reinforcement than another, a learner may spend more time choosing or responding to that activity. In ABA, the Matching Law helps professionals understand how reinforcement affects behavior allocation and choice.
How Does the Matching Law Work?
The original Matching Law focuses on the relationship between response rates and reinforcement rates.
A simplified version can be written as:
B₁ / (B₁ + B₂) = R₁ / (R₁ + R₂)
Here:
- B₁ = behavior directed toward option 1
- B₂ = behavior directed toward option 2
- R₁ = reinforcement obtained from option 1
- R₂ = reinforcement obtained from option 2
The formula may look complicated, but the basic message is easier to understand.
Suppose a learner receives about 70% of the available reinforcement for one response and 30% for another. Under conditions where matching occurs, behavior may be distributed in roughly the same proportion—about 70% toward the first response and 30% toward the second.
Real behavior does not always follow this relationship perfectly. Researchers have identified factors such as bias and sensitivity to reinforcement, and the generalized matching equation was developed to account for systematic differences between behavior and reinforcement.
Why is the Matching Law Important in ABA?
The Matching Law gives behavior analysts a way to think about why a behavior continues to occur.
For example, imagine a child has learned two ways of getting adult attention:
- Asking appropriately for attention
- Engaging in a problem behavior that sometimes produces attention
If both responses are available, the relative amount and timing of attention following each response may influence how often each behavior occurs.
Research has applied matching-law analyses to situations involving appropriate and problem behavior. In one study involving individuals with developmental disabilities, researchers found that the proportional rate of problem behavior relative to appropriate behavior approximately corresponded to the proportional rate of reinforcement associated with those behaviors.
This does not mean that a person consciously calculates reinforcement and then decides what to do. The Matching Law is a way of describing patterns between behavior and environmental consequences.
Matching Law Example in ABA Therapy
Consider a learner who wants access to a preferred toy.
There are two possible responses:
Response A: The learner uses an appropriate communication response to request the toy.
Response B: The learner engages in a problem behavior.
Suppose the environment has historically provided reinforcement more frequently following Response B. The learner may continue using Response B more often.
From a Matching Law perspective, the important question is not simply, “Why is the child choosing the problem behavior?”
Instead, a behavior analyst may examine:
- What happens immediately after each behavior?
- How often does each behavior produce reinforcement?
- How quickly does reinforcement arrive?
- How valuable is the reinforcement?
- Are both response options actually available?
- Is there a difference in effort required for each response?
This broader view can help identify patterns that might otherwise be missed.
Matching Law and Appropriate vs. Problem Behavior
One of the most important applications of the Matching Law in ABA is understanding competing behaviors.
A learner may have both an appropriate behavior and a problem behavior that produce similar outcomes.
For example, a child may:
- Ask for a break appropriately, or
- Engage in a problem behavior to escape a difficult task.
If the problem behavior has historically resulted in a faster or more reliable break, that consequence can influence future behavior.
Research has experimentally examined situations in which reinforcement was arranged for both problem and appropriate responses. Findings showed that relative response rates could approximate the relative rates of reinforcement available for those responses.
This is one reason reinforcement planning matters in ABA. Simply teaching an alternative response may not be enough if the alternative response is less efficient, less reliable, or produces reinforcement much less often than the behavior it is intended to replace.
How the Matching Law Can Inform ABA Practice
The Matching Law is primarily a way to analyze patterns of behavior, but it can also inform how behavior analysts think about competing responses.
1. Look at what reinforces each behavior
A behavior analyst may examine the consequences that follow different responses.
For example, does appropriate communication produce attention while problem behavior produces attention more quickly?
The goal is to understand the relationship rather than assume why a behavior occurs.
2. Consider reinforcement for appropriate behavior
When an appropriate alternative is being taught, the reinforcement arrangement matters.
Suppose a learner is taught to request a break instead of engaging in problem behavior. If the request consistently produces an appropriate break while the intervention is implemented according to the treatment plan, the learner has a clear consequence for the alternative response.
The exact reinforcement procedure should be individualized by a qualified behavior professional based on assessment and the learner’s needs.
3. Consider the effort required
Two behaviors may produce similar outcomes but require different amounts of effort.
For instance, saying “break please” may require more effort than simply pushing materials away. If the appropriate response requires substantially more effort while producing reinforcement less reliably, the learner may continue using the easier response.
This is one reason practitioners consider response effort when evaluating behavior.
4. Consider immediacy
The timing of reinforcement can also affect choice. Research on matching has expanded beyond reinforcement rate to consider other characteristics of reinforcers, including quality and immediacy.
A reinforcer that arrives immediately may have a different effect on choice than one that is delayed, even when the eventual outcome is similar.
A Simple Everyday Example
The Matching Law does not apply only to formal ABA sessions.
Imagine a student has two homework options.
- Activity A is difficult and rarely followed by praise.
- Activity B is easier and frequently followed by positive feedback.
Over time, the student may spend more effort on Activity B.
This example illustrates the basic idea: behavior tends to be distributed in relation to the reinforcement available from different alternatives.
In real-life situations, however, many factors influence behavior. The Matching Law should not be treated as a simple rule that predicts every individual choice.
Matching Law vs. Generalized Matching Equation
You may see two terms when reading about this topic: Matching Law and Generalized Matching Equation (GME).
They are related, but they are not exactly the same.
The basic Matching Law describes proportional relationships between behavior and reinforcement. The Generalized Matching Equation expands this model to account for systematic differences, including sensitivity to reinforcement and bias.
In simple terms:
- Matching Law: Behavior tends to correspond to relative reinforcement.
- Generalized Matching Equation: A more flexible mathematical model that can describe deviations from perfect matching.
These concepts are primarily useful for behavior analysts and researchers working with behavioral data.
Does Matching Always Occur?
No. Matching is a behavioral pattern, not a guarantee that every person’s behavior will perfectly correspond to reinforcement rates.
Researchers have identified situations in which behavior deviates from strict matching. The generalized model accounts for some of these differences through concepts such as bias and sensitivity.
Other variables can influence behavior as well, including:
- Reinforcer quality
- Delay to reinforcement
- Response effort
- Previous learning history
- Environmental conditions
- Availability of competing activities
- Individual preferences
Therefore, the Matching Law should be considered alongside other behavioral principles and direct observation.
Is the Matching Law Used in Autism ABA Therapy?
Yes, matching-law concepts have been studied in applied behavior analysis involving individuals with developmental disabilities, including research examining appropriate and problem behavior.
However, it is important not to interpret the Matching Law as an autism-specific theory.
The principle describes behavior and reinforcement relationships. It can be relevant when analyzing behavior in autistic learners, but it is not a method for diagnosing autism and is not a treatment for autism itself.
A qualified behavior analyst may use behavioral data and assessment results to determine which principles and intervention procedures are appropriate for a particular learner.
What Should Parents Know About the Matching Law?
For parents, the most useful takeaway is simple:
Look at the consequences surrounding behavior.
When a child repeatedly uses one response instead of another, it can be helpful to ask what happens after each response.
For example:
- Does one response get attention faster?
- Does one response reliably produce access to a preferred activity?
- Does an appropriate request require more effort?
- Is reinforcement delayed for the appropriate response?
- Are there competing sources of reinforcement?
These questions do not mean parents should try to conduct a formal matching-law analysis themselves.
Instead, they can provide useful observations to a child’s BCBA or other qualified professional when discussing behavior and support strategies.
Conclusion
The Matching Law in ABA Therapy helps explain how reinforcement can influence behavior and choices. In simple terms, behaviors that receive more frequent or valuable reinforcement may occur more often.
For families, the key takeaway is that what happens after a behavior can affect what happens next. The Matching Law is not a diagnosis or treatment but one concept professionals may use to understand behavior and reinforcement.
Frequently Asked Questions
1. What is the Matching Law in ABA Therapy?
The Matching Law describes a relationship in which the distribution of behavior between available choices tends to correspond to the relative reinforcement obtained from those choices.
2. Who developed the Matching Law?
The Matching Law is most closely associated with Richard Herrnstein, whose research in the early 1960s examined how behavior was distributed between sources of reinforcement.
3. Can the Matching Law explain problem behavior?
It can help behavior analysts examine how relative reinforcement may influence the distribution of appropriate and problem behavior. Research has applied matching-law analyses to both types of behavior.
4. Does the Matching Law mean a child chooses behavior consciously?
No. The principle describes observable relationships between behavior and reinforcement. It does not mean that a child consciously calculates which behavior will produce the most reinforcement.
5. Is the Matching Law a treatment for autism?
No. The Matching Law is a behavioral principle used to understand patterns of responding and reinforcement. It is not an autism treatment or diagnostic tool.
Disclaimer: This article is for general information only and is not medical advice or individualized behavioral treatment. AutismCue is an informational platform, not a healthcare provider.