The Matching Law in ABA: Where Behavior Goes

The matching law is a simple rule about choice. It says we spread our behavior across the options we have. We give more of it to the choice that pays off best. Payoff here means reinforcement, which is a reward that makes a behavior grow. So the option with the richer, faster reward wins more of our time.

This idea matters to everyone who shapes behavior. BCBAs, RBTs, teachers, and parents all see it at work. It explains why a child picks one action over another. It also shows how to change that choice on purpose. When you shift the reward on one side, behavior moves with it.

The teeter-totter idea#

Matt Harrington teaches the matching law like a see-saw. One side holds a hard behavior. The other side holds a better choice, like asking for help. Whichever side has more reinforcement pulls behavior toward it. Add reward to the good side and behavior slides that way.

He points out that most of us already know this in our bones. Matt jokes that the field's favorite sticker slogan says behavior goes where reinforcement flows. He guesses it now sits on half of the laptops at any BCBA event.

The catchy phrase hides a real law. Behavior follows the payoff, not our wishes for it. Matt sums up the core idea in one clean line.

Whatever the organism values and perceives the rate of reinforcement being, that's where they're going. From the talk — Matt Harrington

Why it drives problem behavior#

The matching law helps explain hard behavior. A child may hit, drop, or scream to get something. If that behavior pays off fast, it grows. So we do not just block it. We build a better choice that pays off even more.

That better choice is often a mand, which is a taught way to ask. When we reward the asking well, asking goes up. Matt ties this straight back to the matching law.

The reason why that works when we're also reinforcing man's is because of the matching law. Because as we bump up the reinforcement for man's, then we also see the rate of man's go up as well. From the talk — Matt Harrington

At the same time, we stop paying off the hard behavior. Stopping that reward is called extinction. The two moves work together and behavior shifts.

And because of the matching law, because of our extinction schedules that we've put into place, we're going to see the appropriate behavior increase and the challenging behavior decrease. From the talk — Matt Harrington

This same logic sits at the heart of manding work. The step-by-step version shows up in 5 Days of Manding Mastery.

The bubble picture and assent#

Matt also uses a bubble drawing to make the law easy to see. One bubble holds the good parts of a task. The other bubble holds the parts that feel bad. You want the good bubble bigger than the bad one.

This simple bubble framework of pushing one bubble bigger and the other bubble smaller, it's essentially matching a lot of framework, but I like it because it's a little bit more visual. From the talk — Matt Harrington

This picture connects to assent, which is a client showing they are okay to keep going. When the bad parts stack too high, the child pulls away. That is not stubbornness. It is the matching law doing its job.

based on what we know about the matching law, all of us would not be surprised when we have 10 bad things, and one good thing, that all of our behavior allocation is going to go to moving away from the aversive. From the talk — Matt Harrington

You can see this framing in action in Assent: Don't just say Yes!.

Change the effort or the rate#

The matching law gives you clear knobs to turn. You can change how often a reward comes. You can change how big or good that reward is. You can also change how hard the response is to make. Move any one of these and behavior follows.

Matt points to older research on shifting reward amounts. He cites the Athens and Balmer analysis of the matching law. It showed how you can change the amount of reinforcement to move responding. You do not have to lean on extinction alone.

This gives you a gentler path. You do not always have to remove a reward to change a habit. Sometimes you just make the better choice pay more. That is a kinder way to help a client shift.

What the research says#

The matching law started in the lab with animals. It has since described a wide range of human choice. In one study, the equation captured how children with autism split their time near an adult who offered social contact. It gave a clearer, number-based measure of how social each child was (Morris, S. L. & Vollmer, T. R. (2022). The matching law provides a quantitative description of social time allocation in children with autism. Journal of Applied Behavior Analysis, 55(3), 934-957).

Other work brings the law into the home. In a proof-of-concept study, researchers watched parents and children before and after training. They taught parents to reward good behavior more than problem behavior. The matching law described the shift in the child's choices well (Kronfli, F. R., Lloveras, L. A., & Vollmer, T. R. (2021). Applications of the matching law to observe shifts in problem behavior: A proof-of-concept study. Behavioral Interventions, 36(4), 764-777).

The law even shows up in sports. One study fit the matching equation to strike choices in mixed martial arts. Fighters picked their moves in line with what paid off (Seniuk, H. A., Vu, J. P., & Nosik, M. R. (2020). Application of the matching law to Mixed Martial Arts. Journal of Applied Behavior Analysis, 53(2), 846-856). This wide reach is why the law feels so trustworthy in practice.

FAQ#

What is the matching law in simple terms? It is a rule about how we split our behavior across choices. We give more behavior to the choice that pays off more often or better. So behavior tends to match the rate of reward each option gives.

How do BCBAs use the matching law? They use it to shift behavior toward a better choice. They make the good choice, like asking, pay off well. Then they stop rewarding the hard behavior. Over time, choices move toward the option with the richer reward.

Is the matching law the same as reinforcement? No, but they are close cousins. Reinforcement is a reward that makes a behavior grow. The matching law describes how we divide behavior when two or more rewarded choices exist at once.