How the Matching Law Predicts Severe Problem Behavior in ABA

Borrero and Vollmer's 2002 paper put the matching law on a seesaw, with mands on one side and severe problem behavior on the other, and that same seesaw is the cleanest script a Board Certified Behavior Analyst (BCBA) can hand a parent or grandma on day one of caregiver training. The picture is simple. Wherever the rate of reinforcement is higher, that is where the behavior shows up. If reinforcement only flows when the child screams, hits, or bolts, the seesaw tips that way and stays there. If reinforcement starts to flow for a mand, the seesaw bends back, and severe behavior loses its job. A BCBA who can draw that seesaw on a napkin in a parent meeting will get more behavior change in a week than one who hands the family an eight-page protocol.

What the matching law actually says about severe behavior#

The matching law is the underlying assumption for nearly every assessment a BCBA runs. In plain words, it says that an organism splits its time between two response options in proportion to the reinforcement each option pays out. Pay more reinforcement for response one, get more of response one. Pay more reinforcement for response two, get more of response two. There is no morality in the equation. The child is not choosing severe behavior because they are difficult. They are choosing the response that has been paying.

In a severe behavior case, the two responses are usually a mand and a problem behavior like aggression, elopement, or self-injury. The matching law looks at the rate of reinforcement on each side and predicts which one will dominate. That is the whole frame. A BCBA who keeps the frame that simple can use it in supervision, in caregiver training, in IEP meetings, and in the middle of a crisis.

The reason the matching law belongs at the front of a clinical decision is that it cuts out almost every other variable. Severity, topography, history, diagnosis, none of them change the seesaw. What changes the seesaw is the rate of reinforcement on each side.

The matching law cuts through all of the noise and all of the variables and gives us a really solid look at what changes and tweaks need to be made to get that severe behavior back down and up that missing behavior, that adaptive behavior that's not there. From the talk — Matt Harrington

The Borrero and Vollmer 2002 study in plain words#

Borrero and Vollmer 2002 took the matching law out of the lab and pointed it at severe problem behavior. They watched real kids with real aggression and self-injury and showed that the rate of severe behavior tracked the rate of reinforcement the same way the lab pigeons did. That is the headline. The math the field had been using to describe choice in a research arcade also described the choice between a mand and a meltdown in a clinic.

Two clinical points fall out of that paper. The first is that severe behavior is not magic. It obeys the same rules as any other response class. The second is that the lever a BCBA can actually pull is the reinforcement rate on each side of the seesaw. The math may be heavy, but the lever is light. Change what gets reinforced, and the seesaw moves.

Reading the equation as a teeter-totter, not a calculator#

The classic version of the equation puts R1 over R2 on one side, with the matching rate of reinforcement on the other. R1 is the rate of response one, like a mand. R2 is the rate of response two, like severe behavior. Stare at it long enough and the BCBA exam version comes back. But a clinician supervising eight hours of session a day does not need a calculator. They need a picture.

The picture is a teeter-totter. Mands sit on one end. Severe behavior sits on the other. Reinforcement is the weight a clinician can move from side to side. Move reinforcement to the mand side, the teeter-totter tips toward mands. Move reinforcement to the severe behavior side, it tips back.

That image is enough to drive every clinical move in the next paragraph.

While it looks a little bit like a complicated equation, I like to think of it like a little simple seesaw. And that's what I encourage you to imagine it as is as well. From the talk — Matt Harrington

Why severe behavior dominates when manding rate of reinforcement is zero#

Picture a kid coming in for intake. No mand. No functional communication response yet. The behavior plan has not been written. The team has not coached the family. Severe behavior is doing all the work. Why? Because severe behavior is the only response on the seesaw that has ever paid out. The other side is empty.

The matching law predicts exactly what this case will look like on a graph. Severe behavior, high. Manding, zero. A BCBA who runs preference assessments, who runs a functional analysis, and who never moves a single unit of reinforcement to the mand side will sit there a year later wondering why nothing changed. The plan was tight. The seesaw was untouched.

So what would the rate of reinforcement for manding be? Well, the rate of reinforcement would be a big old zero. So we would expect to see no manding behavior and instead see a heck of a lot of reinforcement for severe behavior and therefore expect to see a lot of severe behavior. From the talk — Matt Harrington

Three pushes that bend the teeter-totter toward mands#

A BCBA does not need to flip the seesaw all at once. The matching law gives three clean pushes.

The first push is teaching the mand. The response effort to access reinforcement has to come down before anything else can happen. If the skill is not in the repertoire, the child cannot pull reinforcement to the mand side, no matter how good the plan is. Functional Communication Training (FCT) is push one for a reason.

The second push is raising the quality, the quantity, or the immediacy of reinforcement on the mand side. Bigger pieces. Faster delivery. Higher-preference items. The seesaw is not just about whether reinforcement happens. It is about how much weight that reinforcement carries. A small chip for a mand will not compete with full escape for aggression. Match the reinforcer to the job.

The third push is dropping response effort. A one-syllable vocal mand, a single picture exchange, a button press. Anything that makes the mand cheaper to do than the severe behavior. The teeter-totter responds to effort the same way it responds to reinforcement rate.

Run all three pushes and the prediction is not subtle. Mands go up. Severe behavior comes down. The graph follows.

Using the matching law to script caregiver training#

Caregiver training is where most behavior plans live or die. The plan can be perfect, but if mom is reinforcing severe behavior at the kitchen table and grandma is reinforcing it on the weekends, the seesaw never tips. The matching law gives a BCBA a script that does not require the family to memorize a single behavior term.

The script has three lines. First, "your child will do whatever pays the most. Right now, the screaming is paying. The asking is not paying yet." Second, "we are going to make the asking pay more than the screaming. Faster, bigger, every single time, no matter how messy it sounds." Third, "we are going to give the screaming a smaller payout, slowly, and only when it is safe." That is the whole frame. No extinction lecture. No fidelity speech. Just a seesaw the family can see.

The matching law also tells a BCBA where caregiver training has to happen. If mom is trained but grandma is not, the seesaw tips during mom's shift and tips back during grandma's. The plan is not failing. The seesaw is being pushed in two directions. The fix is not more parent training for mom. The fix is grandma.

No client is the same. And thus, the changes have to be individualized. That's what the matching law gives us. From the talk — Matt Harrington

When the matching law tells you the intervention is not done yet#

The cleanest use of the matching law in supervision is as a stopping rule. The intervention is not done when severe behavior comes down. The intervention is done when the mand rate is high enough that the seesaw would stay tipped even if a small hit of reinforcement leaked back to the severe behavior side.

That last sentence is the one new BCBAs miss. They pull data, they see severe behavior at zero, and they fade themselves out of the case. Three months later, grandma babysits for a weekend, the seesaw gets a small push toward severe behavior, and the case is back open. The matching law would have predicted that. The mand side was too light.

The decision rule is simple. Before fading, the BCBA asks two questions. Is the rate of manding high enough that a low-fidelity caregiver would still see more mands than severe behavior? Is the reinforcement on the mand side dense enough, fast enough, and easy enough to keep paying out in a real home? If either answer is no, the case is not done yet.

That is the matching law as a clinical decision framework. Not a math drill. A way to look at the seesaw and decide whether to push, hold, or fade.

Frequently asked questions#

What is the matching law in ABA?

The matching law is the rule that says an organism distributes its responses across two options in proportion to the rate of reinforcement each option pays. In a clinic, it is the lens a BCBA uses to predict which response, like a mand or a severe behavior, will dominate based on what is getting reinforced.

How does the matching law apply to severe problem behavior?

Severe behavior follows the same rule as any other response class. Borrero and Vollmer 2002 showed that the rate of severe behavior tracks the rate of reinforcement the same way lab choice data does. A BCBA who wants severe behavior down has to raise the rate of reinforcement for the mand on the other side of the seesaw.

Do I have to do the math during supervision?

No. The math is the language of the science. The clinical move is the seesaw. A BCBA who can draw the teeter-totter for a parent and walk through which side is getting reinforced has the matching law working for them, with or without a calculator.

Why is response effort part of the matching law equation?

Because the seesaw responds to cost, not just to payout. A mand that takes 30 seconds of prompting will not compete with severe behavior that takes one scream. Lower the effort of the mand and the side gets lighter to push. That is why early FCT targets are short, simple, and easy to do.

How do I explain the matching law to parents and RBTs?

Draw a teeter-totter. Put the mand on one side and the severe behavior on the other. Tell them that whichever side pays more, faster, and easier is the side the child will pick. Then walk through what your team is doing this week to move payouts to the mand side. That is the whole conversation.

Watch the full talk#

Matt Harrington walks through the matching law, the Borrero and Vollmer 2002 application to severe behavior, and the three pushes that bend the seesaw, alongside the contingency space and the percentile schedule. If you supervise severe behavior cases or run caregiver training, this is the talk to watch before your next case review.