NCR vs Extinction at Low Fidelity: The Math BCBAs Miss

Extinction run at 75% fidelity lands at about +0.27 contingency strength, while NCR run at the same 75% fidelity lands at about -0.63. That single gap is why the same staff team can run NCR on a Tuesday and quietly tank an extinction plan on a Wednesday.

If you write reduction plans, the choice between NCR and extinction is not about which one is in the textbook. It is about which one survives the room you actually work in. This page walks the math from the CEU and shows where each procedure stands when the staff team is good, and where each one stands when the staff team is real.

Why fidelity is the variable nobody wants to talk about#

Treatment fidelity is how often the plan gets run the way it was written. In a perfect world it is 100%. Every time the target behavior happens, the team does the exact step the plan asked for. In the real world, fidelity is closer to 70% or 80%. Staff get pulled, schedules change, a new RBT is in the room, the learner is having a hard week.

Most plan write-ups ignore this. They pick a procedure based on the function and call it a day. But two plans that look the same on paper can behave very differently once fidelity slides. Contingency space analysis is the tool the talk uses to show this. It plots how often a behavior gets reinforced against how often the same reinforcer shows up for free. The gap between those two numbers is the contingency strength.

A big gap means the learner can tell when the behavior pays off and when it does not. A small gap means the learner cannot tell, so the behavior fades. A negative gap means the free version is actually richer than the earned version, which is the strongest reduction signal you can build.

Most BCBAs have heard the line "NCR is more resistant to change than extinction" in grad school. The CEU shows the math that makes it true.

Extinction at 100 percent fidelity in contingency space#

Extinction at full fidelity is the easy case. Every time the target behavior happens, nothing happens after it. No attention, no escape, no item. The reinforcer that used to follow the behavior is gone.

When you plot this in contingency space, the probability of reinforcement after the behavior is zero. The probability of that reinforcer showing up without the behavior is also zero, because extinction does not give the reinforcer for free either. Both axes sit at zero.

Extinction at 100 percent fidelity, every event is a B, contingency strength is essentially zero.

A "B" event in this system is a behavior with no reinforcer attached. When every single event is a B, the contingency strength score lands around zero. That is exactly what you want for reduction. The learner stops being able to predict that the behavior produces anything, so the behavior loses its job.

Extinction at 100% fidelity works. The catch is that the score is sitting on a knife edge. A small push moves it the wrong direction.

What happens to extinction when you slip to 75 percent#

Now drop fidelity to 75%. Three out of every four behaviors get extinction. One out of every four sneaks through and gets the old reinforcer. This is the situation your team is actually in.

The plot shifts. The probability of reinforcement after the behavior is no longer zero. It is 25%. The probability of that reinforcer showing up for free is still zero, because extinction is not delivering anything on its own. So the gap now favors the behavior.

Extinction at 75 percent fidelity ends up with a contingency strength around 0.27.

A positive contingency strength of 0.27 means the math is now reinforcing the behavior. Not as much as a clean reinforcement schedule, but enough. The behavior gets stronger, the staff team gets blamed for "the plan not working," and the BCBA writes a new plan. The plan was fine. The fidelity was not.

This is what people mean when they say extinction is brittle. The procedure itself is sound. It just has no margin for the messy parts of a real day.

NCR at 100 percent fidelity in contingency space#

NCR, or noncontingent reinforcement, delivers the same reinforcer the behavior used to earn, but on a time schedule. No behavior required. If attention is the reinforcer, the staff member checks in every two minutes whether the learner is climbing the bookshelf or sitting on the floor. The reinforcer is on tap.

At 100% fidelity, the probability of the reinforcer following the behavior is whatever it happens to be at that moment. But the probability of the reinforcer showing up without the behavior is very high, because the schedule is running constantly in the background. The gap between those two numbers is large, and it favors the no-behavior side.

This is the bridge BCBAs sometimes miss. NCR is not "free reinforcement." NCR is a procedure that floods the environment with the maintaining variable so the behavior cannot compete. The contingency strength score is strongly negative, which is the reduction direction.

Why NCR at 75 percent fidelity still holds#

Drop NCR to 75% fidelity. Now the schedule fires three out of four times. One out of four times the staff member is late, distracted, or pulled away. The learner still gets reinforcement for free most of the time.

NCR at 75 percent fidelity gives a negative 0.63 contingency strength, that is why NCR is so powerful with low fidelity.

A contingency strength of -0.63 is a strong reduction signal. Even with one in four scheduled deliveries missed, the free reinforcer rate is still much higher than what the behavior could produce. The behavior cannot out-earn the free schedule, so the behavior fades.

Compare the two numbers head to head. Extinction at 75% lands at +0.27. NCR at 75% lands at -0.63. The same fidelity drop, and the procedures end up on opposite sides of the reduction line. One is rewarding the behavior. The other is starving it.

Picking NCR or extinction by the environment, not by preference#

The choice between NCR and extinction should not be driven by what feels cleaner on paper. It should be driven by what your environment can actually deliver.

If you have a situation where fidelity is worrisome, contingency strength would absolutely argue NCR is a better approach for that behavior reduction.

Ask three questions before you write the plan:

1. What is realistic fidelity in this setting? Look at the staff team, the ratio, the shift changes, and the learner's other behaviors. If your honest answer is 90% or better, extinction is on the table. If it is 70% or 80%, NCR is the safer bet.
2. Can the setting survive an extinction burst? Extinction often comes with a temporary spike in the behavior before it fades. If the behavior is severe, or the setting is a classroom with other learners, a burst is a real safety problem.
3. Is the maintaining reinforcer easy to deliver on a fixed schedule? Attention NCR is easy. Tangible NCR is harder. Escape NCR takes structure. If you cannot deliver the schedule cleanly, the math from the CEU does not protect you.

The right answer is not always NCR. It is whichever procedure has the math on its side once you account for the room.

Where DRO fits in this comparison#

DRO, or differential reinforcement of other behavior, sits between NCR and extinction. DRO delivers the reinforcer on a time schedule, like NCR, but only if the target behavior did not happen in that interval. So it is contingent, but the contingency is on the absence of the behavior.

DRO can land at strong negative contingency strength at high fidelity. The catch is that DRO requires the staff member to track the interval and make a yes-or-no call before each delivery. That is a fidelity tax. If your team cannot reliably time the interval, your DRO turns into something between NCR and a coin flip.

A good rule of thumb from the talk is this: if fidelity is high and the behavior is not severe, DRO gives you the cleanest reduction signal because it does not deliver reinforcement during the behavior. If fidelity is low or the team is new, NCR gives you most of the benefit with less to mess up.

Quick reference: the four numbers from the CEU#

• Extinction at 100% fidelity: contingency strength near 0
• Extinction at 75% fidelity: contingency strength around +0.27 (favors the behavior)
• NCR at 100% fidelity: strongly negative contingency strength
• NCR at 75% fidelity: contingency strength around -0.63 (favors reduction)

Keep these in your head the next time a plan is not working. Before you change the procedure, check the fidelity. The math may already be telling you the answer.

FAQ#

Is NCR more effective than extinction?

Not always. At 100% fidelity, extinction lands at a contingency strength near zero, which is the reduction line. NCR at 100% fidelity lands well below zero, so it has a bigger reduction signal even at full fidelity. As fidelity drops, the gap widens fast. By 75% fidelity, extinction has flipped to a positive contingency strength while NCR is still strongly negative. So NCR is more effective in the conditions most BCBAs actually work in.

Why does NCR survive low fidelity better than extinction?

Because NCR builds the reduction signal on the free side of the contingency. Even if the staff misses a few scheduled deliveries, the rate of free reinforcement is still much higher than what the behavior can earn. Extinction has no free reinforcement to lean on. Every missed deliverable is a reinforcer the behavior got to keep.

What contingency strength value is acceptable for a reduction intervention?

Zero is the floor. Anything positive means the math is on the behavior's side. A strongly negative score, like the -0.63 NCR posts at 75% fidelity, is what you want when you are writing a plan that will actually have to live in a real classroom or home.

When should I pick DRO instead of NCR?

Pick DRO when fidelity is high, the staff team can reliably track intervals, and you want a cleaner reduction signal because the reinforcer never lands during the behavior itself. Pick NCR when fidelity is lower, the team is newer, or the cost of a delivery during the behavior is small compared to the cost of getting the timing wrong.

Does this mean extinction is bad?

No. Extinction at 100% fidelity is a clean and powerful procedure. The point of the CEU math is that extinction is sensitive to fidelity in a way NCR is not. If your setting can run at 95% or better, extinction is a good tool. If it cannot, the same procedure can quietly make the behavior stronger.

Keep going#

The contingency strength numbers in this page come from the live CEU walkthrough. Matt builds the plots, runs the math out loud, and ties each number back to a real case. If you want the full picture, including the matching law and percentile schedule pieces of the same talk, the recording is the fastest way in.

Watch the full CEU on openceu.com