Fixed Ratio Schedule: Definition, Examples, and the Break-and-Run Pattern

How a fixed ratio schedule works

Every schedule answers one question: which responses will be followed by a reinforcer? On a fixed ratio schedule the answer is a count. Each response advances a counter; the response that completes the count is reinforced; the counter resets and the cycle begins again. The requirement is a number of responses, not an amount of time, and the number is the same on every cycle.^[1]

Skinner studied fixed-ratio reinforcement in rats in the 1930s and compared it, in The Behavior of Organisms, with periodic reconditioning, his early name for what is now called a fixed interval. The ratio schedule produced a markedly higher rate of lever pressing.^[2] The reason is built into the rule. On an interval schedule, pressing faster does not make the reinforcer come sooner; only the first press after the interval counts. On a ratio schedule, pressing faster brings the reinforcer sooner in exact proportion, so the time between reinforcers is set not by the experimenter but by how fast the organism works.^[3] Baum's review found that at the same rate of reinforcement, ratio schedules maintain the higher rate of responding.^[4]

Break and run: the post-reinforcement pause

Put a pigeon on FR 50 and let the cumulative recorder run. The record looks like a staircase. After each reinforcer the bird stops pecking and the pen draws a flat line. Then, with no external signal, it starts again and pecks at a high, nearly constant rate — a steep, straight segment — until the fiftieth peck delivers grain and the pattern repeats. Ferster and Skinner reported hundreds of such records in 1957; the two parts, the post-reinforcement pause and the run, make up the break-and-run pattern.^[1] Set the virtual Skinner box to FR 20 to watch it appear.

The pause is lawful. Felton and Lyon trained pigeons on a series of fixed ratios and found that the pause grew longer as the ratio grew larger, while the rate of pecking during the run stayed roughly constant.^[5] Powell showed that the same relation holds when the ratio is raised in small sequential steps rather than in jumps.^[6] Ferster and Skinner had already found that at ratios in the hundreds the pauses could stretch to many minutes, with the runs between them still fast.^[1] The bigger the job, the longer the organism waits before starting it; once started, it works at about the same speed regardless.

Why the pause belongs to the next ratio, not the last reinforcer

The name suggests that the reinforcer causes the pause: the bird has eaten and is resting. Schlinger, Derenne, and Baron reviewed fifty years of research on pausing and concluded that this reading is mistaken. When pigeons work on schedules that alternate between a small ratio and a large one, with a signal showing which is coming, the pause depends on the ratio ahead rather than the one just completed: after the same reinforcer, the bird pauses briefly if a small ratio comes next and at length if a large one does. The pause is better described as a pre-ratio pause, and it behaves less like rest than like avoidance — the start of a long stretch of unreinforced work is aversive, and the organism postpones it.^[7] Anyone who has stared at a blank page for twenty minutes and then written steadily for an hour knows the shape.

Ratio strain: what happens when the ratio is raised too fast

Ratios cannot be raised at will. Move a pigeon from FR 10 to FR 200 in one step and responding breaks down: the pause stretches, the run is interrupted by further pauses, and responding may stop altogether. Ferster and Skinner described this straining at high ratios,^[1] and applied behavior analysts call it ratio strain.^[8] From the organism's side, the schedule has become hard to tell apart from extinction: a long string of unreinforced responses is exactly what extinction looks like, and behavior weakens accordingly.^[9]

Whether a ratio is too high depends on more than the number. Ferster and Skinner maintained food-deprived pigeons on very large ratios, but only by arriving at them gradually.^[1] The ratio that holds up for a hungry pigeon fails for a sated one, and the ratio a bonus will carry is not the ratio a sticker will carry. Strain is a relation among the requirement, the reinforcer, and the organism's motivation.

The signs appear outside the laboratory in the same order: longer delays before starting, work abandoned partway through the count, and finally quitting. A student who stops mid-worksheet after the requirement was doubled and a dog that wanders off from a training session are both ratios stretched faster than the behavior could follow. The remedy is the same in every case: drop back to the last ratio that worked and raise it more slowly.^[8]

What happens when reinforcement stops

Behavior maintained on a fixed ratio outlasts behavior maintained on continuous reinforcement once the reinforcer is withdrawn — the partial reinforcement extinction effect, covered on the continuous versus intermittent page. Ferster and Skinner's extinction records after fixed-ratio training show the schedule's pattern persisting for a while: bursts at the old running rate, separated by pauses that lengthen until responding stops.^[1]

Examples of fixed ratio schedules

Any arrangement in which a reinforcer arrives after a set number of countable responses is a fixed ratio. Three with the best evidence are taken up after the table.

Piece-rate pay

Skinner pointed to piecework as the industrial form of the fixed ratio and warned that it can drive rates to exhausting levels.^[10] The best-documented modern case is Safelite Glass, which in the mid-1990s moved its windshield installers from hourly wages to pay per unit installed, with a guaranteed hourly minimum. Lazear analyzed the company's records and reported that output per worker rose by about 44 percent, roughly half from existing installers installing more and the rest from sorting, as the new pay attracted and kept more productive workers.^[11] It is one of the cleanest field demonstrations that tying reinforcement to a count of responses raises the rate of those responses; what it does not measure is taken up below.

Loyalty punch cards

"Buy ten, get one free" is FR 10 on purchases. Kivetz, Urminsky, and Zheng tracked café customers using stamp cards and found that the time between purchases shrank as the card filled, and that after redeeming a card and starting a fresh one customers slowed down again, a lull the authors called post-reward resetting.^[12] The acceleration toward the goal is not a pigeon's flat run, but the lull after the reward and the rush before it are the same shape.

Reading logs and sticker charts

A classroom reading chart that pays a sticker after every five books is FR 5, and it behaves like one: a flurry of reading as the fifth book approaches, a quiet spell after the sticker. Both are the schedule working, not the child slacking. If the quiet spell matters, lower the ratio, make the reinforcer larger, or move to a variable ratio so that there is no predictable moment at which the next reinforcer is far away.^[7]

One caution. The schedule is defined by what is counted, and the counted unit is often not the behavior you care about. A commission per sale is FR 1 on sales, but the salesperson's behavior is making calls, and a sale follows an unpredictable number of calls, so the calling is on a variable ratio.

Fixed ratio vs. variable ratio, fixed interval, and variable interval

All four basic schedules are defined by two questions — count or time, fixed or variable — and the fixed ratio is the "count, fixed" cell.

The contrast with the variable ratio matters most, because both are ratio schedules and both maintain high rates. What the fixed count adds is predictability: the organism, in effect, knows how far away the next reinforcer is, and it is the certainty that it is far away that produces the pause. On a variable ratio the very next response might be the one that pays, and Ferster and Skinner's records show the pauses largely disappearing.^[1][7] The contrast with the fixed interval is a matter of shape. Both begin with a pause, but the fixed-interval record curves upward — the scallop — as the rate builds gradually, while the fixed-ratio record breaks abruptly from flat to steep, and on the interval schedule responding faster does not help.^[1][9] The variable interval shares neither the count nor the predictability and produces a moderate, steady rate with little pausing.

How to use a fixed ratio schedule

The fixed ratio is the natural first step away from continuous reinforcement, because it is the easiest schedule to count and to explain. The protocol is the one applied behavior analysts use to thin a schedule, whoever the learner is.^[8]

1. Define the unit. Decide what counts as one response — one completed problem, one sit, one paragraph — and make it unambiguous. The schedule reinforces exactly what it counts.
2. Start at FR 1. Reinforce every response until the behavior is fluent. A new behavior put straight onto a lean ratio extinguishes before it is learned.
3. Raise the ratio in small steps. FR 1 to FR 2, FR 2 to FR 3, FR 3 to FR 5, moving up only after the behavior is stable at the current step. Even small increases lengthen the pause; large jumps invite strain.^[6]
4. Watch for strain and back off. Longer delays before starting, runs abandoned partway, quitting. At the first sign, return to the last ratio that worked and hold there longer.^[8]
5. Match the reinforcer to the ratio. A large ratio needs a reinforcer worth the work, or a conditioned reinforcer — a token, a point, a check mark — that bridges to one. That is what a token economy is for.
6. Decide whether you want the pause. If the goal is steady behavior with no dead time, switch to a variable ratio once the behavior is established. If the pause is harmless, the fixed ratio is simpler and more transparent.
7. Hand off to natural reinforcers. The contrived count is scaffolding. Fade it once the behavior is maintained by what it produces on its own, as in building habits.

Common mistakes

• Jumping the ratio. FR 1 to FR 20 in one move is how many home and classroom programs fail. The behavior looks as if it stopped working; the schedule broke it.
• Counting the wrong thing. A count of pages read reinforces turning pages; a count of problems attempted reinforces attempting. Make the unit the behavior itself, not a proxy.
• Treating the pause as laziness. The pause is the schedule's signature, governed by the size of the ratio ahead.^[7] Scolding a child for it adds punishment to a situation the schedule created. Shrink it by lowering the ratio or switching to a variable ratio.
• Counting quantity when quality matters. If the count is units, care is not reinforced unless it is also measured. Build quality into the definition of a countable response or arrange a separate consequence for it.
• Calling anything with a number a fixed ratio. "Read for ten minutes, then play" is time-based, not count-based, and pays the same whether one page or twenty is read. A salary is neither; it is paid on time regardless of the number of responses.
• Expecting the fixed ratio to be the most persistent schedule. It is more durable than continuous reinforcement and less durable than a variable ratio. If persistence is the goal, it is a step on the way, not the destination.

What the evidence does not show

Break-and-run, the growth of the pause with ratio size, and ratio strain are among the most reliable findings in the experimental analysis of behavior. They were established with pigeons and rats, and three limits apply when the schedule is used with people.

People follow rules as well as schedules. Lowe showed that adult human performance on simple schedules often departs from the animal patterns: on fixed-interval schedules, adults tend to respond either at a very low rate or at a high, steady one rather than producing the scallop, and the difference tracks the rules they form about the contingency.^[13] A customer who reads "every tenth coffee free" is responding to the rule as much as to the count, and the schedule alone does not predict what the rule will do. Field results like the stamp-card study are consistent with the laboratory pattern, but they are not a test of it.^[12]

Piece rates raise output, and the evidence is about output. Lazear's Safelite study measured units installed per worker and reported that they rose. He reports no sign that quality fell, since a broken windshield had to be replaced on the installer's own time, but quality was not the outcome the study measured.^[11] The general concern is a matter of contingency, not of any particular finding: a schedule reinforces what it counts, and if the count is units, care is reinforced only insofar as it is also counted or separately consequated. Skinner's related worry was that the schedule can push rates to exhausting levels.^[10] Neither point is an argument against piece rates; both are arguments for counting what you want.

The pause is not rest, and the fixed ratio is not the most durable schedule. The evidence reviewed by Schlinger and colleagues counts against the intuitive story that the organism pauses because it has just eaten; the pause is governed by the work ahead.^[7] A fixed ratio is more persistent than continuous reinforcement, but as the hub page explains, the variable ratio is the schedule to choose when persistence is the goal.^[9]

Key takeaways

• A fixed ratio schedule delivers a reinforcer after a set number of responses. FR 1 is continuous reinforcement, FR 20 pays every twentieth response, and the organism's own rate sets how often reinforcers arrive.
• The pattern is break-and-run: a pause after each reinforcer, then a fast, steady run. The pause lengthens as the ratio grows while the running rate stays about the same, and it is controlled by the ratio ahead rather than by the reinforcer just received.
• Ratios raised too fast produce ratio strain — long pauses, broken runs, and quitting — because a long string of unreinforced responses is what extinction looks like. Drop back and raise the ratio more gradually.
• Piece-rate pay, loyalty punch cards, reading logs, and "collect ten" quests are fixed ratios, and field evidence such as the productivity gain at Safelite shows count-based reinforcement doing what the laboratory predicts.
• To use one, define the unit, start at FR 1, raise the ratio in small steps, watch for strain, match the reinforcer to the ratio, and switch to a variable ratio if the pause is a problem. The schedule reinforces only what it counts, and people also follow the rules they are given.

Check yourself

A teacher gives a sticker after every five completed math problems. A student finishes five, collects the sticker, and then sits doing nothing for several minutes before starting the next five. Is the program failing?

No. The idle stretch is the post-reinforcement pause, the signature of a fixed ratio schedule, and the evidence says it is governed by the size of the ratio ahead rather than by the sticker just received. If the dead time matters, lower the ratio, make the reinforcer larger, or switch to a variable ratio so there is no predictable moment when the next sticker is far away.

A café changes its loyalty card overnight from "buy ten, get one free" to "buy twenty-five, get one free." What does the schedule predict?

Ratio strain. The requirement was raised in one large step, so expect longer gaps between purchases, cards abandoned partway, and some customers dropping the program altogether, because from the customer's side a long run of unrewarded purchases looks like extinction. The schedule-informed alternative is to raise the ratio in smaller steps or make the reward worth the larger count.

A company pays a commission on every sale. Is the salesperson's work on an FR 1 schedule?

Only if the counted unit is the sale. The behavior the salesperson emits all day is making calls, and a sale follows an unpredictable number of calls, so the calling is on a variable ratio. The commission is FR 1 on sales and VR on calls, and it is the variable count that shapes the pattern of the working day.

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