The seventy-seventh article reported a finding whose magnitude we could not obtain. This one reports a finding whose magnitude is quoted constantly, in several mutually incompatible versions, by people selling loyalty schemes.
Key Takeaway
The abstract reports that "customers who receive a 12-stamp coffee card with 2 preexisting 'bonus' stamps complete the 10 required purchases faster than customers who receive a 'regular' 10-stamp card."[1] An academic account records that the effect was constrained to participants who completed their cards, and that non-completers showed no change[2]. On our own arithmetic, a card on an 80 percent margin needs a quarter of one extra sale to break even.
The Verdict, Stated First
Five claims, in descending order of confidence.
One. The research is unusually good. A field experiment, secondary customer data, paper-and-pencil problems, four separate findings, and explicit statistical and experimental controls ruling out alternatives.
Two. The figures in commercial circulation are unreliable. For the same study we found sample sizes of 300 and 948, and accelerations of 20 percent and 2.4 times, in sources that cite it confidently.
Three. The limitation is the important part. The effect was reportedly confined to people who finished their cards, and those who did not finish showed no change in behaviour at all.
Four. The economics are forgiving, which is why this survives. On our own arithmetic a stamp card on a high-margin product costs about 2 percent of revenue and needs almost nothing in return to pay.
Five. The one real risk is a reset nobody measures. If half of completers pause for three weeks after collecting, our own figures say the acceleration is wiped out entirely.
Our Grades For These Claims
Applying the scheme from the first article in this series.
Grade A for the 2006 abstract, obtained verbatim from a research database record filed by a field experiments archive.
Grade B for the acceleration figure, which comes from the authors' own university publication quoting one of them, rather than from the paper.
Grade B for the completers limitation, described by an academic preprint characterising the paper.
Grade D for every other number in circulation, which reach us through practitioner websites and contradict one another.
Grade A for our own arithmetic, on entirely invented commercial parameters.
Our position: the study is better than its reputation and the reputation is quantitatively unreliable, which is an unusual combination and worth setting out carefully.
A Note On Method
Everything here is verified to August 2026.
We obtained the 2006 paper's abstract verbatim from a research database record, filed under a field experiments archive[1]. We did not obtain the paper.
The acceleration figure and the café's setting come from the authors' own university's review publication[3], which quotes one of the authors directly.
The limitation about completers comes from an academic preprint characterising the study[2]. We did not obtain the section it describes.
Several figures in wide circulation reach us only through practitioner websites[4], flagged at every use, and those sources disagree with each other.
We did not obtain the 2006 companion paper on endowed progress, and report its design from an encyclopedia and its citation from reference lists[5].
All arithmetic is ours and every commercial parameter in it is invented.
This article discusses research on motivation. It is not marketing, pricing or commercial advice.
The Finding
What is being claimed, before any dispute about numbers.
The abstract states the origin: "The goal-gradient hypothesis denotes the classic finding from behaviorism that animals expend more effort as they approach a reward. Building on this hypothesis, the authors generate new propositions for the human psychology of rewards."[1]
Three observations, ours.
The hypothesis is old and came from animal research, which the title's word "resurrected" acknowledges. The 2006 contribution is testing it in humans buying things.
The methods listed are unusually varied for a single paper: "a field experiment, secondary customer data, paper-and-pencil problems, and Tobit and logit models."[1]
And the abstract closes by saying the authors "rule out alternative explanations" using statistical and experimental controls[1], which is a claim this series usually has to note the absence of.
One point of framing before the evidence, because it shapes how this article should be read. We are not here to debunk anything. The study is good, the effect is real, and the technique is cheap enough that a small business could reasonably run it on the arithmetic alone.
What this article does is separate what the paper says from what is said about it, which turn out to differ enough to matter, and then work out whether the difference changes any decision. It mostly does not, which is itself worth knowing.
The 2006 Paper
The source.
Kivetz, R., Urminsky, O., and Zheng, Y. (2006), The Goal-Gradient Hypothesis Resurrected: Purchase Acceleration, Illusionary Goal Progress, and Customer Retention, Journal of Marketing Research, 43(1), 39–58, DOI 10.1509/jmkr.43.1.39, also filed as Natural Field Experiments 00658 with a field experiments archive[1].
Four observations, ours.
The paper was a finalist for two named awards, in 2007 and 2011, according to one author's university profile[3]. That is not evidence of correctness and it does indicate the field took it seriously.
It is filed with a field experiments archive, which matters. This is a real intervention on real customers rather than a questionnaire, and the seventy-fifth article's central complaint about hypothetical choices does not apply here.
The three authors are at three separate universities according to a university review article[3], which is normal and worth noting only because it means the study was not one department's project.
And we did not obtain the paper, which given how much of this article concerns disputed numbers is the limitation to keep in view throughout.
Four Findings In One Abstract
What was found, verbatim and in full, because the four are usually collapsed into one.
"The key finding indicate that (1) participants in a real cafe reward program purchase coffee more frequently the closer they are to earning a free coffee; (2) Internet users who rate songs in return for reward certificates visit the rating Web site more often, rate more songs per visit, and persist longer in the rating effort as they approach the reward goal; (3) the illusion of progress toward the goal induces purchase acceleration... and (4) a stronger tendency to accelerate toward the goal predicts greater retention and faster reengagement in the program."[1]
Four observations, ours.
Finding (2) is the one nobody mentions and it is arguably the most impressive. People rating songs for reward certificates showed acceleration on three separate measures: visit frequency, songs per visit, and persistence.
That matters because it is a different domain with no money changing hands, which makes the effect harder to explain as a purchasing artefact.
Finding (4) is the commercially relevant one and is almost never quoted. Acceleration predicts retention and reengagement, which is the thing a loyalty scheme is actually for.
And we note that the abstract as reproduced reads "The key finding indicate", which is a typographical error in the record we obtained and which we quote as we found it rather than silently correcting.
The Illusionary Progress Result
The finding that makes this a technique rather than an observation.
"(3) the illusion of progress toward the goal induces purchase acceleration (e.g., customers who receive a 12-stamp coffee card with 2 preexisting 'bonus' stamps complete the 10 required purchases faster than customers who receive a 'regular' 10-stamp card)."[1]
Four observations, ours.
The two cards require exactly the same ten purchases. Nothing material differs; only the framing of where the customer stands.
The authors call it an illusion in their own abstract, which is unusually direct language for describing something they are also demonstrating works.
The outcome measured is speed of completion, not whether people completed. That is worth holding, because the companion study below measured completion instead and the two get merged.
And the abstract gives no magnitude for this comparison, which is the single figure a business owner would most want and which the sections below show is quoted in several incompatible forms.
One structural point about the manipulation deserves stating, because it is what makes the result surprising rather than obvious. The twelve-stamp card is objectively worse-looking. A customer comparing the two would see a longer card and might reasonably prefer the shorter one.
So the finding is not that people like getting something free. It is that the same requirement, presented as partial completion of a larger task, produces faster completion than presented as a smaller task started from zero, which no account of rational choice predicts.
The Goal Distance Model
The theoretical result, which is more useful practically than it sounds.
"The conceptualization and empirical findings are captured by a parsimonious goal distance model, in which effort investment is a function of the proportion of original distance remaining to the goal."[1]
Four observations, ours.
The operative word is proportion. Effort depends on the fraction of the original distance left, not the absolute number of steps remaining.
That is exactly why the bonus stamps work. Two stamps of twelve is one sixth of the journey removed, and the model says effort responds to that fraction rather than to the ten purchases still required.
It also predicts something a business can use directly. The same absolute progress is worth more motivationally on a shorter scheme, because it represents a larger proportion.
And it explains why a very long programme is weak at the start. The first stamp of fifty moves the proportion by two percent, which on this model is almost nothing.
Post-Reward Resetting
What happens after the reward, which the abstract touches and a secondary source states plainly.
The abstract's finding (4) links acceleration to retention. A study-aid site summarising the paper records the other half: "just after reward attainment, customers exhibited a drop in activity (post reward resetting) and were also most likely to defect."[4]
This is a study-aid site, not an academic source, flagged here and at every use, and we did not obtain the section it describes.
Four observations, ours.
If accurate, this is the cost side of the mechanism and it is structurally guaranteed. A model in which effort depends on proportional distance to a goal predicts collapse the moment the goal is reached and the proportion resets to one.
The word defect is the serious one. Not merely slowing down, but leaving, and at the moment they have just been rewarded.
That is counterintuitive enough to be worth stating twice. The point of maximum churn risk is immediately after you have given someone something free, which is the opposite of what a loyalty scheme is supposed to achieve.
And it is the reason we compute a reset cost below. No commercial account of this literature we encountered prices it at all.
The Limitation Nobody Quotes
The most important thing in this article, and it comes from an academic paper describing the study rather than from the abstract.
It records: "The authors recognized the existence of a group of participants who did not complete their coffee cards for the duration of the study, and did not exhibit a noticeable change in their coffee purchasing habits. They concluded that the loyalty card effect was constrained to the population of participants who handed in their completed loyalty cards in exchange for the free-coffee reward."[2]
We did not obtain the paper and report this characterisation of it.
Four observations, ours.
If this holds, the effect applies to a self-selected subgroup: the people who finished. Those who did not finish showed no change at all.
That creates an attribution problem the sixty-sixth article would recognise. People who were going to buy a lot finish their cards, and people who finish their cards show acceleration, and separating those two requires exactly the controls the abstract says were applied and which we could not read.
The commercial consequence is direct and unwelcome. A scheme that works only on people who complete is working on your best customers, who are the ones least in need of persuading.
And we would flag this as the finding most worth someone obtaining the paper to check, because it is the difference between a scheme that grows a business and one that discounts loyal customers.
Two readings of that limitation are possible and they point opposite ways, which is why we would want the original. The pessimistic reading is selection: heavy buyers finish cards and heavy buyers were always going to buy, so the acceleration is a property of the people rather than the card.
The optimistic reading is that the card only works on people who engage with it, which is unsurprising and not a flaw. Someone who abandons a card after two stamps has effectively left the programme, and no scheme influences people who ignore it.
The abstract's own statement that alternative explanations were ruled out by statistical and experimental controls[1] is directly relevant here and is exactly what we could not read. Whether the controls address this specific concern is the question, and we cannot answer it.
The Endowed Progress Companion
The other 2006 paper, which is the one usually quoted with numbers.
Nunes, J. C., and Drèze, X. (2006), The Endowed Progress Effect: How Artificial Advancement Increases Effort, Journal of Consumer Research, 32(4), 504–512, March, DOI 10.1086/500480[5].
An encyclopedia describes the design: "Half of the cards required ten stamps to receive the reward (a free car wash), but these cards were endowed with two stamps, therefore these patrons only required eight additional stamps to receive a free car wash."[5] This is an encyclopedia, not an academic source, flagged at every use.
Three observations, ours.
The design is structurally the same manipulation as the coffee card study's third finding, run independently, in a different business, and published in a different journal the same year.
The outcome differs in a way that matters. This study measured completion rates; the coffee study measured speed of completion, and a scheme designer cares about both but not equally.
And we did not obtain this paper either, which is why the completion figures appear below only with a heavy warning attached.
Numbers That Contradict Each Other
What we found when we went looking for the magnitudes, set out plainly. Ours.
On the sample size of the café study: one practitioner site records "948 real café loyalty members"; another records "300 café customers in Chicago"[4]. The authors' own university publication gives no number at all and describes "a café located within the campus of a large university"[3].
On the size of the acceleration: the same university publication, quoting one of the authors, reports that "the average time between purchases accelerated by about 20 percent from the first to the last stamp"[3]. A practitioner site reports "an average of 12 days elapsed between the first and second stamp, but only 5 days between the ninth and tenth" and concludes customers bought "2.4 times more frequently"[4].
Four observations.
Those two acceleration figures are not compatible. Twelve days falling to five is a reduction of about 58 percent in the interval, and about 20 percent is a different claim entirely.
The sample sizes differ by a factor of more than three, and both are stated without hedging by sources recommending the technique.
One of those sites gives 300 as the sample for both the café study and the car wash study[4], which is either a coincidence or a number that has migrated between two papers.
And none of these sources is dishonest. This is what happens to a finding after twenty years of being repeated by people who did not read it, which is the pattern the sixty-ninth article documented and this is a live instance of it.
Two things distinguish this case from that one and are worth setting out, because they cut in opposite directions.
Here the underlying study is excellent and freely checkable. The sixty-ninth article dealt with an unpublished dissertation nobody could read; this abstract is in a public research database and states the design precisely. The drift happened anyway, which is the discouraging part.
And the figures being garbled are not load-bearing. Whether the sample was 300 or 948, and whether purchases accelerated by twenty percent or two point four times, the arithmetic below shows a stamp card on a high-margin product pays across the whole range. The technique survives its own bad citations, which is not something we could say about the decoy tier in the seventy-fifth article.
Which Number We Would Believe
Our own reasoning, offered as reasoning rather than as a finding.
Four observations.
We would take the 20 percent figure over the 2.4 times figure, because it appears in a publication of the university employing one of the authors, describing his own study, which is closer to the source than a practitioner blog.
The same publication gives a second framing that is easier to check and harder to garble: "members purchased two more coffees in the time it took to complete the card than they would have if they hadn't accelerated"[3].
That figure is also internally consistent with a 20 percent acceleration on a ten-purchase card, which the larger claim is not.
And we would hold even that at Grade B and use it only where the conclusion does not turn on it. A university review article is a good secondary source and it is not the paper, and this article's arithmetic below is built to work across a range rather than on one number.
Two Studies Being Merged
A specific mechanism producing the confusion, which we can demonstrate. Ours.
Four observations.
The coffee study's manipulation, from its own abstract, is a 12-stamp card with 2 bonus stamps against a regular 10-stamp card, both requiring ten purchases[1].
The car wash study's manipulation, from an encyclopedia, is a 10-stamp card with 2 endowed stamps against a regular 8-stamp card, both requiring eight purchases[5].
Several practitioner accounts describe the coffee study using the car wash numbers, or attribute the car wash completion rates to the coffee paper. The two designs are similar enough that the details cross over and nobody notices.
And that is worth knowing before you quote either. If a source describes a coffee card with eight stamps, it has merged two papers, and whatever else it says about them should be treated accordingly.
One more reason the merger happens, and it is not carelessness. The two designs really are the same idea, published independently in the same year by different teams in different journals, which is unusual and is itself evidence the effect is robust.
So the confusion has a silver lining worth stating. Two research groups arrived at the same manipulation and both reported it working, in coffee and in car washes, which is a form of replication and a stronger basis for the technique than either paper alone.
A Citation We Could Not Verify
A specific oddity, recorded because this series keeps a count.
One practitioner reference list gives two different 2006 papers by the same two authors on the same effect: the Journal of Consumer Research paper cited above, and a second given as "The endowed progress effect: Feeling like you've already started makes you want to finish, Journal of Experimental Social Psychology, 42(3), 394–403"[4].
Three observations, ours.
We could not verify the second citation. Every other source we consulted gives only the Journal of Consumer Research paper.
The subtitle reads more like a description of the effect than a paper title, which is what a citation looks like when someone has written down a summary and it has hardened into a reference.
We are not asserting the paper does not exist. We are recording that a reference list recommending this technique contains a citation we could not confirm, alongside numbers that contradict other sources.
Why This Finding In Particular
An observation about which findings get their numbers mangled, since this series has now watched it happen several times. Ours.
Four observations.
The findings that drift are the ones with a memorable concrete detail and a commercial use. Stamp cards, tapping songs on a table, a magazine subscription menu. Nobody garbles the numbers in a paper on probability weighting.
The mechanism is straightforward once stated. A story gets retold and a number gets retold with it, and each reteller is working from the previous telling because the paper is behind a paywall and the blog post is not.
What makes this case unusual is that the drift is checkable. The abstract is freely available in a research database, states the card design precisely, and disagrees with several of the accounts built on it.
And the practical instruction is one search. Find the abstract before quoting the number, which for this paper takes under a minute and would have caught every discrepancy in this article.
What Actually Survives
Our reading, stated directly.
Five statements.
The effect is real and the study is a good one. A field experiment with secondary data, multiple domains, and explicit controls ruling out alternatives.
Proportional distance is the mechanism, on the authors' own model, which predicts both the bonus-stamp result and the collapse after the reward.
The effect was reportedly confined to people who completed their cards, and non-completers showed no change, which is the qualification that matters most commercially.
Acceleration predicts retention and reengagement, which is the abstract's fourth finding and almost never quoted.
And the magnitudes in commercial circulation are unreliable, differing by a factor of three on sample size and being mutually incompatible on effect size.
What A Stamp Card Costs
Turning it into a decision. Our own arithmetic, with invented figures throughout: a five dollar item, buy ten get one free.
The cost of the free item as a share of the revenue from the ten paid ones:
At an 80 percent gross margin: the free item costs $1.00 against $50.00 of revenue, an effective discount of 2.00 percent.
At 70 percent: 3.00 percent. At 60: 4.00. At 50: 5.00. At 40: 6.00 percent.
Four observations.
On a high-margin product the scheme is extremely cheap, which is the real reason coffee shops run stamp cards and behavioural research is not.
The cost triples across that margin range. A 40 percent margin business is running a six percent discount, which is a serious promotion rather than a nudge.
So the same scheme is a different proposition in different businesses. The advice travels from cafés to trades without the margin travelling with it.
And this is the calculation to do before any behavioural question arises. What the card costs is arithmetic; what it earns is the disputed part.
Two refinements a careful owner would add, both of which make the scheme look better. The free item is often not a full unit of cost, since a redeemed coffee frequently comes with a purchased pastry, and the marginal customer redeeming at a quiet hour costs less than at a busy one.
And a meaningful share of cards are never completed, which the completers limitation above implies directly. Every abandoned card is a customer who bought some number of items and cost nothing, so the realised discount is lower than the headline rate.
How Many Extra Sales It Needs
The break-even. Ours, same invented figures.
Extra purchases required per completed card of ten, for the incremental margin to cover the free item:
At 80 percent margin: 0.25 extra sales. At 70: 0.43. At 60: 0.67. At 50: 1.00. At 40: 1.50.
Four observations.
At a high margin the bar is a quarter of one extra sale per card, which is close to trivially easy to clear.
The reported acceleration, on the authors' own institution's account, is two extra coffees per card[3], which would clear that bar eightfold.
At a 50 percent margin the requirement is a full extra sale, and at 40 percent it is one and a half, which are real targets rather than rounding.
And the general rule is worth stating. Break-even extra sales equals the ratio of cost to margin, which for a business at margin m is simply one minus m over m, and takes ten seconds to compute for any product.
That formula has a property worth noticing, because it explains an entire industry practice. It does not depend on the price of the item at all, only on the margin, so a card on a five dollar coffee and one on a five hundred dollar service need the same proportional response.
And it explains why stamp cards cluster where they do. Coffee, hairdressing, car washes and sandwich shops are all high-margin repeat purchases, which is precisely the corner where the break-even is a fraction of one sale and the scheme is nearly free to run.
Sooner Is Not The Same As More
The question the whole literature leaves open, and which decides everything above. Ours.
Four observations.
The finding is acceleration: people buy sooner as they approach the reward. That is not the same as buying more over a year, and the distinction is invisible inside a study that watches one card.
Someone who drinks fourteen coffees a month and buys them slightly faster near the end of a card has bought no additional coffee at all. The card has changed the timing and not the total.
On our own arithmetic, taking the two extra coffees at face value and varying how much of it is genuinely new: at 100 percent new the card nets $7.00 per completion; at 75, $5.00; at 50, $3.00; at 25, $1.00; and at zero, it loses $1.00, which is exactly the cost of the free item.
That asymmetry is the honest case for these schemes, and it is stronger than the behavioural one. The upside is several dollars and the downside is capped at the cost of the giveaway, so on a high-margin product the scheme is a cheap bet regardless of what the research says.
Two ways an owner can actually find out which case they are in, since nothing in the research settles it. Compare annual spend for cardholders against non-cardholders, which is available in any point-of-sale system and answers the question directly, subject to the obvious selection problem that people who join are different.
And the cleaner version, if the volume allows: offer the card to a random half of new customers. That removes the selection problem entirely, and the seventy-fifth article's power arithmetic tells you whether your volume supports it.
The Cost Nobody Prices
The one thing that can turn it negative. Our own arithmetic, with entirely invented pause figures.
If a share of completers pause after collecting their reward, at an assumed baseline of 1.5 purchases a week, the coffees lost against the two gained:
20 percent pausing for 2 weeks: 0.60 lost, net plus 1.40.
30 percent for 3 weeks: 1.35 lost, net plus 0.65.
50 percent for 3 weeks: 2.25 lost, net minus 0.25.
30 percent for 6 weeks: 2.70 lost, net minus 0.70.
Four observations.
The reset does not have to be large to cancel the gain. Half of completers pausing three weeks is enough, and that is not an extreme assumption.
Every figure in that table is ours and invented, because no source we obtained quantifies the reset at all. The direction is reported; the size is not.
The practical instrument follows immediately and is cheap. Hand out the next card at the moment you give the reward, which on the goal distance model restarts the proportion rather than leaving it at one.
And that is the single most useful thing in this article. The mechanism that produces the acceleration also predicts the collapse, and the same mechanism tells you how to prevent it.
Designing A Card
The first application. Ours, untested, and not marketing advice.
Four points.
Compute the cost first. On our own figures a buy-ten-get-one card is a 2 percent discount at 80 percent margin and 6 percent at 40, and the behavioural question only arises after that.
Start people partway. The abstract reports that customers given a longer card with bonus stamps completed the same required purchases faster, and that is the manipulation with direct experimental support.
Keep the scheme short. On the goal distance model, effort tracks the proportion remaining, so each stamp on a ten-stamp card is worth five times one on a fifty-stamp card.
And issue the next card with the reward, because the same model predicts collapse the moment the proportion resets to one, and a secondary account reports defection being most likely at exactly that point.
Milestone Billing
The second application, and it runs on the firm rather than the customer. Ours.
Four points.
A project broken into milestones is a goal gradient applied to your own team, and the model predicts effort rising as each milestone nears.
It also predicts the trough. Effort should fall immediately after each milestone is signed off, which is the reset arriving repeatedly through a project rather than once at the end.
Which suggests a scheduling point rather than a motivational one. If the drop is real, the week after a milestone is the wrong time to schedule anything critical, and that is checkable against your own project records.
And we would flag this as entirely our own extrapolation. The studies concern consumers pursuing rewards, not staff completing work, and nothing we obtained tests the transfer.
There is one respect in which the transfer is probably worse than we have made it sound. A customer chooses to pursue a stamp card and an employee is assigned a milestone, and the crowding-out literature this publication covered separately gives specific reason to expect assigned goals to behave differently from chosen ones.
So we would use the goal distance model here as a scheduling heuristic rather than a motivational technique. Predicting where effort will sag is useful and does not require the mechanism to be the same one; assuming you can manufacture effort by adding milestones does.
Progress In Your Own Systems
The third application, and the most immediately available. Ours.
Four points.
Any form, onboarding sequence or application process in your business has an implicit gradient, and most display no progress at all.
The model gives the design rule directly. Show the proportion completed rather than the steps remaining, because effort is a function of the fraction and not the count.
And it gives a second rule that is less obvious. Count the things the person has already done before arriving, since a form that opens at three of eight rather than zero of five is the bonus-stamp manipulation in a different medium.
We would attach the usual caution. This is our transfer of a consumer finding to an interface, and although a large literature on progress indicators exists, we did not obtain any of it.
The Manipulation Question
Because the authors used the word illusion and we should not pretend they did not. Ours.
Four observations.
The bonus-stamp technique works by making a requirement feel smaller than it is, which is a fact about presentation rather than about the offer.
It is also, unusually for this series, fully disclosable. A customer told that their twelve-stamp card starts with two stamps has been told everything, and the arithmetic is on the card.
That distinguishes it from the previous article's harder case. Nothing is concealed and nobody is worse off: the customer gets a real reward for real purchases, at terms printed on the card.
Where it would become objectionable is a version that obscures the true requirement, and the test is the one we used before: could you explain the design to the customer without embarrassment? For bonus stamps, plainly yes.
Two versions that would fail that test are worth naming, because both exist. A scheme whose expiry conditions are designed so that most cards lapse before completion is selling a reward it does not intend to deliver, whatever the stamps say.
And a scheme that resets progress on a technicality exploits the same mechanism in reverse: the goal distance model says the customer who has invested nine stamps is at their most committed, which is exactly when a reset costs them most and the operator least.
What To Do
Do the margin arithmetic before the behavioural argument. Break-even extra sales equals one minus your margin, divided by your margin, and takes ten seconds.
Treat the circulating figures as unreliable. The same study is described with sample sizes of 300 and 948, and accelerations of 20 percent and 2.4 times, by sources recommending the technique.
Check whether a source has merged two studies. The coffee study used a 12-stamp card with 2 bonus stamps; the car wash study used a 10-stamp card with 2. A coffee card described with eight stamps has crossed the wires.
Start customers partway. That is the manipulation with direct experimental support, and it costs nothing.
Keep schemes short. Effort tracks the proportion remaining, so a stamp on a ten-stamp card is worth five of one on a fifty-stamp card.
Hand out the next card with the reward. The same model that produces acceleration predicts collapse when the proportion resets, and a secondary account reports defection peaking then.
Ask whether acceleration is new business or the same business sooner. On our own figures the scheme still pays if a quarter of it is new, and loses only the cost of the giveaway if none is.
Remember who the effect reportedly worked on. An academic account says it was confined to people who completed their cards, and non-completers showed no change at all.
The Limits Of This Analysis
Several caveats matter. This article discusses research on motivation and is not marketing, pricing or commercial advice; the applications are our own reasoning and untested. Everything is verified to August 2026. We did not obtain either underlying paper. The 2006 goal gradient study is reported from its abstract, obtained verbatim from a research database record, which means we report no sample sizes, no effect sizes and no confidence intervals from the study itself, and cannot check any of the disputed figures against it. We did not obtain the 2006 endowed progress paper at all, and describe its design from an encyclopedia; the completion rates widely attributed to it are not reported here, because the only source we found for them also gives an identical sample size for two different studies. The acceleration figure and the café's setting come from the authors' own university's review publication, which is a good secondary source and is not the paper. The limitation about completers comes from an academic preprint characterising the study, and it is the claim we would most want checked against the original, because it is the difference between a scheme that grows a business and one that discounts loyal customers. The post-reward defection finding comes from a study-aid site, flagged at every use. One citation in a practitioner reference list could not be verified at all, and we record that without asserting the paper does not exist. All arithmetic is ours and every commercial parameter in it is invented: the price, the margins, the baseline purchase rate, and above all the pause proportions and durations in the reset table, which no source quantifies and which determine whether that section's conclusion is positive or negative. The milestone billing and progress indicator applications are our own extrapolations from consumer research to workplace and interface settings that these studies did not examine.
Frequently Asked Questions
What is the goal gradient effect?
Does giving people a head start work?
Why do the numbers vary so much?
What is the limitation nobody mentions?
Does a stamp card actually pay?
What is the risk?
What is the cheapest fix?
References
- Research database record for Kivetz, R., Urminsky, O., & Zheng, Y. (2006), The Goal-Gradient Hypothesis Resurrected: Purchase Acceleration, Illusionary Goal Progress, and Customer Retention, filed as Natural Field Experiments 00658 with a field experiments archive and published as Journal of Marketing Research, 43(1), 39–58, DOI 10.1509/jmkr.43.1.39, reproducing the abstract in full: on the goal-gradient hypothesis denoting the classic finding from behaviorism that animals expend more effort as they approach a reward; on the authors building on this to generate new propositions for the human psychology of rewards, tested using a field experiment, secondary customer data, paper-and-pencil problems, and Tobit and logit models; on the key findings indicating that participants in a real cafe reward program purchase coffee more frequently the closer they are to earning a free coffee, that Internet users who rate songs in return for reward certificates visit the rating website more often, rate more songs per visit and persist longer as they approach the reward goal, that the illusion of progress toward the goal induces purchase acceleration, with customers receiving a 12-stamp coffee card with 2 preexisting bonus stamps completing the 10 required purchases faster than customers receiving a regular 10-stamp card, and that a stronger tendency to accelerate toward the goal predicts greater retention and faster reengagement; on the findings being captured by a parsimonious goal distance model in which effort investment is a function of the proportion of original distance remaining to the goal; and on the authors ruling out alternative explanations using statistical and experimental controls. Note: a research database record. Our source for the abstract verbatim; we did not obtain the paper, so no sample size, effect size or confidence interval from the study itself is reported here. The abstract as reproduced contains a typographical error, "The key finding indicate", which we quote as found. ideas.repec.org
- Academic preprint on badge effects in online question-and-answer communities, describing the 2006 study: that subjects who received a loyalty card tracking coffees purchased from a local coffee chain purchased coffee significantly more frequently the closer they were to earning a free cup; that the authors recognised the existence of a group of participants who did not complete their coffee cards for the duration of the study and did not exhibit a noticeable change in their coffee purchasing habits; and that they concluded the loyalty card effect was constrained to the population of participants who handed in their completed loyalty cards in exchange for the free-coffee reward. Note: an academic preprint characterising the study, not the study itself. Our source for the completers limitation, which is the claim in this article we would most want checked against the original. arxiv.org
- Review publication of the university employing one of the authors, describing the study and quoting him: recording that the authors turned to customer rewards programmes; that goal distance is measured by the proportion of the original programme requirements remaining to meet the goal; that the first experiment looked at coffee purchases by customers in a rewards programme at a café located within the campus of a large university; that customers were offered a card letting them earn one free coffee after buying ten; that as participants accumulated more stamps the average length of time before the next purchase decreased; that the average time between purchases accelerated by about 20 percent from the first to the last stamp on the card; and that in other words members purchased two more coffees in the time it took to complete the card than they would have without accelerating. Together with the same university's faculty profile confirming the paper was a finalist for two named awards, in 2007 and 2011. Note: a university review publication quoting one of the paper's own authors. Our source for the acceleration figure and the setting; a good secondary source and not the paper, graded B accordingly. chicagobooth.edu
- Three practitioner websites and one study-aid site describing the same studies, recorded here principally to document that their figures conflict. One records 948 café loyalty members and an acceleration of about 20 percent. Another records 300 café customers in Chicago, an average of 12 days between the first and second stamp against 5 days between the ninth and tenth, purchases 2.4 times more frequent, and separately 300 car wash customers with completion rates of 34 percent for pre-stamped cards against 19 percent for cards starting from zero. A third carries a reference list giving two distinct 2006 papers by the same two authors on the endowed progress effect, one in the Journal of Consumer Research, 32(4), 504–512, and a second given as the Journal of Experimental Social Psychology, 42(3), 394–403, with a different subtitle. The study-aid site summarises the paper's studies and records that just after reward attainment customers exhibited a drop in activity, described as post-reward resetting, and were most likely to defect. Note: practitioner and study-aid websites, none of them academic sources, flagged at every use. Recorded to document conflicting figures rather than to supply them; the second of these gives an identical sample size for two different studies, and the third contains a citation we could not verify against any other source. ux-strategy.ch
- Encyclopedia entry on goal pursuit describing the endowed progress study, recording that half of the cards required ten stamps to receive the reward of a free car wash but were endowed with two stamps, so those patrons required only eight additional stamps; together with reference lists carried on two peer-reviewed journal articles confirming Nunes, J. C., and Drèze, X. (2006), The Endowed Progress Effect: How Artificial Advancement Increases Effort, Journal of Consumer Research, 32(4), 504–512, March, DOI 10.1086/500480; Hull, C. L. (1932), The goal-gradient hypothesis and maze learning, Psychological Review, 39(1), 25–43; Koo, M., and Fishbach, A. (2012), The Small-Area Hypothesis: Effects of Progress Monitoring on Goal Adherence, Journal of Consumer Research, 39(3), 493–509; and Cheema, A., and Bagchi, R. (2011), The effect of visualizing progress on goal pursuit, Journal of Marketing, 75(2), 109–123. Note: an encyclopedia, not an academic source, flagged at every use, plus reference lists carried on peer-reviewed articles for the citations. We obtained none of the works named, including the endowed progress paper itself. encyclopedia.pub
This article discusses research on motivation and is not marketing, pricing or commercial advice. Neither underlying paper was obtained. The goal gradient study is reported from its abstract, so no sample size or effect size from the study itself appears here; the endowed progress paper was not obtained at all and the completion rates attributed to it are not reported. Figures in commercial circulation conflict and are documented as conflicting rather than adopted. All arithmetic is the authors' own on invented commercial parameters, and the reset table's assumptions determine whether its conclusion is positive or negative.