Endowed Progress Effect: The Math and the 2006 Paper

If you are here for the paper: it is Joseph C. Nunes and Xavier Dreze, "The Endowed Progress Effect: How Artificial Advancement Increases Effort," Journal of Consumer Research 32, no. 4 (March 2006): 504-512, doi:10.1086/500480. The publisher page is on Oxford Academic; an author-posted copy sits on SSRN. The finding: reframing an eight-step task as a ten-step task with two steps already done raises completion and shortens time to completion, even though the real work is identical.

The rest of this page is the mechanism, the arithmetic for sizing it, and the places it fails.

What the study actually did

The abstract states the design plainly: the authors converted a task requiring eight steps into a task requiring ten steps with two steps already complete, which reframes the job as begun-and-unfinished rather than not-yet-started. That reframing increases the likelihood of completion and decreases the time taken to complete.

The field setting was a car wash loyalty card. One card needed eight stamps and started blank. The other needed ten stamps and arrived with two already stamped. Both required exactly eight paid washes to earn the free one. Completion over the tracked period was 19 percent on the blank eight-stamp card and 34 percent on the pre-stamped ten-stamp card.

Two details most summaries drop

The abstract names two things that matter more than the headline number.

First, the mechanism. The effect is attributed to perceptions of progress rather than to reluctance to forfeit the head start. It is not sunk cost. People are not protecting the free stamps. They are responding to being partway along.

Second, the moderators. The paper flags the reason given for the endowment, and the currency progress is recorded in, as variables that change the size of the effect. An unexplained head start is not the same intervention as an explained one. If you copy the tactic and skip the explanation, you are not running the experiment you read about.

On the effect size

Nineteen to thirty-four percent is a 1.789x relative lift. It is one field study, in one category, on one purchase cycle. Treat it as evidence that the direction is real and the magnitude can be large. Do not treat 1.789x as a number you get to plug into your own forecast. Below I discount it by half before applying it anywhere else, and I say so in the code.

The maths of artificial advancement

The trick is that two fractions describe the same remaining work.

A customer with a blank eight-stamp card is at 0/8. A customer with a pre-stamped ten-stamp card is at 2/10. Both need eight more purchases. But 0/8 is zero percent of a goal, and 2/10 is twenty percent of a goal.

Write it generally. Let r be the real number of actions you require. Endowment means printing a goal of g = r + e and granting e up front. Perceived starting progress is e / (r + e), while real remaining work stays at r in both designs. The endowment is free by construction: you never hand out a reward you would not have handed out anyway.

The design question is only how big e should be. Two forces push against each other.

• —Larger e raises perceived starting progress, which is the thing doing the work.
• —Larger e raises the printed goal, and a printed goal that looks unreachable suppresses the whole effect. A ten-stamp card reads as achievable. A forty-stamp card with eight free does not, even though the real work is thirty-two either way.

I have not found a published optimum for e. The study used e/g = 0.2. That is the only ratio with a field result behind it, and it is where I start.

Three implementations, sized

Same restructure, three surfaces. Every input below that is not the published 19/34 is an assumption, labelled as one.

Assumptions behind those columns: a $10 wash at $3 cost of goods with a free wash on completion, so $53 of margin per completed card; an activated user assumed to be worth $162 of gross margin over their life; a referred user assumed to be worth $40 of contribution against a $50 reward, so $150 net per completed milestone. The punch card row uses the published 1.789x because it is the same context. The other two rows discount it to 1.395x, half the published relative lift, because nothing about a SaaS checklist has been shown to behave like a car wash.

"""Endowed progress: size the arithmetic. stdlib only."""

# --- the one published number we anchor on (Nunes & Dreze 2006, JCR) ---
RATE_PLAIN, RATE_ENDOWED = 0.19, 0.34
RELATIVE_LIFT = RATE_ENDOWED / RATE_PLAIN          # 1.789
HALF_STRENGTH = 1 + (RELATIVE_LIFT - 1) / 2        # discount for transfer


def sized(base_rate, population, value_per_completer, lift):
    """Incremental completers and value from an endowed-progress restructure."""
    new_rate = base_rate * lift
    delta = (new_rate - base_rate) * population
    return new_rate, delta, delta * value_per_completer


# 1. punch card, replicating the study's own economics
#    ASSUMED: $10 wash, $3 cost of goods, 8 paid washes, free wash on completion
MARGIN_PER_CARD = 8 * (10.0 - 3.0) - 3.0           # $53
_, card_delta, card_value = sized(RATE_PLAIN, 150, MARGIN_PER_CARD, RELATIVE_LIFT)

# 2. onboarding checklist: 4 real steps shown as 6 with 2 pre-credited
#    ASSUMED: 1,000 signups/month, 22% finish today, $162 margin per activated user
onb_rate, onb_delta, onb_value = sized(0.22, 1000, 162.0, HALF_STRENGTH)

# 3. referral milestone: 5 real referrals shown as 6 with 1 gifted
#    ASSUMED: 4,000 eligible users, 6% reach it, $40 per referred user, $50 reward
REF_NET = 5 * 40.0 - 50.0                          # $150
ref_rate, ref_delta, ref_value = sized(0.06, 4000, REF_NET, HALF_STRENGTH)

print(f"published relative lift : {RELATIVE_LIFT:.3f}x  (34% / 19%)")
print(f"half-strength assumption: {HALF_STRENGTH:.3f}x\n")

rows = [
    ("punch card (150 enrolled)", RATE_PLAIN, RATE_PLAIN * RELATIVE_LIFT,
     card_delta, MARGIN_PER_CARD, card_value),
    ("onboarding (1,000 signups)", 0.22, onb_rate, onb_delta, 162.0, onb_value),
    ("referrals (4,000 eligible)", 0.06, ref_rate, ref_delta, REF_NET, ref_value),
]
print(f"{'implementation':<27}{'base':>7}{'endowed':>9}{'extra':>8}{'each':>9}{'value':>12}")
for name, base, new, delta, each, value in rows:
    print(f"{name:<27}{base:>6.1%}{new:>9.1%}{delta:>8.1f}{each:>9,.0f}{value:>12,.0f}")

total = card_value + onb_value + ref_value
print(f"\ntotal incremental contribution (all assumptions above): ${total:,.0f}")

# break-even: how weak can the transferred effect get before onboarding stops paying?
COST_TO_BUILD = 2_000.0
need = COST_TO_BUILD / (0.22 * 1000 * 162.0)
print(f"onboarding rebuild costs ${COST_TO_BUILD:,.0f}; it pays if the lift "
      f"is at least {1 + need:.3f}x")

assert round(card_delta, 6) == 22.5, card_delta
assert round(card_value, 2) == 1192.50, card_value
assert 1.39 < HALF_STRENGTH < 1.40

Output:

published relative lift : 1.789x  (34% / 19%)
half-strength assumption: 1.395x

implementation                base  endowed   extra     each       value
punch card (150 enrolled)   19.0%    34.0%    22.5       53       1,193
onboarding (1,000 signups)  22.0%    30.7%    86.8      162      14,068
referrals (4,000 eligible)   6.0%     8.4%    94.7      150      14,211

total incremental contribution (all assumptions above): $29,471
onboarding rebuild costs $2,000; it pays if the lift is at least 1.056x

The last line is the one that decides anything. Under those assumptions the onboarding rebuild pays for itself at a 1.056x lift. The published effect is 1.789x. You can be wrong about how well the effect transfers by a factor of fourteen and still be in profit. That asymmetry, not the headline percentage, is the reason to ship it.

The caveat on the punch card row

That $1,193 counts completers only. Non-completers in both arms still bought washes, and a completion-rate experiment does not separate their spend. Some of the extra completions came from customers who were going to buy several washes regardless and simply finished the card. The direction holds. The precision does not.

Where endowed progress stops working

I have watched this fail more often than it works, in four recognisable ways.

The goal is not credible. Perceived progress helps only if the endpoint looks reachable. Inflating the printed goal to make the fraction prettier moves the endpoint out of reach and kills the effect you were buying.

The endowment has no story. The paper explicitly lists the reason given for the endowment as a moderator. "Here are two free stamps because you signed up today" is a different stimulus from two unexplained stamps. Say why.

The credited steps were not real. If the checklist shows 2/6 and the user cannot name what those two steps were, you have not endowed progress, you have printed a number. The first time someone works out that the bar is decorative, every other number in your product loses credibility with it.

The base rate is already high. A multiplicative lift on a 60 percent completion rate has very little room to run, and the goal gradient is already doing the work near the finish. This is worth most where completion is low and the drop-off sits at step zero.

There is also a timing question this mechanism does not answer. Endowed progress changes whether people start, not how long they persist once a streak is running. The hazard-rate view of persistence is in streak mechanics and the hazard rate, and the schedule that keeps people coming back after the first milestone is a different tool entirely, worked out in variable reward schedules.

Where it becomes manipulative

The honest test is simple. Could you show the user exactly what the endowed steps were and have them agree it was a gift or a real action?

The first two are the car wash. The last two are a different product decision wearing the same interface. If you are drawing that line for a team, the taxonomy I use is in incentive design ethics and dark patterns, and the pricing analogue, charging for the thing that protects accumulated progress, is in loss aversion and streak freeze pricing.

FAQ

Where can I find the Nunes and Dreze 2006 endowed progress effect PDF?

The paper sits behind the Journal of Consumer Research paywall at doi:10.1086/500480. An author-posted version is on SSRN, and the publisher abstract page is on Oxford Academic. Full citation: Nunes, Joseph C., and Xavier Dreze. "The Endowed Progress Effect: How Artificial Advancement Increases Effort." Journal of Consumer Research 32, no. 4 (2006): 504-512.

What is the endowed progress effect?

Giving someone artificial advancement toward a goal makes them work harder to reach it, even when the real effort required is unchanged. A ten-step goal with two steps pre-completed outperforms an identical eight-step goal starting from zero.

Is the endowed progress effect the same as the goal gradient effect?

No, though they compound. The goal gradient is about acceleration near the finish. Endowed progress is about the start: it moves someone from not-begun to begun, which is where most abandonment happens.

How many free stamps should I give?

The only ratio with a field result behind it is the study's: two endowed out of a printed ten, so twenty percent. Larger endowments need a larger printed goal, and a goal that reads as unreachable suppresses the effect. If you are setting thresholds across several tiers rather than one card, the arithmetic is different and lives in loyalty tier threshold calculus.

Sizing an incentive and unsure whether the lift covers the build? I model these before anyone writes code, with the assumptions written down where you can argue with them. See my services or get in touch.