Referral Experiments and Limits to Spread
Examine research on referred-customer value, incentive experiments, and viral diffusion, and why assuming K above 1 is risky.
Written and reviewed by Eric Han · Co-founder & CTO, reopt
Key takeaways
- Do not assume K exceeds 1 in a plan. Large datasets show 73–95% of online diffusion stops at the seed, and average content cascade size is 1.3. We found no large public dataset directly measuring K for referral programs.
- Referred customers had 16% higher predicted six-year CLV and 25% higher observed value over roughly three years (33 months), based on nonrandomized data from one German bank.
- Observational data substantially overstate peer effects: Facebook estimates were 317–498% too high.
- A wording change can produce a noticeable relative increase. Reminding referred customers that they joined through a referral increased their referrals about 21% over two days versus a generic request, but the absolute increase was very small.
- Whether one-sided or two-sided rewards work better depends on context. There is no single established winner.
Most Spread Stops in the First Generation
| Evidence | Figures | Scale | Grade |
|---|---|---|---|
| Goel, Watts, and Goldstein, 2012 | 73–95% never spread beyond the seed; fewer than 1% exceed seven nodes | Seven online domains | B |
| Goel et al., 2016 | Mean cascade size 1.3; about 99% of adoptions at the root or its direct followers | About one billion Twitter events | B |
| Leskovec et al., 2007 | Customer base grew linearly; 27.8% of buyers forwarded referrals | 15.65 million referrals | B |
| Gershon and Jiang | Cumulative successful referrals per customer at observation: 0.18–0.30, organic versus referred customers | 41.2 million people | B |
In Leskovec's online-retail data, effects saturated quickly as received referrals increased. Purchase probability peaked at two referrals for books, while DVDs saturated around ten.
Twitter content is not purchase conversion. Use it only as an anchor for diffusion structure.
The exponential-growth trap
Starting with 10 people, 10 invitations each, and 20% conversion gives K=2. Skok's illustration uses this to reach 20,000 people after 20 days. It illustrates a principle, not realistic forecast inputs. Most large datasets above concern content sharing. Selecting only large cascades can produce a reproduction number near 1.8 (Cheng et al., 2018), but this is temporary and conditional on a selected sample.
The Value of Referred Customers
Schmitt, Skiera, and Van den Bulte (2011) study about 10,000 customers at one German bank (acquired in 2006, observed for about 33 months, nonrandomized, grade B).
| Metric | Difference for referred customers |
|---|---|
| Daily contribution margin | +25%, declining over time |
| Churn hazard | About −18% |
| Customer value during observation | About +25%, or +35% including acquisition-cost differences |
| Predicted six-year CLV | About +16%, or EUR 40 |
| Reward ROI | About 60% over six years, based on a EUR 25 reward |
“Referred customers are 16% more valuable” isolates one particular condition. Because the comparison is nonrandomized, better customers may have selected into referrals. A follow-up by Van den Bulte et al. (2018) finds lower referred-customer churn only while their referrer remains; it recommends referrers with at least six months of tenure, high margins, and low churn risk.
Referred customers also refer more. In Gershon and Jiang, the gap shrank from 75% in the baseline model to 57% controlling for purchase counts and 31% with double machine learning. This illustrates why observational effects need discounting.
Randomized Experiments
| Experiment | Context | Result | Grade |
|---|---|---|---|
| Gershon and Jiang | Message comparison among more than 10 million referred customers | About +21% versus a generic referral request over two days; very small absolute increase | A |
| Aral and Walker, 2011 | 9,687 Facebook app users | Automatic broadcasts +246%; adding active invitations +344%, measured as peer-adoption hazard | A |
| Li, Li, and Belo, 2026 | More than 160,000 users of a Chinese telecom app | Uncertain referrer rewards raised total referrals 20.9%; uncertain friend rewards reduced them 12.3% | A (summary) |
| Sun et al., 2021 | More than 75,000 daily-deal users | Disclosing the referrer's purchase increased purchases only; mentioning rewards increased downstream referrals only. Showing both had no effect | A (summary) |
| Hinz et al., 2011 | Two small randomized experiments and a telecom campaign with post-hoc cohort comparison, over 200,000 people | Highly connected seeding +39–52% versus random, up to 8 times versus low-connectivity seeding (conference manuscript); due to activity, not greater persuasiveness | A (summary) |
| Gershon, Cryder, and John, 2020 | 6,364 app customers, five conditions | Friend-benefiting rewards had slightly higher conversion than referrer-benefiting rewards; condition-level figures unverified | A (summary) |
| Bapna and Umyarov, 2015 | Randomly induced Last.fm paid adoption, 3.8 million people | Friends' adoption odds increased more than 60% | A (summary) |
Reward Structures in the Market
Among 351 referral programs studied by Gershon and colleagues, about 55% benefited both sides, 40.5% the referrer, and 2.6% the friend. Friend-only rewards were rarely used despite performing reasonably in experiments.
Bias in Observational Estimates
| Evidence | Finding | Grade |
|---|---|---|
| Eckles, Kizilcec, and Bakshy, 2016 | Observational estimates for posting and feedback to others overstated experimental effects by 317–498%; replies were instead underestimated by 36% and 68% | A |
| Aral et al., 2009 | Observational methods overstated peer effects by 300–700% | B |
| Libai, Muller, and Peres, 2013 | In simulations, about 26–32% of word-of-mouth value came only from acceleration; the rest from market expansion. Stronger brands had a larger acceleration share | B (simulation) |
“Acceleration” brings forward customers who would eventually arrive without referrals. This is why a simulation should not assume 100% incrementality. We found no public incremental-share estimate for actual programs.
Reward Size and Side Effects
- Research suggests larger rewards increase volume while lowering referred-customer profitability (Wolters et al., 2020, secondary citation; figures unverified).
- About 3.8% of accounts were suspected of fraud in Gershon and Jiang's cashback app.
- Recruiting loyal customers does not always work. In the Godes and Mayzlin, 2009 field test, 381 loyal customers generated no additional sales.
Simulation Inputs
| Scenario | Anchor | Use |
|---|---|---|
| Pessimistic | Decompose round-level K using invitation conversion around 0.5% purchases per referral | Budget approval |
| Cross-check | Cumulative successful referrals of 0.18–0.30 over about four years | Upper-bound check; already successful referrals, so do not multiply by purchases per referral |
| Base | Your industry's vendor median from a single dataset | Planning |
| Optimistic | ReferralCandy top 10% | Upper-bound check |
Limit the referral forecast to two generations. When is below 0.1, the referral-funnel multiplier 1÷(1−) is nearly the same as the two-generation sum. If looks large, question the inputs before trusting the sum. Treat incremental share as a scenario. Worked Scenario 3 compares a single judgment-based round with the cumulative anchor, rather than calculating all four scenarios above.
Referral Funnel Metrics
Compare industry sharing, invitation conversion, acquisition, and time-to-first-referral metrics, aligning vendor denominators to build a referral forecast.
Influencer Marketing Conversion
Trace the $5.78 influencer ROI claim, distinguish discount-code attribution from incrementality, and assess follower size, disclosure, and Korean live-commerce figures.