Regression Discontinuity
A quasi-experimental design that identifies causal effects by comparing units just above and just below a threshold that determines treatment.
What Is Regression Discontinuity?
Regression discontinuity (RD) exploits sharp thresholds that determine treatment assignment. Users just above the cutoff get treated; those just below don't. If the cutoff is quasi-random at the margin, comparing outcomes across the threshold identifies the causal effect locally — no randomization needed, only a credible cutoff.
Also Known As
- Data science: RDD, regression discontinuity design
- Growth: threshold-based causal estimation
- Marketing: eligibility-cutoff analysis
- Engineering: discontinuity-based effect identification
How It Works
Your freemium product gives "Pro" perks to users with a usage score ≥ 75. You plot retention against usage score, fit flexible curves on either side of the 75 threshold, and measure the jump at 75. If retention jumps from 42% at 74.9 to 58% at 75.1, the local causal effect of Pro status on retention is +16pp at that threshold. Users at 74 and 76 are nearly identical on everything except treatment status, so the discontinuity isolates treatment effect.
Two flavors: sharp RD (threshold fully determines treatment) and fuzzy RD (threshold changes probability of treatment; analyzed like IV). Modern practice uses local linear or local polynomial regression with data-driven bandwidth selection.
Best Practices
- Test for manipulation at the cutoff (McCrary density test) — if users can game the running variable, RD is invalid.
- Use local linear regression with a small bandwidth rather than global polynomials.
- Show the graph. A visible jump at the cutoff is the single most persuasive evidence in RD.
- Run placebo tests at non-threshold values to show no fake discontinuities.
- Interpret locally. RD identifies effects near the threshold, not globally.
Common Mistakes
- Fitting high-order polynomials — this produces spurious discontinuities from curve-fitting artifacts.
- Ignoring manipulation. If users know the cutoff and can adjust their score, RD estimates are biased.
- Extrapolating beyond the threshold. RD tells you about the users right at the margin, not about users far from it.
Industry Context
In SaaS/B2B, RD is perfect for analyzing effects of plan tier cutoffs, usage-based feature gating, and contract thresholds. In ecommerce, free shipping thresholds and loyalty tier cutoffs are natural RD settings. In lead gen, lead scoring cutoffs that trigger SDR outreach are an ideal RD setting to measure true incremental pipeline.
The Behavioral Science Connection
RD is a clever use of a common behavioral feature: humans and systems create bright-line rules (credit limits, plan tiers, eligibility cutoffs). These lines are often arbitrary — why 75 and not 74? That very arbitrariness is what makes them powerful causal identifiers, since users on either side are substantively identical except for the rule.
Key Takeaway
Whenever your business uses a threshold to determine who gets what, you have a potential regression discontinuity design sitting in your data. Used carefully, it rivals RCTs for causal credibility.