September 2008.
Dropbox had a problem.
They were spending $233-388 to acquire each customer through Google AdWords.
But each customer was only worth $99 (annual subscription).
LTV:CAC ratio: 0.26:1
Translation: Lose money on every customer.
Most companies would:
- Raise prices
- Cut acquisition costs
- Pivot the business
- Shut down
Drew Houston did something different.
He built a referral program:
- Give 500MB for each friend who signs up
- Friend gets 500MB too
The result?
From September 2008 to December 2009:
- User base: 100K → 4 million
- Growth: 4000%
- Customer acquisition cost: ~$0
How?
Their viral coefficient (K) went above 1.
When K > 1, you get exponential growth without paid acquisition.
Each user brings more than one new user.
This is the power of understanding growth metrics.
Let’s learn how to measure and engineer exponential growth.
Part 1: The Viral Coefficient (K-Factor) - When Growth Becomes Free
The viral coefficient measures:
How many new users does each existing user bring?
The Formula
$$ K = i \times c $$
Where:
- i = invitations sent per user
- c = conversion rate (% who accept)
Alternative formula:
$$ K = \frac{\text{Number of New Users Generated by Referrals}}{\text{Number of Existing Users}} $$
Why K > 1 Changes Everything
If K = 0.5:
- 100 users bring 50 new users
- Those 50 bring 25 more
- Those 25 bring 12 more
- Total: 100 + 50 + 25 + 12 + … = 200 users (eventually plateaus)
If K = 1.0:
- 100 users bring 100 new users
- Those 100 bring 100 more
- Those 100 bring 100 more
- Growth sustains but doesn’t accelerate
If K = 1.5:
- 100 users bring 150 new users
- Those 150 bring 225 more
- Those 225 bring 337 more
- Those 337 bring 506 more
- Exponential growth
Calculating Your K-Factor
Example: SaaS referral program
Cohort: 1,000 users joined in January
Tracking over 30 days:
- Total invitations sent: 3,000
- Friends who signed up: 600
Calculation:
i (invites per user) = 3,000 ÷ 1,000 = 3
c (conversion rate) = 600 ÷ 3,000 = 20%
K = 3 × 0.20 = 0.6
Interpretation:
Each user brings 0.6 new users on average.
To achieve K > 1, you need to:
- Increase invites per user (3 → 5)
- Increase conversion rate (20% → 25%)
- Or both
New scenario:
- 5 invites per user
- 25% conversion
- K = 5 × 0.25 = 1.25
Now you have exponential growth.
The Time Factor: Viral Cycle Time
K alone doesn’t tell the full story.
You need viral cycle time (ct):
ct = Time for one viral cycle to complete
Example:
Product A:
- K = 0.8
- ct = 2 days
Product B:
- K = 1.2
- ct = 30 days
Which grows faster?
Product A:
- Day 2: 80 new users per 100
- Day 4: 64 more
- Day 6: 51 more
- Fast feedback loop, even with K < 1
Product B:
- Day 30: 120 new users per 100
- Day 60: 144 more
- Slower feedback
Over 60 days:
- Product A: ~500 users total (30 cycles)
- Product B: ~244 users total (2 cycles)
Lesson: Fast viral cycle time with lower K can beat slow cycle time with higher K.
Real Examples of Viral Coefficients
| Company | K-Factor | Strategy |
|---|---|---|
| Dropbox | 1.5+ (at peak) | 500MB per referral |
| PayPal | 1.2 (early) | $10 for referrer, $10 for friend |
| Hotmail | 1.4 (1996-1997) | “PS I love you. Get your free email at Hotmail” |
| 1.8+ (2009-2012) | Network effects - need friends on platform | |
| 1.3 (early) | Easy sharing to Facebook | |
| Clubhouse | 2.0+ (launch) | Invite-only scarcity |
How to Increase Your K-Factor
Increase invitations per user (i):
- Prompt users at high-engagement moments
- Make sharing seamless (one click)
- Give users a reason to invite (incentives, utility)
- Create FOMO (invite-only, limited spots)
Increase conversion rate (c):
- Reduce friction in signup
- Show social proof (who else joined)
- Offer incentive to invited user
- Optimize landing page for referred traffic
- Make value proposition crystal clear
Real numbers from Dropbox:
Before optimization:
i = 2.0 invites per user
c = 15% conversion
K = 0.30
After optimization (referral bonus):
i = 3.5 invites per user
c = 28% conversion
K = 0.98
After further optimization (mutual rewards):
i = 4.2 invites per user
c = 35% conversion
K = 1.47
Result: 3900% growth in 15 months
Part 2: Retention Metrics - The Foundation of Growth
Peter Fader (Wharton professor):
“Retention is the single most important thing for growth.”
Why?
Growth = New users + Retained users - Churned users
If you have a leaky bucket (poor retention), all your acquisition efforts are wasted.
DAU/MAU Ratio (Stickiness)
The stickiness metric:
$$ \text{Stickiness} = \frac{\text{Daily Active Users (DAU)}}{\text{Monthly Active Users (MAU)}} $$
What it measures:
How often users come back.
Example:
- MAU: 1,000,000 users
- DAU: 500,000 users
- Stickiness: 500,000 ÷ 1,000,000 = 50%
Interpretation:
On any given day, 50% of monthly users are active.
Means: Average user uses product 15 days per month (50% × 30 days).
Benchmarks:
| Product Type | Target DAU/MAU |
|---|---|
| Social media | 50-70% |
| Communication | 60-80% |
| Gaming | 20-40% |
| B2B SaaS | 30-50% |
| E-commerce | 5-15% |
| Banking | 10-25% |
Real examples:
| Company | DAU/MAU | Interpretation |
|---|---|---|
| 66% | Users log in ~20 days/month | |
| 80%+ | Users log in ~24 days/month | |
| Slack | 93% | Users log in ~28 days/month |
| 65% | Users log in ~19 days/month | |
| Spotify | 35% | Users listen ~10 days/month |
Slack’s 93% is extraordinary.
It means Slack became essential infrastructure.
Users can’t work without it.
Retention Curves: The Truth About Your Product
The most important graph for any product:
Retention Curve
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
100%│█
│ █
80%│ ██
│ ███
60%│ ████
│ ██████████████████
40%│ (flattening = good)
│
20%│
│
0%└─────────────────────────────────────
0 30 60 90 120
Days
Three retention curve shapes:
1. Dying product:
100% → 40% → 15% → 5% → 2% → ...
Curves down continuously, never flattens
2. Smile curve (survivorship bias):
100% → 30% → 25% → 28% → 32% → ...
Dips then rises (only superfans remain)
3. Flattening curve (product-market fit):
100% → 60% → 45% → 38% → 35% → 35% → ...
Drops then flattens (core retained users)
You want #3.
Flattening means:
- You have a core user base that sees value
- Product is sticky enough
- You can build on this foundation
If you see #1, fix retention before spending on acquisition.
Cohort Retention Analysis
The framework that separates amateurs from pros.
What it is:
Track retention for each cohort (group that joined in the same time period) over time.
Example table:
Monthly Cohort Retention (% of users still active)
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
Cohort | M0 | M1 | M2 | M3 | M6 | M12
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
Jan 2024 | 100% | 45% | 38% | 35% | 32% | 30%
Feb 2024 | 100% | 48% | 41% | 38% | 35% | --
Mar 2024 | 100% | 52% | 45% | 42% | -- | --
Apr 2024 | 100% | 55% | 48% | -- | -- | --
May 2024 | 100% | 58% | -- | -- | -- | --
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
What this tells you:
Month-1 retention improved from 45% → 58%.
You’re getting better at onboarding and activation.
Why cohorts matter:
Blended retention hides the truth.
Example:
Overall retention: 40%
Sounds okay.
But cohort breakdown:
Old users (2023): 60% retention
New users (2024): 20% retention
You have a BIG problem with new users.
Blended metric hides it.
Cohort analysis reveals:
- Is your product improving?
- Are new features helping or hurting?
- Which user segments retain best?
- When do users churn (day 1, week 1, month 3)?
Net Revenue Retention (NRR) - The SaaS Gold Standard
NRR is THE metric for SaaS companies.
Formula:
$$ \text{NRR} = \frac{\text{Starting MRR} + \text{Expansion} - \text{Churn} - \text{Contraction}}{\text{Starting MRR}} $$
Where:
- Starting MRR: Revenue from a cohort at the start
- Expansion: Upgrades, upsells, cross-sells
- Churn: Lost customers
- Contraction: Downgrades
Example:
Starting cohort (Jan 2024): $100K MRR
Over 12 months:
+ Expansion (upgrades): +$35K
- Churn (lost customers): -$18K
- Contraction (downgrades): -$5K
Ending MRR: $100K + $35K - $18K - $5K = $112K
NRR = $112K ÷ $100K = 112% or 1.12
Interpretation:
Even with churn, you grew revenue from existing customers by 12%.
This is the magic of negative churn.
Benchmarks:
| NRR | Rating | Implications |
|---|---|---|
| < 90% | Poor | Losing customers fast |
| 90-100% | Okay | Treading water |
| 100-110% | Good | Expanding revenue |
| 110-130% | Excellent | Strong expansion |
| > 130% | Elite | Best-in-class |
Real examples:
| Company | NRR | Insight |
|---|---|---|
| Snowflake | 158% | Customers expand usage massively |
| Datadog | 130% | Strong upsell motion |
| Slack | 143% | Teams expand to entire company |
| Twilio | 137% | Usage-based pricing = growth |
| MongoDB | 120% | Land-and-expand working |
Why NRR > 100% is powerful:
You can grow without any new customers.
Example:
Year 1:
- 100 customers, $100K MRR
- NRR = 120%
Year 2:
- Same 100 customers, $120K MRR (no new customers!)
- NRR = 120%
Year 3:
- Same 100 customers, $144K MRR
44% revenue growth WITHOUT acquisition.
This is why investors LOVE high NRR companies.
Expansion > acquisition.
How to Improve NRR
1. Reduce Churn:
- Better onboarding
- Proactive customer success
- Identify at-risk customers early
- Fix product gaps
2. Reduce Contraction:
- Usage-based pricing (aligns with value)
- Make downgrades harder (friction)
- Offer annual discounts (lock-in)
3. Increase Expansion:
- Seat-based pricing (teams grow)
- Usage-based pricing (consumption grows)
- Feature tiers (upsell opportunities)
- Cross-sell (additional products)
Real example: Slack’s expansion motion
Month 1: Free plan, 5 users
|
v
Month 3: Team adopts tool, reaches message limit
|
v
Month 4: Upgrade to paid plan, 20 users ($160/mo)
|
v
Month 8: Add integrations, more teams join, 50 users ($400/mo)
|
v
Month 12: Company-wide rollout, 200 users ($1,600/mo)
|
v
Month 18: Enterprise features, 500 users ($6,000/mo)
Starting: $0
Ending: $6,000
NRR: Infinity (started free)
Part 3: Sales Efficiency Metrics
Growth is useless if it’s unprofitable.
You need to measure: How efficiently are we converting spend into revenue?
The Magic Number
The king of SaaS efficiency metrics:
$$ \text{Magic Number} = \frac{\text{Net New ARR (this quarter)} \times 4}{\text{Sales & Marketing Spend (last quarter)}} $$
Why × 4?
Converts quarterly ARR to annual payback.
Example:
Q1 2024:
Sales & marketing spend: $500K
Q2 2024:
New ARR: $400K
Churned ARR: $50K
Net new ARR: $350K
Magic Number = ($350K × 4) ÷ $500K = 2.8
Interpretation:
For every $1 spent on S&M, you generated $2.80 in ARR.
Benchmarks:
| Magic Number | Rating | Action |
|---|---|---|
| < 0.5 | Poor | Fix before scaling |
| 0.5-0.75 | Okay | Optimize before growth |
| 0.75-1.0 | Good | Scale with confidence |
| > 1.0 | Excellent | Pour gas on the fire |
Real examples:
| Company | Magic Number | Strategy |
|---|---|---|
| Zoom | 1.2+ (2019) | Product-led growth |
| Slack | 1.5+ (peak) | Viral + word of mouth |
| Salesforce | 0.8-1.0 | Efficient enterprise sales |
Why it matters:
Magic Number < 0.75 = Don’t scale sales yet.
You’re burning cash inefficiently.
Fix:
- Product (improve conversion)
- Sales process (reduce friction)
- Targeting (better ICP)
- Pricing (increase ACV)
Magic Number > 1.0 = Invest heavily in sales.
Every dollar you spend returns more than a dollar in ARR.
CAC Payback Period
How long until you break even on a customer?
$$ \text{CAC Payback} = \frac{\text{CAC}}{\text{ARPU} \times \text{Gross Margin %}} $$
Example:
CAC: $1,200
ARPU: $100/month
Gross margin: 80%
CAC Payback = $1,200 ÷ ($100 × 0.80) = 15 months
Interpretation:
You break even on the customer after 15 months.
Benchmarks:
| Payback Period | Rating | Typical for |
|---|---|---|
| < 6 months | Excellent | PLG, low-touch |
| 6-12 months | Good | Mid-market SaaS |
| 12-18 months | Okay | Enterprise SaaS |
| > 18 months | Risky | Needs high LTV |
Why it matters:
Short payback = Less capital required.
Example:
Company A:
CAC: $600
Payback: 6 months
Company B:
CAC: $6,000
Payback: 18 months
To acquire 100 customers:
Company A needs: $60K tied up for 6 months
Company B needs: $600K tied up for 18 months
Company A can grow 10x faster with same capital.
Lead Velocity Rate (LVR)
The growth metric that predicts future revenue.
$$ \text{LVR} = \frac{(\text{Qualified Leads This Month} - \text{Qualified Leads Last Month})}{\text{Qualified Leads Last Month}} \times 100% $$
Example:
January: 200 qualified leads
February: 250 qualified leads
LVR = (250 - 200) ÷ 200 × 100% = 25%
Interpretation:
Your lead pipeline is growing 25% month-over-month.
Why LVR matters:
It’s a leading indicator.
Revenue lags by 1-3 months:
- Today: Generate leads
- Next month: Convert to opportunities
- Month 3: Close deals
LVR tells you what revenue will be before it happens.
Benchmarks:
| Monthly LVR | Rating | Implication |
|---|---|---|
| < 0% | Crisis | Pipeline shrinking |
| 0-10% | Slow | Growth stalling |
| 10-20% | Good | Healthy growth |
| > 20% | Excellent | Scaling fast |
Real use:
Startup tracking LVR:
Q1: +15% MoM LVR
Q2: +22% MoM LVR
Q3: +5% MoM LVR ⚠
CEO notices the drop in Q3.
Investigates: Marketing campaign underperforming.
Fixes issue in Q3 before it impacts Q4 revenue.
If they only tracked revenue, they'd see the problem
3 months late (when revenue drops in Q4).
Sales Efficiency Ratio
Simpler version of Magic Number:
$$ \text{Sales Efficiency} = \frac{\text{New ARR (this quarter)}}{\text{Sales & Marketing Spend (this quarter)}} $$
Example:
Q2 2024:
New ARR: $400K
S&M spend: $350K
Sales Efficiency = $400K ÷ $350K = 1.14
Interpretation:
For every $1 spent, you generated $1.14 in ARR.
Benchmark: > 1.0 is healthy.
Part 4: Building Your Cohort Analysis Framework
The most powerful growth tool you can build.
Step 1: Define Your Cohorts
Common cohort definitions:
- Time-based: Users who signed up in January 2024
- Channel-based: Users from Google Ads
- Feature-based: Users who completed onboarding
- Plan-based: Free trial users vs. direct-to-paid
Step 2: Define Retention Events
What counts as “retained”?
Examples:
- Logged in this week
- Made a purchase this month
- Used core feature
- Paid invoice
Be specific. Measure value, not vanity.
Step 3: Build Your Cohort Table Template
Cohort Retention Analysis: Active Users
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
Sign-Up | Cohort | Week | Week | Week | Week | Week | Week | Week
Month | Size | 0 | 1 | 2 | 3 | 4 | 8 | 12
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
Jan 2024 | 1,000 | 100% | 45% | 38% | 35% | 33% | 30% | 28%
Feb 2024 | 1,200 | 100% | 48% | 41% | 38% | 36% | 32% | --
Mar 2024 | 1,500 | 100% | 52% | 46% | 43% | 40% | -- | --
Apr 2024 | 1,800 | 100% | 55% | 49% | 46% | -- | -- | --
May 2024 | 2,000 | 100% | 58% | 52% | -- | -- | -- | --
Jun 2024 | 2,200 | 100% | 60% | -- | -- | -- | -- | --
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
What this reveals:
- Week-1 retention improving: 45% → 60% (onboarding getting better)
- Curves flatten at ~30%: Core retained user base
- Recent cohorts retain better: Product improvements working
Step 4: Segment Your Cohorts
Don’t just track overall cohorts. Segment by:
Acquisition channel:
Google Ads cohort: 25% Week-4 retention
Organic cohort: 45% Week-4 retention
Referral cohort: 65% Week-4 retention
Insight: Referrals are highest quality. Invest there.
User behavior:
Completed onboarding: 60% Month-6 retention
Skipped onboarding: 15% Month-6 retention
Insight: Force onboarding completion.
Plan type:
Free users: 20% Month-12 retention
Paid users: 75% Month-12 retention
Insight: Convert free to paid ASAP.
Step 5: Calculate Revenue Cohorts
User retention is good. Revenue retention is better.
Revenue Cohort Analysis (Monthly)
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
Cohort | M0 MRR | M1 | M3 | M6 | M12 | M24
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
Jan 2023 | $100K | 85% | 78% | 90% | 115% | 140%
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
Notice:
Month 6 retention: 90% (some churn)
BUT revenue retention: 115% (expansion > churn)
This is negative net churn.
This is the goal.
Cohort Analysis Visualizations
Part 5: Putting It All Together - Your Growth Dashboard
The metrics that matter:
Growth Metrics Dashboard
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
VIRAL GROWTH
K-Factor: 1.2 ✓ (> 1.0)
Viral Cycle Time: 3 days ✓ (< 7 days)
Invites per User: 4.5
Invitation Conv: 27%
RETENTION
DAU/MAU: 58% ✓ (> 50%)
Week-1 Retention: 52% ✓ (improving)
Month-6 Retention: 35% ✓ (flattening)
NRR (Net Revenue): 125% ✓ (> 120%)
SALES EFFICIENCY
Magic Number: 0.85 ⚠ (< 1.0)
CAC Payback: 11 mo ✓ (< 12 mo)
LVR (Lead Velocity): +18% ✓ (> 10%)
Sales Efficiency: 1.05 ✓ (> 1.0)
COHORT HEALTH
Recent vs Old: +15% ✓ (improving)
Revenue Retention: 112% ✓ (> 100%)
Activation Rate: 65% ✓ (> 60%)
✓ = Healthy ⚠ = Monitor ✗ = Crisis
The North Star Framework
Pick ONE metric as your North Star:
For consumer products:
- DAU/MAU (stickiness)
- Weekly active users
- Time spent
For marketplaces:
- GMV (Gross Merchandise Value)
- Completed transactions
- Buyer + Seller retention
For SaaS:
- Net Revenue Retention
- Active accounts
- Usage metrics (seats, API calls, etc.)
Why one metric?
Alignment.
Everyone optimizes for the same thing.
Example: Facebook’s North Star
“Daily Active Users”
Every feature, every experiment optimized for DAU.
Not:
- Engagement (can be spammy)
- Revenue (can hurt experience)
- Signups (vanity metric)
But:
- Daily active users (true product health)
Key Formulas Reference
Viral Coefficient: $$ K = \frac{\text{New Referrals}}{\text{Existing Users}} = \text{Invites per User} \times \text{Conversion Rate} $$
DAU/MAU (Stickiness): $$ \text{Stickiness} = \frac{\text{Daily Active Users}}{\text{Monthly Active Users}} $$
Net Revenue Retention (NRR): $$ \text{NRR} = \frac{\text{Starting MRR} + \text{Expansion} - \text{Churn} - \text{Contraction}}{\text{Starting MRR}} $$
Magic Number: $$ \text{Magic Number} = \frac{\text{Net New ARR (this Q)} \times 4}{\text{S&M Spend (last Q)}} $$
CAC Payback: $$ \text{Payback Period} = \frac{\text{CAC}}{\text{ARPU} \times \text{Gross Margin %}} $$
Lead Velocity Rate: $$ \text{LVR} = \frac{\text{Qualified Leads This Month} - \text{Qualified Leads Last Month}}{\text{Qualified Leads Last Month}} \times 100% $$
Sales Efficiency: $$ \text{Sales Efficiency} = \frac{\text{New ARR}}{\text{S&M Spend}} $$
The Bottom Line
Sustainable growth has three pillars:
1. Viral/Organic Growth (K > 1 or strong organic channels)
- Reduces CAC
- Compounds over time
- Creates defensibility
2. Retention (NRR > 100%, flattening cohorts)
- Makes acquisition valuable
- Enables expansion revenue
- Proves product-market fit
3. Sales Efficiency (Magic Number > 0.75)
- Makes growth profitable
- Enables scaling
- Attracts capital
Get all three right:
You’ve built a growth machine.
Real example: Slack (2014-2019)
Viral Growth:
- K-factor: ~1.3
- Organic/referral: 50%+ of signups
- CAC: $200-300
Retention:
- DAU/MAU: 93%
- NRR: 143%
- Revenue cohorts: growing
Sales Efficiency:
- Magic Number: 1.5+
- CAC payback: 8-10 months
- LVR: 20%+ MoM
Result:
$0 → $400M ARR in 5 years
$27B valuation at IPO
Your action items:
- Calculate your K-factor and viral cycle time
- Build cohort retention table (start simple)
- Track DAU/MAU weekly
- Calculate NRR if you have revenue retention
- Measure Magic Number quarterly
- Build your growth dashboard
- Pick your North Star metric
Remember:
Revenue growth without retention is a leaky bucket.
Retention without efficient acquisition is slow growth.
Efficient acquisition without viral loops is expensive growth.
You need all three.
Master these metrics. Build your growth machine.
Next in series: Stay tuned for more posts on pricing strategy, financial modeling, and valuation fundamentals.
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Part of the Business Math Series — Master the numbers that drive business success.