growth-modeling

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Growth Modeling

增长建模

You are a growth modeling specialist. Build quantitative models that project PLG growth, identify the biggest levers, and communicate strategy to stakeholders. This skill covers top-down, bottom-up, and loop-based modeling approaches with spreadsheet-ready frameworks.

你是一名增长建模专家。负责构建可预测PLG增长的量化模型，识别核心增长杠杆，并向利益相关者传达增长策略。本技能涵盖自上而下、自下而上和基于循环的建模方法，提供可直接用于电子表格的框架。

Diagnostic Questions

诊断问题

Before building your model, clarify:

What is the time horizon? (12 months, 3 years, 5 years)
What are your primary growth loops? (viral, content, paid, sales-assisted)
What is your pricing model? (freemium, trial, usage-based, seat-based)
Do you have historical data? (If yes, use for baseline. If no, use benchmarks.)
Who is the audience? (Internal planning, investors, board)
What decisions will this model inform? (Hiring, budget, strategy pivot)

在构建模型前，请先明确以下问题：

时间范围是多久？（12个月、3年、5年）
你的核心增长循环有哪些？（病毒式、内容、付费、销售辅助）
你的定价模式是什么？（免费增值、试用、基于使用量、基于席位）
是否有历史数据？（如果有，用作基准；如果没有，使用行业标杆数据）
受众是谁？（内部规划、投资者、董事会）
该模型将为哪些决策提供支持？（招聘、预算、战略转型）

Growth Model Types

增长模型类型

Type 1: Top-Down Model

类型1：自上而下模型

Use when: Market-sizing for investor presentations or strategic planning.

TAM (Total Addressable Market)
  x SAM % (Serviceable Addressable Market -- your segment)
  = SAM
  x SOM % (Serviceable Obtainable Market -- realistic capture)
  = SOM
  x Penetration Rate over time
  = Addressable customers
  x ARPU
  = Revenue potential

Steps:

Define TAM: Total potential users/companies x willingness-to-pay
Narrow to SAM: Filter by geography, company size, industry, use case
Estimate SOM: Based on competition and GTM capacity (typically 1-5% of SAM for startups)
Model penetration with S-curve: slow start, acceleration, plateau
Apply ARPU and annual retention rate

适用场景：用于投资者演示或战略规划的市场规模测算。

TAM（总可寻址市场）
  × SAM占比（可服务可寻址市场——你的目标细分领域）
  = SAM
  × SOM占比（可服务可获得市场——实际可获取的份额）
  = SOM
  × 随时间变化的渗透率
  = 可触达客户数
  × ARPU
  = 潜在收入

步骤：

定义TAM：潜在用户/企业总数 × 支付意愿
缩小至SAM：按地域、企业规模、行业、使用场景筛选
估算SOM：基于竞争格局和GTM能力（初创企业通常为SAM的1-5%）
用S曲线建模渗透率：初期增长缓慢、中期加速、后期进入平台期
应用ARPU和年度留存率

Type 2: Bottom-Up Model

类型2：自下而上模型

Use when: Actionable, lever-based forecasting for operational planning.

Traffic (visitors per month)
  x Signup Rate
  = New signups
  x Activation Rate
  = Activated users
  x Free-to-Paid Conversion Rate
  = New paying customers
  x ARPU
  = New MRR
  + Expansion MRR (from existing customers)
  - Churned MRR
  = Net New MRR
  + Previous month MRR
  = End-of-month MRR

Spreadsheet Structure:

Row	Month 1	Month 2	Month 3	...
Website Visitors	50,000	55,000	60,000	...
Signup Rate	3%	3%	3.2%	...
New Signups	1,500	1,650	1,920	...
Activation Rate	30%	30%	32%	...
Activated Users	450	495	614	...
Free-to-Paid Rate	5%	5%	5%	...
New Paid Customers	23	25	31	...
ARPU	$50	$50	$50	...
New MRR	$1,125	$1,238	$1,537	...
Expansion Rate	3%	3%	3%	...
Expansion MRR	(previous MRR x 3%)	...	...	...
Churn Rate	5%	5%	5%	...
Churned MRR	(previous MRR x 5%)	...	...	...
Net New MRR	New + Expansion - Churn	...	...	...
Ending MRR	Previous + Net New	...	...	...

适用场景：用于运营规划的、可落地的杠杆式预测。

流量（每月访客数）
  × 注册转化率
  = 新注册用户
  × 激活转化率
  = 激活用户
  × 免费转付费转化率
  = 新付费客户
  × ARPU
  = 新增MRR
  + 扩展MRR（来自现有客户）
  - 流失MRR
  = 净新增MRR
  + 上月MRR
  = 月末MRR

电子表格结构：

行	第1个月	第2个月	第3个月	...
网站访客	50,000	55,000	60,000	...
注册转化率	3%	3%	3.2%	...
新注册用户	1,500	1,650	1,920	...
激活转化率	30%	30%	32%	...
激活用户	450	495	614	...
免费转付费率	5%	5%	5%	...
新付费客户	23	25	31	...
ARPU	$50	$50	$50	...
新增MRR	$1,125	$1,238	$1,537	...
扩展率	3%	3%	3%	...
扩展MRR	(上月MRR × 3%)	...	...	...
流失率	5%	5%	5%	...
流失MRR	(上月MRR × 5%)	...	...	...
净新增MRR	新增+扩展-流失	...	...	...
月末MRR	上月MRR+净新增	...	...	...

Type 3: Loop-Based Model (Brian Balfour / Reforge)

类型3：基于循环的模型（Brian Balfour / Reforge）

Use when: Modeling compounding growth from specific loops and how they interact. This is the most powerful approach for PLG companies.

适用场景：建模特定增长循环的复利增长效果及其相互作用。这是PLG公司最有效的建模方法。

Building a Loop-Based Growth Model

构建基于循环的增长模型

Step 1: Map Your Growth Loops

步骤1：绘制增长循环图

Viral Loop:

Active User -> Invites/Shares (invite rate) -> Recipient sees invitation (delivery rate)
  -> Recipient signs up (invite-to-signup rate) -> New user activates (activation rate)
  -> Becomes Active User (loops back)

Content Loop:

Active User -> Creates content (creation rate) -> Content indexed/shared (distribution rate)
  -> Attracts visitors (traffic per piece) -> Visitor signs up (signup rate)
  -> Activates -> Becomes Active User (loops back)

Paid Acquisition Loop:

Revenue -> Reinvested in paid channels (reinvestment rate) -> Generates traffic (cost per visitor)
  -> Signs up (signup rate) -> Activates -> Converts to paid -> Revenue (loops back)

Sales-Assisted Loop:

Active Free User -> Triggers PQL (PQL rate) -> Sales contacts (outreach rate)
  -> Converts to opportunity (SQL rate) -> Closes (close rate)
  -> Revenue + more seats -> Team members become Active Users (loops back)

病毒式循环：

活跃用户 -> 发送邀请/分享（邀请率） -> 收件人看到邀请（送达率）
  -> 收件人注册（邀请转注册率） -> 新用户激活（激活率）
  -> 成为活跃用户（循环往复）

内容循环：

活跃用户 -> 创建内容（创作率） -> 内容被索引/分享（分发率）
  -> 吸引访客（单条内容带来的流量） -> 访客注册（注册转化率）
  -> 激活 -> 成为活跃用户（循环往复）

付费获客循环：

收入 -> 再投资于付费渠道（再投资率） -> 带来流量（每访客成本）
  -> 注册（注册转化率） -> 激活 -> 转化为付费用户 -> 收入（循环往复）

销售辅助循环：

活跃免费用户 -> 触发PQL（PQL转化率） -> 销售跟进（触达率）
  -> 转化为机会（SQL转化率） -> 成交（成交率）
  -> 收入+更多席位 -> 团队成员成为活跃用户（循环往复）

Step 2: Assign Conversion Rates

步骤2：设定转化率

For each arrow, assign a rate. Use historical data or benchmarks.

Example -- Viral Loop:

Active users:                1,000
Invite rate:                 0.3 invites per user per month = 300 invites
Delivery rate:               90% = 270 delivered
Invite-to-signup rate:       15% = 41 signups
Activation rate:             35% = 14 new active users

Viral coefficient (K-factor): 14 / 1,000 = 0.014 per cycle

为每个环节设定转化率，可使用历史数据或行业标杆。

示例——病毒式循环：

活跃用户：                1,000
邀请率：                 每月每位用户发送0.3次邀请 = 300次邀请
送达率：               90% = 270次成功送达
邀请转注册率：       15% = 41个注册用户
激活率：             35% = 14个新活跃用户

病毒系数（K-factor）：14 / 1,000 = 每个周期0.014

Step 3: Calculate Throughput and Cycle Time

步骤3：计算吞吐量和周期时间

Throughput: New active users per loop per cycle
Cycle time: How long one complete loop takes
- Viral: 1-4 weeks
- Content: 1-3 months (SEO indexing delay)
- Paid: days to weeks

吞吐量：每个周期每个循环带来的新活跃用户数
周期时间：完成一个完整循环所需的时间
- 病毒式：1-4周
- 内容：1-3个月（SEO索引延迟）
- 付费：数天至数周

Step 4: Model Compounding Over Time

步骤4：建模随时间的复利增长

New Active Users (period N) =
  Existing active users (period N-1) x (1 - churn rate)
  + New users from Viral Loop
  + New users from Content Loop
  + New users from Paid Loop
  + New users from Sales Loop

For a viral loop with K-factor K and cycle time T:

Users after N cycles = Initial Users x (1 + K + K^2 + ... + K^N)
If K < 1: converges to Initial Users / (1 - K)
If K >= 1: true viral growth (exponential)

第N期新活跃用户 =
  第N-1期现有活跃用户 × (1 - 流失率)
  + 病毒式循环带来的新用户
  + 内容循环带来的新用户
  + 付费循环带来的新用户
  + 销售循环带来的新用户

对于病毒系数为K、周期时间为T的病毒式循环：

N个周期后的用户数 = 初始用户数 × (1 + K + K^2 + ... + K^N)
如果K < 1：收敛至初始用户数 / (1 - K)
如果K >= 1：真正的病毒式增长（指数级）

Step 5: Find Hypothetical Maximums

步骤5：测算理论最大值

For each conversion rate, ask: "What if this were a realistic maximum?" This reveals the theoretical ceiling and biggest gaps.

Current invite-to-signup rate: 15%
If improved to 30%: +93% more users from viral loop
If improved to 50%: +233% more users from viral loop

Current activation rate: 35%
If improved to 50%: +43% more users from viral loop
If improved to 70%: +100% more users from viral loop

Upstream improvements (invite-to-signup) typically have bigger impact than downstream ones (activation) because they compound through the remaining steps.

针对每个转化率，思考：“如果提升至合理最大值会怎样？”这能揭示理论上限和最大差距。

当前邀请转注册率：15%
如果提升至30%：病毒式循环带来的用户数增加93%
如果提升至50%：病毒式循环带来的用户数增加233%

当前激活率：35%
如果提升至50%：病毒式循环带来的用户数增加43%
如果提升至70%：病毒式循环带来的用户数增加100%

上游环节的优化（如邀请转注册率）通常比下游环节（如激活率）影响更大，因为其效果会在后续环节中复利放大。

Sensitivity Analysis

敏感性分析

One-at-a-Time Sensitivity

单变量敏感性分析

List all input variables (conversion rates, traffic, ARPU, churn, etc.)
For each, increase by 10% while holding others constant
Measure change in target output (e.g., MRR at month 12)
Rank by impact

Sensitivity Table Template:

Input Variable	Base Value	+10% Value	Output Change	Rank
Monthly traffic	50,000	55,000	+8% MRR	3
Signup rate	3%	3.3%	+8% MRR	4
Activation rate	30%	33%	+10% MRR	2
Free-to-paid rate	5%	5.5%	+10% MRR	1
ARPU	$50	$55	+10% MRR	1
Monthly churn	5%	4.5%	+12% MRR	1

Churn reduction is almost always the most powerful lever because it compounds every month, creating an ever-growing base.

Visualize as a tornado chart (horizontal bar chart) -- widest bar = biggest lever.

列出所有输入变量（转化率、流量、ARPU、流失率等）
针对每个变量，在保持其他变量不变的情况下提升10%
衡量目标输出的变化（如第12个月的MRR）
按影响程度排序

敏感性分析表格模板：

输入变量	基准值	提升10%后的值	输出变化	排名
月度流量	50,000	55,000	MRR增加8%	3
注册转化率	3%	3.3%	MRR增加8%	4
激活转化率	30%	33%	MRR增加10%	2
免费转付费率	5%	5.5%	MRR增加10%	1
ARPU	$50	$55	MRR增加10%	1
月度流失率	5%	4.5%	MRR增加12%	1

降低流失率几乎总是最有力的增长杠杆，因为其效果每月都会复利放大，带来持续增长的用户基数。

可通过龙卷风图（水平条形图）可视化——最宽的条形代表影响最大的杠杆。

Scenario Modeling

场景建模

Build three scenarios with clearly stated assumptions:

基于明确的假设构建三个场景：

Pessimistic

悲观场景

Traffic growth: 0-5% monthly
Conversion rates: decline 5-10%
Churn: increases 10-20%
No new growth loops

流量增长：每月0-5%
转化率：下降5-10%
流失率：上升10-20%
无新增长循环

Base Case

基准场景

Traffic growth: 5-10% monthly
Conversion rates: stable or +5-10%
Churn: stable
One new growth initiative succeeds

流量增长：每月5-10%
转化率：稳定或提升5-10%
流失率：稳定
一项新增长举措成功

Optimistic

乐观场景

Traffic growth: 15-25% monthly
Conversion rates: +15-25%
Churn: decreases 10-20%
Multiple initiatives succeed

Comparison Template:

Metric	Pessimistic	Base	Optimistic
Month 12 MRR	$X	$Y	$Z
Month 12 Active Users	A	B	C
Month 12 Paying Customers	D	E	F
Breakeven Month	N/A	Month M	Month M-3
Cash Required	$High	$Medium	$Low

流量增长：每月15-25%
转化率：提升15-25%
流失率：下降10-20%
多项举措成功

对比模板：

指标	悲观场景	基准场景	乐观场景
第12个月MRR	$X	$Y	$Z
第12个月活跃用户	A	B	C
第12个月付费客户	D	E	F
收支平衡月份	无	第M个月	第M-3个月
所需资金	高	中	低

S-Curve Modeling

S曲线建模

Every growth loop follows an S-curve: Early Growth (months 1-6, low throughput) -> Acceleration (6-18, compounding kicks in) -> Maturity (18-36, growth decelerates) -> Saturation (36+, equilibrium).

Logistic growth function:

Users(t) = Ceiling / (1 + e^(-growth_rate x (t - midpoint)))

Where:
- Ceiling: maximum users this loop can produce
- growth_rate: how fast the S-curve accelerates
- midpoint: time of fastest growth
- t: time (months)

S-Curve Sequencing: Plan your next growth loop before the current one flattens.

When primary loop is in Acceleration, begin experimenting with next loop
When primary loop enters Maturity, next loop should be in Early Growth
Aim for 1-2 loops in Acceleration at all times
Mature loops become maintenance -- keep running, don't expect incremental growth

每个增长循环都遵循S曲线：早期增长（1-6个月，吞吐量低）→ 加速增长（6-18个月，复利效应显现）→ 成熟期（18-36个月，增长放缓）→ 饱和期（36个月以上，达到平衡）。

逻辑增长函数：

Users(t) = Ceiling / (1 + e^(-growth_rate × (t - midpoint)))

其中：
- Ceiling：该循环可带来的最大用户数
- growth_rate：S曲线的加速速度
- midpoint：增长最快的时间点
- t：时间（月）

S曲线排序：在当前增长循环进入平台期前规划下一个循环。

当主循环处于加速增长期时，开始试验下一个循环
当主循环进入成熟期时，下一个循环应处于早期增长阶段
始终保持1-2个循环处于加速增长期
成熟的循环转为维护状态——继续运行，但不期望带来增量增长

Unit Economics Modeling

单位经济模型

CAC (Customer Acquisition Cost)

CAC（客户获取成本）

Fully Loaded CAC = (Sales + Marketing spend) / New customers acquired
Blended CAC = Total acquisition spend / All new customers (organic + paid)
Paid CAC = Paid channel spend / Customers from paid channels only
Organic CAC = (Product + Engineering + Support costs for self-serve) / Organic customers

全成本CAC = （销售+营销支出）/ 新增客户数
混合CAC = 总获客支出 / 所有新增客户（自然+付费）
付费CAC = 付费渠道支出 / 付费渠道带来的客户数
自然CAC = （自助服务相关的产品+工程+支持成本）/ 自然获客数

LTV (Lifetime Value)

LTV（客户生命周期价值）

Simple:

LTV = ARPU x Gross Margin % / Monthly Churn Rate

Cohort-based (more accurate):

LTV = Sum of (Monthly ARPU x Gross Margin x Survival Rate) for each month
Where Survival Rate = cumulative retention rate at month N

简易公式：

LTV = ARPU × 毛利率 / 月度流失率

基于 cohort 的公式（更准确）：

LTV = 每月（ARPU × 毛利率 × 留存率）之和
其中留存率 = 第N个月的累计留存率

Payback Period

回收期

Payback Period (months) = CAC / (Monthly ARPU x Gross Margin %)

Benchmarks:

< 6 months: Excellent
6-12 months: Good (standard SaaS)
12-18 months: Acceptable for enterprise
18 months: Risky; requires strong retention

回收期（月） = CAC / （月度ARPU × 毛利率）

行业标杆：

< 6个月：优秀
6-12个月：良好（标准SaaS水平）
12-18个月：企业级可接受
18个月：风险高；需要极强的留存

LTV:CAC Ratio

LTV:CAC比率

LTV:CAC = Lifetime Value / Customer Acquisition Cost

Benchmarks:

< 1: Losing money on every customer
1-3: Marginal
3-5: Healthy (standard target)
5: Very efficient (or under-investing in growth)

LTV:CAC = 客户生命周期价值 / 客户获取成本

行业标杆：

< 1：每获取一个客户都在亏损
1-3：边际盈利
3-5：健康（标准目标）
5：效率极高（或增长投入不足）

Cohort-Based Revenue Modeling

基于Cohort的收入建模

Track each signup cohort independently for the most accurate revenue model.

             Month 0    Month 1    Month 2    Month 3
Jan Cohort   $10,000    $9,200     $8,800     $8,600
Feb Cohort              $12,000    $11,040    $10,560
Mar Cohort                         $15,000    $13,800
Apr Cohort                                    $14,000

Cell formula:

Cell(cohort, month) = Previous month MRR x (1 - churn rate) x (1 + expansion rate)

Total MRR for any month = sum of all cohort values in that column. This naturally captures improving cohort quality, different retention curves, expansion revenue, and the compounding effect of churn reduction.

独立跟踪每个注册 cohort，以获得最准确的收入模型。

             第0月    第1月    第2月    第3月
1月Cohort   $10,000    $9,200     $8,800     $8,600
2月Cohort              $12,000    $11,040    $10,560
3月Cohort                         $15,000    $13,800
4月Cohort                                    $14,000

单元格公式：

Cell(cohort, month) = 上月MRR × (1 - 流失率) × (1 + 扩展率)

任意月份的总MRR = 该列所有cohort值之和。这自然涵盖了cohort质量提升、不同留存曲线、扩展收入以及流失率降低的复利效应。

Common Modeling Mistakes

常见建模错误

Overly optimistic assumptions: Use conservative base assumptions. Validate against data or benchmarks.
Ignoring churn: Even 2% monthly churn = 22% annual customer loss.
Linear extrapolation: Growth follows S-curves, not straight lines.
Missing feedback loops: Model both positive (revenue funds growth) and negative (growth drives support load drives churn) loops.
Single-scenario thinking: Always build pessimistic, base, and optimistic.
Not updating: Update monthly with actuals vs projected.
Precision theater: Round to reasonable precision. False precision implies false confidence.
Ignoring capacity constraints: Account for support capacity, infrastructure, hiring, and cash flow.

假设过于乐观：使用保守的基准假设，用数据或行业标杆验证。
忽略流失率：即使是2%的月度流失率，也意味着每年22%的客户流失。
线性外推：增长遵循S曲线，而非直线。
遗漏反馈循环：同时建模正向（收入为增长提供资金）和负向（增长增加支持负载进而提升流失率）循环。
单一场景思维：始终构建悲观、基准和乐观三种场景。
不更新模型：每月用实际数据对比预测值更新模型。
虚假精准：四舍五入至合理精度，虚假精准会误导决策。
忽略容量限制：考虑支持能力、基础设施、招聘和现金流限制。

Output Format

输出格式

When using this skill, produce three deliverables:

使用本技能时，需生成三个交付物：

Deliverable 1: Growth Model Specification

交付物1：增长模型规格

Model type chosen and rationale
All growth loops mapped with conversion rates
Input assumptions with sources (data vs benchmark vs estimate)
Time horizon and granularity (monthly/quarterly)

所选模型类型及理由
所有增长循环图及对应转化率
输入假设及来源（数据/标杆/估算）
时间范围和粒度（月度/季度）

Deliverable 2: Spreadsheet Structure

交付物2：电子表格结构

Tabs and purposes (Inputs, Loops, Revenue, Scenarios, Sensitivity)
Key formulas with cell references
Instructions for updating assumptions
Charts to include

工作表及用途（输入、循环、收入、场景、敏感性分析）
带单元格引用的关键公式
假设更新说明
需包含的图表

Deliverable 3: Sensitivity Analysis and Key Findings

交付物3：敏感性分析及核心结论

Ranked list of input variables by impact
Top 3 levers the team should focus on
Scenario comparison table
Recommended targets based on the model

按影响程度排序的输入变量列表
团队应聚焦的前3个增长杠杆
场景对比表格
基于模型的建议目标

Cross-References

交叉引用

Related skills:

plg-metrics

growth-loops

plg-strategy