TL;DR

Introduction

Understanding the incremental value of subscribers is essential to subscription services. Marketing or product investments generally aim to increase acquisition of new subscribers or retention of exist- ing subscribers. The evaluation of these core investments is difficult because the costs of such investments are easily measured, yet the monetary benefits are not obvious. Without the ability to evaluate investments, businesses cannot optimize towards profitable future investments leading to sub optimal business outcomes. This paper develops a methodology to accurately quantify the monetary value of acquired or retained subscribers.

By definition, subscription-based services grow by acquiring and retaining subscribers. To do so, they may launch new content or fea- tures [2], run marketing campaigns [20], or offer pricing packages that better suit subscriber needs [6]. Measuring the causal impact on acquisition or retention (in units of subscribers) from these interventions can be difficult, but approaches based on randomized control trials [22] or observational studies [16] exist.

However, it is not clear what monetary value to assign to an acquired or retained subscriber. Although it is common practice, we demonstrate that using LTV (or remaining LTV in the case of retention) will tend to overstate the value of acquisition or retention for a subscription business. Instead, we demonstrate that the difference between on and off-service LTV, incremental LTV, is the more appropriate quantity of interest and develop a Markov chain based estimation approach.

Conceptually, acquiring a new subscriber or retaining an existing subscriber transitions (or saves from the perspective of the business) a customer from an off-service state to an on-service state. Naturally then, the value of that acquisition or retention to the business is the difference between the expected cumulative revenue from that individual in the on-service state and from that same individual if they were in the off-service state. Note crucially that the latter is positive if there is a positive probability of an individual becoming a subscriber when off-service. By using LTV to value acquisition or retention, one is implicitly assuming that the value of off-service states are zero. However, if there is positive probability of a non- subscriber joining, or rejoining, then LTV is likely upwards biased since it fails to subtract the baseline value associated with the off- service state.

Methodology

$V$表示状态$s$下的剩余累计收益（为了方便去掉下标$s$) $V=\sum_{k=0}^\infty \beta^k \cdot m_k \cdot c_k$ 其中$m_k$表示第$k$个周期下用户是否订阅，$c_k$表示价格，$\beta$表示长期的折扣系数。

• 获取新的订阅用户，$\Delta V_\text{acq}(i)=V(i_1)-V(0) \quad i\in\{A,B\}$
• 重新激活订阅用户，$\Delta V_\text{reacq}(i,j,k)=V(i_1)-V\Big(j_{\min\{-M,-k-1\}}\Big) \quad \forall i,j \in\{A,B\},1\leq k\leq M$
• 留存已订阅用户，$\Delta V_\text{ret}(i,j,k)=V\Big(i_{\max\{N,k+1\}}\Big)-V(j_{-1})\quad \forall i,j \in\{A,B\},1\leq k\leq M$

1. 在原有状态的基础上，多考虑一些变量的影响，去做状态转移概率的预估
2. 考虑Propensity Score做纠偏

Application

Subscriber Forecasting

1. 采用降维分组的手段，将转移概率相近或者时间分桶下相邻的状态合并统计
2. 显示考虑转移矩阵的不确定性