Customer Revenue

UCSD MGT 100 Week 09

Kenneth C. Wilbur and Dan Yavorsky

Let’s reflect

• Bass (1969)

• This paper was published several years before even I was born
• It has been cited 11,000 times. Probably the most cited paper in marketing
• One of the first predictive analytics papers published in any business discipline
• This is a differential equation model, in which the change in a function modeled as a function of the level of the function
• Model was borrowed from epidemiology
• Performs well, but not overall, only relative to all other failed attempts to predict the future

Importance of Customer Acquisition

• Einav et al. (2021) analyzed all US Visa CC transaction data

  - >$1T spent in 32B transactions by 428MM cards at 1MM stores from 2016-19
  - Assume card~=customer 

\(\text{BrandRev.} = \sum spend \equiv \sum \frac{stores}{1} \frac{cards}{stores} \frac{transactions}{cards} \frac{spend}{transactions}\)

• Research question: How well does each factor explain brand revenue?

• Regressed log revenue on log RHS with merchant and year fixed effects

• Row B is the most representative and controls for merchant dummies and year dummies
• Compare column 2 to other columns: ( # unique customers / store ) explains 68-84% of variation in merchant revenue
• Far more than other variables

• Similar finding across merchant types
• Remarkably consistent across sectors. These numbers are above 70pct bc it’s a subsample of offline retailers
• Explains why companies focus more on customer-level metrics than store, visit or transaction level metrics

Customer Revenue Metrics

• Market size: How many customers might purchase?
• Diffusion: How does the served market change over time?
• CLV: How profitable are customer relationships?

• Until now, we have taken the perspective of a dispassionate economist or market analyst. But, most customer analytics work happens inside firms. Let’s consider how you look at the market when you’re inside a company.

Market Size

• Market size (\(N\)): # of people who might pay to address the core need in a given time period

  - Alternatively measured in $, units or volume
  - Noisy but helps inform potential returns to investments 
  - Typical investor's first question: How big is the market?
    $100B market is viewed differently than a $100MM market
  - How will you know if you got the right answer?
  - What happens if you overestimate market size?

• “Marketing myopia:” Neglecting nontraditional competitors, e.g. Zoom v. Uber or Carnival v. Whistler

• Market size counts both purchasers and non-purchasers
• The idea would be that for people who have a core need to work, they might alternately use Uber to work in an office, or Zoom to work from home; hence Uber and Zoom compete
• How will the investor react if your market size estimate sounds off? Some might proceed anyway; some might immediately pass, figuring they can’t trust you; some might want to dive into the details to see if you know something they don’t, or if you have solid math backing up your claims

Market Size

• 3 ways to estimate:
  • “Top Down” Total Addressable Market (TAM) :
    How many people have the core need?
  • “Bottom up” Served Available Market (TAM):
    How many people currently pay to solve the core need?
    • TAM=SAM+Unserved
  • Analyst estimates
• Best practice: Use all three, triangulate, gauge sensitivity

Case study: US Mattress Market

• USA population : ~340 million

• Assumption : \(TAM\approx SAM\) (why? pros, cons?)

• Assumption : Avg mattress lasts 7 years (pros, cons?)

• Market size \(\approx\) 47.1 million people annually

• Average mattress price : $283, across all bed sizes

• Market size \(\approx\) $13.3B/year

• Let’s check Grand View Research & ISPA

• Consider 2nd homes & hotels vs. homeless population
• How much do those analyst reports cost?
• What are analyst incentives? How should they price? How often should they update their estimates?

Diffusion curves

• There are claims that diffusion curves are speeding up in recent years. That may be consistent with social media and generally accelerating information diffusion
• Consider product complementarities, eg electricity + TV, or substitution between products, eg telephone + cellphone

• Important: these products are not randomly selected, they are intentionally selected to make a point
• Of course there remain many technology products with slow adoption. Think about robot vacuums, time-lapse or other phone peripherals, etc etc etc
• But there does seem to be something to the idea that social media has the potential to dramatically accelerate diffusion for some “winning” products

New Products by Year

• For completeness we should consider the full scope of products launched every year
• Even if we limit ourselves to food & drug channels, it’s massive, on the order of 35-40k new SKUs launched in a typical year
• 90-95% fail completely within 6 months, as in revenues go to zero and manufacturer withdraws the product (Wilbur & Farris 2014)
• Unfortunately USDA stopped updating these data publicly, probably because Mintel increased price too much

Predicting Diffusion: Bass (1969)

• \(M\) : Market size (we’ll estimate this)

• \(t\) : Time periods

• \(A(t)\) : Accumulated sales before time \(t\)

  - AKA "installed base"
  - A(0)=0 by assumption

• \(\frac{dA(t)}{dt}\) : number of new adopters in time \(t\)

• \(R(t)\) : Remaining customers who have yet to adopt, \(R(t)\equiv M-A(t)\)

• Can you see where we’re going? DiffEQ using A(t) to predict dA/dt

• Bass (1969) proposed:

\[\frac{dA(t)}{dt}=pR(t)+q\frac{A(t)}{M}R(t)\]

• \(p\) : “coefficient of innovation”

• \(q\) : “coefficient of imitation”

  - p and q assumed constant

• LHS is sales in time period t.
• R(t) is # of potential buyers who have not bought yet.
• p is the share of remaining market who would buy at any given moment irrespective of previous sales (“innovators”).
• q is the share of nonadopters who adopt at t because they observe past purchasers (“imitators”)
• so qR is the number of nonadopters who adopt at t because they observe past purchasers
• and A/M is the fraction of the market who has adopted, and therefore could possibly be observed
• so we scale qR by A/M because each nonadopter’s chance of observing an adopter increases with the number of adopters available to be observed

Estimating Bass model via NLLS

\[\frac{dA(t)}{dt}=pR(t)+q\frac{A(t)}{M}R(t)\]

• This is a first-order diffEQ with analytic solution

  \[A(t)=M\frac{1-e^{-(p+q)t}}{1+\frac{q}{p}e^{-(p+q)t}}\]

• If you have sales data by time, you can use Nonlinear Least Squares to estimate \(p\), \(q\) and \(M\), i.e. choosing parameters to minimize square errors \((LHS-RHS)^2\)

• We state this without proof, because differential equations is not a prerequisite, and the solution technique is mechanical and uninteresting

Estimating Bass model via OLS

• Or, notice that \(\frac{dA(t)}{dt}=pR(t)+q\frac{A(t)}{M}R(t)\) \(=p(M-A(t)) + q* \frac{A(t)}{M}(M-A(t))\) \(=pM + (q-p)A(t)-\frac{q}{M} A(t)^2\)

• We can regress \(\frac{dA(t)}{dt}\) on a quadratic in installed base

  - Then recover p, q & M from the parameter estimates
  - We'll do both

• Extensions: Multiple markets, hazard models,
  types of “influence”

Models:estimators aren’t 1:1?

• Consider 3 OLS estimators:

\[\hat{\beta}=(X'X)^{-1}X'Y\]

\[min_\beta (Y-X\beta)'(Y-X\beta)\]

\[min_\beta [X'(Y-X\beta)]^2\]

"In theory, there's no difference between theory & practice. In practice, there is." 
Many models offer multiple estimators. Some models have no estimators
Subfield that studies estimators: "econometrics"

• Estimation performance may depend on numerical properties, availability of existing algorithms, etc.
• Estimators may differ in speed, complexity, efficiency and econometric properties

• These are two of the graphics from the OG paper. He even forecasted sales of black & white TVs
• I kind of cherry picked these examples. others were not so clean, but I’m glad he showed the non-clean examples, it helps to show that he didnt cherrypick what to include or not.
• Think about what an advance this looked like at the time. with just a few data points of sales, you could reasonably predict the future, which would help to inform investment decisions
• Important to note: As is typical in predictive analytics, every single prediction is wrong. Keep your expectations in check

Inspired by epidemiology

• Distinguish between current and cume sales in the graph
• Discuss similarities between disease contagion & product adoption
• Spend a few minutes talking about the phases; mention Moore (1991)’s “chasm” or “saddle” idea between initial growth and takeoff

Which new products will catch on?

Fastest way to get rich: Invent a new product that sells a lot That requires addressing a real customer need that people will pay for And it requires going to market successfully Success in the market is notoriously hard to predict, most new products fail quickly Addressing a real core need is necessary but far from sufficient Which of these new products will succeed?

More: Kickstarter, Product Hunt, Gizmodo

Rogers’ ACCORD Framework (2003)

• Diffusion depends on Relative Advantage, Perceived Complexity, Compatibility, Observability, Risk, Divisibility (aka “Trialability”)

  - Summarized 40 years of research, incredibly influential on practice 
  - Provided diagnostics to interpret Bass (1969)'s predictive analytics
  - E.g., a prototype could be evaluated on these 6 dimensions then modified
  - Early example of HARKing but likely useful

More explanations for diffusion curves

• Heterogeneity might drive adoption timing

  - Adoption driven by consumer income, need or risk attitudes?

• Markets typically evolve after introduction

  - Production becomes more efficient, prices and costs fall
  - New features, technology generations, safety improves 
  - Competitors enter and target unserved customers
  - Network effects, e.g. smartphone compatibility with chargers or accessories
  - Complementors, e.g. Verizon stores, iFixIt, Genius Bar
  - Consumer preferences, e.g. reliability matters more with time

• Features: Smartphone cameras improve, GPS improves, 4G beats 2G, etc
• Complementors: Apps improve, payment processors accept mobile payments, etc.
• Apple drops the headphone jack, Android keeps it
• Early in a category lifecycle, competitors may benefit each other, e.g. ads promote category consumption more than brand share. those interactions become zero-sum when the category matures
• Bass+Rogers is kind of an intellectual trap, where you have a logical story and data, and then get blinded to alternate explanations

Source

Core Needs Data: Google Trends

• It’s relatively easy to measure Served Available Market

• Google Trends reports search volume indices by keyword, place, time, service

  - Also identifies keyword topics, trending terms & related queries
  - Samples the query database, reports estimates not totals
  - Requires a minimum query volume to avoid privacy violations
  - Free, so it could get sunsetted

• A 2012 introduction and demonstration by Google’s chief economist
• Or see a more recent analysis

Customer Lifetime Value

• CLV is the most powerful customer analytics metric

  - Expresses the firm's value of an individual customer relationship as the net present value of expected future customer profits
  - Pioneered in catalogue retailers in the 1980s
  - Has spread widely, but not yet everywhere
  - CLV metrics enable quantification, and hence serious discussion, of <br>novel policies

• Catalogue retailers had huge customer databases, and mailed out expensive books multiple times per year. Had to test which customers were worth sending books, how often

CLV Example: Housing First

• “In 2005, Utah set out to fix a problem that’s often thought of as unfixable: chronic homelessness. The state had almost 2,000 chronically homeless people. Most of them had mental-health or substance-abuse issues, or both. Utah started by just giving the homeless homes…
• The cost of shelters, emergency-room visits, ambulances, police, and so on quickly piles up. Lloyd Pendleton, the director of Utah’s Homeless Task Force … said that the average chronically homeless person used to cost Salt Lake City more than $20,000/year. Putting someone into permanent housing costs the state just $8,000 [including case managers]…
• Utah’s first pilot program placed 17 people in homes scattered around Salt Lake City, and after twenty-two months not one of them was back on the streets. In the years since, the number of Utah’s chronically homeless has fallen by 74%.”

• http://www.politico.com/magazine/story/2016/12/what-works-albuquerque-homeless-solution-housing-policy-214527
• I’m not sure your stereotype about utah, but many would not guess they invented housing first. It was CLV metrics that showed it to be a no-brainer. It’s the serious effort to quantify lifetime value that moved this from dream to reality. Humanitarian upsides have been tremendous.

• Source

Housing First: Looking deeper

• Housing First has certainly not solved homelessness

  - "Chronic" means disabled and unhoused for 1+ yrs, or 4x in 3 yrs
  - ~28% of CA homelessness is chronic (2019)
  - UT originally claimed 90% reduction, then revised their metric definitions
  - Reliable efficacy metrics are rare    
  - Housing First has been implemented haphazardly
  - UT built new apartments. CA cities mostly use shelters, SROs, vouchers  
  - Key Q: Require wraparound services? E.g. Addiction treatment, etc
  - Key Q: Does Housing First somehow encourage homelessness?

• I claim: Quantification enables bold policy shifts

  - U.S. HUD adopted Housing First as preferred approach to homelessness in 2014
  - CLV quantifies policy costs and benefits & enables ex-post evaluations
  - We then can use data to refine CLV estimates and policies

• UT annual homeless figures inflate a January count using a multiplier
• Officials changed the multiplier over time but did not revise past figures
• For more, https://www.sltrib.com/news/politics/2020/05/11/utah-was-once-lauded/

Calculating CLV

• \(T\) : planning horizon
• \(m_t\) : contribution margin of serving customer \(i\) in time \(t\)
• \(r\) : retention probability that customer buys in \(t+1\)
• \(i\) is the cost of capital
• \(CLV=\sum_{t=0}^T\frac{m_t r^t}{(1+i)^t}\)
• \(m_t\) and \(r\) observable in past data; future values are predictions

• Often set arbitrarily at T=3 years, but Bezos says Amazon’s 7-year horizon lets them amortize and justify investments that competitors can’t match
• \(m_t\) and should depend on future firm strategy and market conditions
• Extensible to model purchase frequency, basket size, profitability
• Heterogeneity: \(m\) and \(r\) often vary across cohorts and segments, but we’ll disregard that for simplicity

CLV Example

• A tennis club charges an annual fee of $300
• The average club member spends $100 a year at the club (concessions, etc.)
• The average contribution margin on these additional expenditures is 60%
• Historically, 80% of the members rejoin the club in any given year. The club’s cost of capital is 15%
• What is the club’s CLV over a 1-year horizon?
• What is the club’s avg. CLV over a 2-year horizon?
• What is the club’s avg. CLV over a 3-year horizon?
  

• Notice how quickly avg. CLV starts to asymptote as T grows large
• is i=.15 realistic? yes– business payday loans industry like mulligan funding

Using CLV for Customer Acquisition

• Marketing campaigns should be profitable if Avg. Customer Acquisition Cost (CAC) \(<\) CLV

  - Caveat: So long as acquired customers have CLV>=avg CLV of existing customers
  - Often, managers impose a "fudge factor" as a speedbump

• Suppose the tennis club has a chance to pay $20k for a billboard. It will be seen by 100K people with an expected conversion rate of .1%. Should we do it?

• Similar “break-even” calculations possible for

  - partnerships, opening new stores, price promotions, etc. Anything that requires an upfront outlay to potentially acquire new customers, increase current customer retention, or develop current customer spending

• Common fudge factors: 3, 7. Why?

CLV Metrics in Practice

• CLV popularity rose alongside CRM data systems

  - e.g. Oracle, SAP, Salesforce
  - Services and retailers used CLV to set customer experiences: high-CLV flyers got upgraded, high-CLV lodgers got better rooms, high-CLV shoppers got sterling return service and attention, high-CLV callers got shorter wait times and more consideration

• In the 00s, consulting firms published claims that 20-30% of customers were unprofitable. Many firms tried to “fire” unprofitable customers

  - American Express offered some cardholders $300 to cancel their cards. Best Buy stopped notifying some shoppers about upcoming promotions. Banks used minimum balances and teller fees to drive away some accountholders

• Customers talk to each other; firing customers is a brand risk

• In other words, line up all the customers from most profitable to least profitable, and the bottom 20% or more would show negative CLV. If true, then you immediately increase your profit by dropping your bottom 20% of customers. Note, this is very simplistic thinking; maybe prices are too low or return policies are too generous?

• Graph shows cumulative online gambling operator revenue by gambler net loss rank, in a 5-year cohort of 717,000 gamblers

• 5% of gamblers cost online gambling operators 20% of their revenue
• So, operators block and limit frequent winners. Pros use “beards.” More here

CLV Cautions & Risks

• CRM data may be incomplete, disconnected, error prone

  - E.g., can you connect customer identity across different credit card #s?
  - Think about measurement error in retention rate

• CLV models are typically misspecified & uncertain

  - CLV-based policies may be self-fulfilling
  - Treat someone as unprofitable, they may act that way      

• Guiding Principle

  - The firm and the customer share an interest in creating an optimum level of customer value. Using CLV metrics for value creation benefits everyone
  - The firm and the customer have opposing interests in price. Using CLV for margin extraction creates perverse incentives for customers
  - Customer dissatisfaction may reveal CLV flaws; requires careful attention
  - Hence many firms now measure point-of-sale satisfaction

• Think about the retention measurement error this could cause, and the dramatic change in CLV
• POS satisfaction: e.g. NPS or those “smiley face” 1-button indicators. Try to detect issues faster before they affect customer relationships.
• This frontier is actively moving

  - Suppose you tutor a high school student for $250/month. There is a 10% chance the student will move and find a new tutor in any given month. There are six months remaining in the school year, at which point the tutoring arrangement will definitely end. 

  - What missing information do you need to calculate the current value of the tutoring arrangement?

Class script

• Let’s estimate the Bass model

Wrapping up

Homework

• Let’s take a look

Recap

• Customer acquisitions best predict revenues
• Market size estimates how many people share a core need
• Diffusion models predict how served market changes
• CLV metrics can quantify and enable novel policies

Going further

• Innovation Diffusion and New Product Growth Models (Peres et al. 2009)

• Customer-Base Valuation in a Contractual Setting with Heterogeneity (Fader & Hardie 2010)

• Exploring the Distribution of Customer Lifetime Value (Fader & Hardie 2017)

• Firing your best customers (Avery & Fournier 2012)