Uplift Modelling for Cross-Selling: White Paper Available

I'm pleased to announce the availability of a new white paper entitled Generating Incremental Sales: Maximizing the incremental impact of cross-selling, up-selling and deep-selling through uplift modelling.

Abstract

There is a subtle but important difference between

targeting people who are likely to buy if they are included in a campaign

and

targeting people who are only likely to buy if they are included in a campaign.

It transpires that this single-word distinction is often the difference between a strongly profitable and a severely loss-making campaign. We have seen many cases in which moving to targeting on the second basis (for incremental sales) has more than doubled the extra sales generated by a campaign. Conventional “response” models—despite their name—target on the former basis, and have a marked tendency to concentrate on people who would have bought anyway, thus misallocating marketing resources by increasing costs and failing to maximize sales. This paper discusses the use of a radical new type of predictive modelling—uplift modelling—that allows campaigns to be targeted on the second basis, i.e. so as to maximize incremental sales from cross-sell, up-sell and other sales-generation campaigns.

It's available as a PDF download here (216K, no registration required).

Financial Services Retention White Paper Available

I've recently completed a counterpart to my white paper on retention in financial services—"Identifying who can be saved and who will be driven away by retention activity". It's a counterpart to the previous telecoms-focused white paper on the same theme. The new one focuses on the incremental impact of retention campaigns in financial services. The abstract is below.

Abstract

It has been repeatedly demonstrated that the very act of trying to ‘save’ some customers provokes them to leave. This is not hard to understand, for a key targeting criterion is usually estimated churn probability, and this is highly correlated with customer dissatisfaction. Often, it is mainly lethargy that is preventing a dissatisfied customer from actually leaving. Interventions designed with the express purpose of reducing customer loss can provide an opportunity for such dissatisfaction to crystallise, provoking or bringing forward customer departures that might otherwise have been avoided, or at least delayed. This is especially true when intrusive contact mechanisms, such as outbound calling, are employed. Retention programmes can be made more effective and more profitable by switching the emphasis from customers with a high probability of leaving to those likely to react positively to retention activity. This paper discusses how targeting on the basis of such ‘savability’ can be achieved, illustrating the effectiveness of the approach with case studies. Insofar as a paper can be summarised in a motto, this paper’s is “savability is the key to retention activity”.

It's available as a PDF download here (228K, no registration required).

Jim Novo on Control Groups

There are a couple of good posts on control groups from Jim Novo at his Marketing Productivity Blog. the first is about The Benefits of Using Control Groups. The second is, well, kind of about the same thing, but more specifically discusses how to justify the use of control groups.

Well worth a read, and he's promising more to come.

Uplift Modelling FAQ

[This is a post that will be updated periodically as more FAQs are added, so if you subscribe to the feed, it may keep re-appearing.]

1. Q. What is Uplift Modelling?
   A. Uplift modelling is a way of predicting the difference that an action makes to the behaviour of someone. Typically, it is used to predict the change in purchase probability, attrition probability, spend level or risk that results from a marketing action such as sending a piece of mail, making a call to someone, or changing some aspect of the service that the customer receives.
2. Q. Uplift Modelling sounds like Response Modelling. How is it different?
   A. Ordinary "response" modelling actually doesn't model a change in behaviour (even though it sounds as if it should): it models the behaviour of someone who is subject to some influence. Uplift models instead model the change in behaviour that results when someone is subject to an influence—typically, how much more that person spends, how much less likely (s)he is to leave etc.
   Mathematically, a response model predicts something like

   P (purchase | treatment)

   ("the probability of purchase given some specific treatment", such as a mailing), whereas an uplift model predicts

   P (purchase | treatment) – P (purchase | no treatment)

   ("the difference between the probability of purchase given some specific treatment and the corresponding probability if the customer is not subject to that treatment").
3. Q. Uplift modelling sounds like Voodoo. How can it possibly know the change in behaviour of a single individual?
   A. Uplift modelling can't know the change in behaviour for any individual, any more than a normal model can know the behaviour of an individual in a future. But it can predict it. It does this by looking at two groups of people, one of which was subject to the marketing action in question, and the other of which was not (a control group). Just as it is standard to measure the incrementality of a campaign by looking at the overall difference in purchase rate between the treated group and an otherwise equivalent control group, uplift modelling models the difference in behaviour between these two groups, finding patterns in the variation.
4. Q. Does Uplift Modelling Really Work?
   A. Uplift modelling can work, and has been proven to do so with in-market tests. Uplift models are harder to build than conventional models, because they predict a second-order effect—usually the difference between two probabilities. This means that the error bars tend to be larger than for conventional models, and sometimes there is simply not enough signal for current techniques to model accurately. This is especially true when, as if often the case, the control group is small.
5. Q. When does uplift modelling predict different things from non-uplift models?
   A. It's perhaps easier to say when they predict the same thing. This is usually when there is essentially no behaviour in the control group. For example, if a set of people purchase product X after a mailing, but no one purchases it without the mailing, and uplift model should predict the same thing as a conventional response model. Their predictions are most different when the variation in the change in behaviour opposite from the variation in the underlying behaviour. For example, suppose the background purchase pattern (the one you see if you don't do anything) is that mostly men by product X, but the effect of a marketing action is to make more women buy it, but fewer men, even though still more men than women buy when treated. In this case, uplift models will make radically different different predictions from "response" models. A response model will concentrate on the fact that more men buy (when treated) that women; but an uplift model will recognize that women's purchases are increased by the treatment whereas men's is suppressed.
6. Q. How do you measure the quality of an uplift model?
   A. Standard quality measures for models (such as gini, R-square, classification error etc.) don't work for uplift models as they are all based on comparing an actual, known outcome for an individual with a predicted outcome. However, since a single person can't be simultaneously treated and not-treated, we can't make this comparison.
   There is, however, a generalization of the gini measure called Qini that has some of the characteristics as gini, but which does apply to uplift models. This has been described in the paper referenced as [1].
7. Q. What are the main application so of uplift modelling?
   A. So far the biggest successes with uplift modelling have been in the areas of customer retention and demand generation (cross-sell and up-sell, particularly).
   The state-of-the-art approach to customer retention is to predict which customers are at risk of attrition (or "churn") and then to target those at high risk who are also of high value with some retention activity. Unfortunately, such retention efforts quite often backfire, triggering the very attrition they were intended to save. Uplift models can be used to identify the people who can be saved by the retention activity. There's often a triple win, because you reduce triggered attrition (thus increasing overall retention), reduce the volume targeted (and thus save money) and reduce the dissatisfaction generated by those who don't react well to retention activity.
   The other big successes have come in the area of cross-sell and up-sell, particularly of high-value financial products. Here, purchase rates are often low, and the overall incremental impact of campaigns is often small. Uplift modelling often allows dramatic reduction in the volumes targeted while losing virtually no sales. In some case, where negative effects are present, incremental sales actually increase despite a lower targeting volume.
8. Q. Are there any disadvantages of uplift modelling?
   A. Uplift modelling is harder and requires valid controls groups to be kept, which have to be of reasonable size. Experience shows that it is also easy to misinterpret the results of campaigns when assessing uplift, especially when it is first adopted. Adoption of uplift models usually results in reductions in contact volumes, which is sometimes seen as a negative by marketing departments. An uplift modelling perspective also often reveals that previous targeting has been poor, and sometimes brings to light negative effects that had not previously been identified.
   There is also some evidence that uplift models also seem to need to be refreshed more frequently than conventional models, and there are clearly cases where either data volumes are not adequate to support uplift modelling or where the results of uplift modelling are not significantly different from those of conventional modelling. Anecdotally, this seems to be the case in the retail sector more than in financial services and communications.
9. Q. How does uplift modelling relate to incremental modelling?
   A. It's the same thing. Various people have apparently independently come up with the idea of modelling uplift, and different statistical approaches to it. There is no broad agreement on terminology yet. Names include
   • uplift modelling
   • differential response analysis
   • incremental modelling
   • incremental impact modelling
   • true response modelling
   • true lift modelling
   • proportional hazards modelling
   • net modelling.
   These are all the essentially the same thing.

References

[1]	Using Control Groups to Target on Predicted Lift: Building and Assessing Uplift Models, Nicholas J. Radcliffe, Direct Marketing Journal, Direct Marketing Association Analytics Council, pp. 14–21, 2007.

Back

The Scientific Marketer has been on vacation.

But no longer.

Neither A Response Modeller nor a Penetration Modeller Be

In The Fundamental Campaign Segmentation I introduced a theoretical classification of customers according to how their behaviour is affected by a marketing action such as a mailshot. Today I want to look at a softer, more practical version of that segmentation, and use this to look at the rather serious shortcomings of both response models and penetration models.

The “hard” version of the segmentation that I talked about previously depended on knowing whether each customer buys if treated, and also whether she buys if not treated. Such knowledge allows us to talk of “Persuadables”, who buy only if treated, “Sure Things”,1 who buy either way, “Lost Causes”, who don't buy either way, and “Boomerangs”, who only buy if not treated. But of course, we can never know which segment anyone falls into, because we can't both treat and not treat someone.

What we can do more easily, both conceptually and in practice, is to estimate the probability of someone's purchasing when treated, and the corresponding probability of purchasing when not treated. This suggests a “soft” version of the Fundamental Segmentation as follows:

The horizontal axis shows the probability of purchase if the customer is not treated, while the vertical axis shows the corresponding probability under treatment. A customer who is completely unaffected by the campaign will lie along the centre of the white stripe (the “leading diagonal”). The more positively the action affects the customer's purchase probability, the further toward the top left she will lie on the graph, and conversely, if the action actually reduces her probability of purchase, she will lie further towards the bottom right corner.

Given this framework, it is natural to define soft versions of the segments with boundaries parallel and perpendicular to the diagonal representing “completely unaffected” customers. The key point is that our returns are proportional to the distance from that diagonal (which represents the uplift). Distance from the diagonal towards the top left corner quantifies positive incremental impact (extra sales generated), while distance below and to right represents negative effects (destruction of incremental sales).

The Problem with Penetration Models

Let's look at penetration models through the clarifying lens of our Fundamental Segmentation in its “soft” form. Penetration models simply look at the proportion of people who purchase a product without any particular stimulation. In other words, they model purchase probability without treatment—exactly what we are plotting on the horizontal axis. So let's look at what happens if we target some campaign action on the basis of such a penetration model. The usual practice is to target everyone with a “propensity” above some cutoff, i.e. everyone to the right of some vertical line on the graph. One such is shown on the diagram below.

As the diagram makes fairly plain, the problem with penetration models is that they tend to target all of the Boomerangs, thereby actively driving away business, as well as wastefully picking up all of the Sure Things, who would buy anyway. Perhaps more surprisingly, they don't even encourage us to target all of the Persuadables. This is because penetration models are built on an untreated population and have absolutely no information about what would happen if we stimulated these customers.

Clearly, if our goal is to maximize the return on a direct marketing campaign, the last thing we want to do is target on the basis of a penetration model.

The Problem with Response Models

So if penetration models don't look to be doing anything very close to what we want, what about traditional “response” models? The difference between a penetration model and a response model is that where the former is built on an untreated population, the latter is built on a treated population. Assuming, again, that some threshold value is picked for probability of purchase if treated, the impact of targeting with a response model is shown below.

The good news is that the “response” model (so called) does something closer to what we want, while still being far from ideal. On the positive side, it does capture all the Persuadables—the people whose purchase probability is materially increased by our marketing action. On the less positive side, it also targets all the Sure Things (who would have bought anyway) and a good proportion of the Boomerangs, for whom our efforts are counterproductive.

How Uplift Modelling Does the Right Thing

The problem with both penetration models and response models is that they misdirect our targeting efforts by modelling the wrong thing. If our goal is to maximize the incremental business we generate, we would like to target the Persuadables and no one else. If we model uplift—the increase in purchase probability resulting from treatment—this is exactly what we are able to do, regardless of exactly how much “uplift” we require to break even. This is illustrated below.

Attrition, Churn and Lapsing: Retention Targeting

If our goal is retention, the story is similar, but with some intriguing (and perhaps unexpected) differences.

The soft version of the Fundamental Campaign segmentation for retention presented previously is exactly as you would expect, and is shown here.

The Problem with Attrition Models

The standard approach to model-driven targeting of retention activity is to model the probability that a customer is going to leave and then to target valuable customers thought it identifies as having an unacceptably high risk of leaving.

For applications such as cross-selling, we saw that a response model (built on a treated population) was a significant advance on a penetration model (which is built on a non-treated population). As we shall see, this pattern is reversed for retention.

If we have an established retention programme, the likelihood is that most, if not all, high-risk customers will be subject to retention activity. As a result, when we build our attrition models (churn models), these will usually be based on a population that is largely or entirely made up of customers who have been (at least in the high-risk segments). We can see the effect of targeting on this basis on the overlay below.

It might at first seem strange that a retention model built on a treated population has exactly analogous failings to a penetration model for demand stimulation: it misses some of the Persuadables, (customers who can be saved, or at least made more likely to stay, by our retention activity) while targeting all Sleeping Dogs (who are driven away by it) as well as many who will go regardless of our actions (the Lost Causes).

As the next overlay shows, if we are going to target on the basis of probability of leaving, it should at least be the probability of leaving if we do nothing. Ironically, this is easiest to achieve if we have a new retention programme, and therefore an untreated population.

So while for demand generation, a response model built on a treated population is somewhat better than a penetration model built on a treated population, this situation is reversed for retention activity: we are better off targeting people based on their probability of leaving if untreated than the corresponding probability when subject to a retention action. And it is particularly important to get this right for retention because most retention activity actually triggers defection for a significant minority of those we try to save (and occasionally a majority).

Uplift to the Rescue

Needless to say, once again the real solution is to target based on that which actually affects campaign profitability, the incremental effectiveness of the action, or the uplift. We can see this clearly on our final diagram.

As I said before, it is important that we model that which is important, and if our goal is to maximize the incremental impact of our campaigns, that is uplift.

Footnote

1In fact, the name I used for Sure Things in the previous post was “Dead Certs”, but it seems that is a bit of UK-centric idiom (“cert” being an abbreviation of certain); Sure Things appears a bit more international, i.e. American. ↩

Boomerangs in Search of a Name

I talked in The Fundamental Campaign Segmentation about the four possible classes of targets for marketing. Three of these have names that everyone seems reasonably happy with:

• Persuadables, who are made likely to buy (or stay) by our actions;
• Dead Certs / Sure Things, who are likely to buy (or stay) whether we treat them or not. (Originally I was calling these “Dead Certs”, but it seems that this is a bit of UK-only idiom, while “Sure Things”, being American, is in some sense more “international”);
• Lost Causes, who are unlike to buy (or stay) whether we treat them or not.

However, the last group, containing those we affect negatively by treatment, is more controversial. In a retention context, these are the people whom we actually trigger to leave. I had called them “Sleeping Dogs”, because we should “let them lie”. In a cross-selling context, where the effect is real but less pronounced, I had called them “Boomerangs”, because they come back and hit you in the face.

Ironically, rather like controversial advertising that polarizes customers, these two terms seem adored by some, and hated by others (at least within Portrait). The people who like them like the fact that they are memorable, particularly once they've been explained. The people who hate them, dislike the fact that they tend to need to be explained, which is much less true of the other segment names.

This blog's pretty young, but in case anyone is reading, I thought I'd list some other possibilities and solicit feedback and alternative suggestions. Here are some other possibilities, most of which could apply in a retention or a selling context, but some of which are specific to retention.

• Boomerangs
• Sleeping Dogs (probably retention only)
• Contrarians
• Hair Triggers (only for retention)
• Perverse-Like-Cats
• Cats
• Backfires
• Shoot-Yourself-in-the-Foots
• Suicides
• Too-Hot-to-Handles
• Only-Make-Things-Worses
• Drive Aways
• Lose-Loses
• Don't-Even-Think-About-Its
• Worse-than-Nothings
• Negative Impacts
• Negative Reactors.
• Renegades
• Do Not Disturbs
• UXBs
• Rebels
• Repelled

Needless to say, neither “Perverts” (OED, perverse a. Persistent in error; different from what is reasonable or required…) nor “Screw You”s (or worse) is considered usable, however apposite they may be!

Use the comments or mail me (see the Author link) if you have any thoughts, suggestions, alternatives or comments.

Uplift and Lift: Not the Same Thing at All

A lot of this blog is about Uplift. You may wonder why I use an ugly, slightly redundant term like uplift when marketers normally talk simply about lift. The reason is that they are completely different.

Lift is a measure of targeting effectiveness that tells you how much better than random your targeting is. The idea is simple. Suppose you get a 1% purchase rate if you target randomly, and a 3% purchase rate if you target only segment A. Then the lift is 3% / 1% = 3. If you have a score (say, purchase probability) then you can plot lift as a function of volume targeted (starting with the best customers), and it will look something like this (assuming your score allows better-than-random targeting):

Lift curves show the same information as Gains Charts (with which they are often confused) but display it in a different way. And they always end at 1 because of course if you target the whole population, you get the same response rate as if you target randomly (on average).

In contrast, uplift directly measures the (additive) difference between the expected outcome in a treated group and control group. For a binary outcome, such as purchase, this is

P (purchase | treatment) – P (purchase | no treatment).

For a continuous outcome, such as spend, this is

E (spend | treatment) – E (spend | no treatment).

So in summary,

• Lift measures the effectiveness of targeting. It quantifies how much better the outcomes are in a target group than they would be in a randomly chosen group (multiplicatively: 2 = twice as good).
• Uplift quantifies the effectiveness of treatment. It measures the difference in outcome between a treated group and an equivalent non-treated group (additively: 10% uplift means that if a person's probability of purchase without treatment is 5%, with treatment it's 15%.) Strictly, uplift for binary outcomes is measured in percentage points, while for continuous outcomes, e.g. incremental spend, uplift is simply the difference in expected spend between the treated and non-treated group.

The Fundamental Campaign Segmentation

I am going to attempt to change forever the way you think about marketing campaigns, but I need your help: I need you to suspend disbelief for a few paragraphs,

Let's think about a direct marketing campaign intended to stimulate purchase of a particular product—Product X. We'll make it very clean, by assuming our goal is simply to get people to purchase Product X within one month of the campaign drop.

We get to choose whether to include each customer in the campaign, and each customer either does or does not purchase Product X. Of course, customers can buy Product X even if they're not included in the campaign. As rational marketers, our goal is to generate incremental sales, i.e. ones that would not have occurred without the campaign.

Now let's segment these customers into four groups as follows.

• The Persuadables. These are the people who only buy the product if we include them in the campaign. They are our true targets.
• The Dead Certs. This group buy the product whether or not we treat them. Think of the people who queue for days to be the first to get a new games console.
• The Lost Causes. Like the Dead Certs, the Lost Causes are completely unaffected by the campaign—the difference is that whether or not we treat them, they don't buy.
• The Boomerangs. We have to accept, at least in principle, the possibility that there is fourth group—people who only buy if we don't include them in the campaign. You may be skeptical that this last group exists, but for now at least accept their logical possibility. One name for this group is the Boomerangs, because—metaphorically—they come back and hit you in the face if you target them.

I'm not a great fan of Boston Boxes, but this does seem like a case screaming out for one, so here it is.

If our goal is truly to maximize the return on our marketing investment, and if we assume for now, that there are no side effects (warm fuzzy feelings generated by being given an offer, even if you don't take it up—that sort of thing), it is clear that the ideal targeting strategy would be to treat only the Persuadables. That way, if you treat 100,000 people, you get 100,000 incremental sales, which is perfect. (I know, I know, people could buy two. Or Seventeen. And they could tell their friends. And you could win the lottery three weeks running…)

If you've hung in this long, there are a couple of obvious big questions. One is whether the “Boomerangs” actually exist. The other is whether we can identify these groups, even if we accept, in principle, that they must (or might) exist. I'll tackle the first of these today; the other will be the subject of a separate, future post.

Boomerangs, Sleeping Dogs, Triggered Cancellation and Negative Effects

There is one case in which the existence of Boomerangs (people for whom the marketing campaign has the reverse of the desired effect) is both simple to demonstrate and easy to understand—the case of retention activity. My company, Portrait, has seen numerous cases of retention campaigns that increase the rate of customer loss in certain segments, and in some cases actually increase it overall. This is not as strange as it may seem.

The mainstream state-of-the-art approach to customer retention for contract-based products (e.g. phone contracts, insurance policies, and fixed-term loans) is first to build a model of how likely people are to fail to renew. In the communications industry, such models are called “churn models”, while in financial services they are normally known as “attrition models”. In the simplest case, people with a high modelled propensity to leave are targeted with a retention action. A more sophisticated approach weights the attrition probability with an estimate of customer value, so that retention activity focuses more on revenue (or profit) at risk than on customers per se.

It's obvious that there is a strong correlation between a customer's level of satisfaction with a service and his or her likelihood of renewing. So modelling attrition probability is pretty similar to predicting dissatisfaction, i.e. the customers most commonly targeted by the standard approach are those who are unhappy with the provider.

Many of us, however, are lazy. Even though I might hate my phone provider or insurance company, there's a good chance that I won't, make the effort to dig out a number and call them up to cancel. It's just too much hassle.

But what if that company takes the trouble to call me up just before my renewal is up? Needless to say, this removes a crucial obstacle to my cancelling, and there's a very good chance I'll say “Ah, I don't suppose just cancel right now is there?” Especially if the call itself annoys me, as is the case for many people.

We have overwhelming evidence that such triggered cancellation is a real and common phenomenon. Boomerangs definitely exist in many, if not most, retention campaigns, though I tend to think of this segment more as “Sleeping Dogs” who are best left to lie. (Though my colleague, Neil, tells me that in Liverpool the phrase is “Don't let sleeping dogs lie.” What can I say?)

But even where such Sleeping Dogs do exist, unless the retention action is spectacularly inept there will be other segments in which the retention efforts can bear fruit. The trick is to separate the wheat from the chaff—or in this case, the Persuadables from the Sleeping Dogs.

Here is the corresponding Boston Box for retention campaigns

For demand generation campaigns—cross-selling, up-selling, deep-selling etc.—negative effects are usually smaller. However, we have compelling evidence that they do exist. This matters because even a company happy to lavish attention on customers whose behaviour will not be positively affected by it should think twice before actually spending money to drive business away.

As you might expect, more intrusive contact mechanisms (particularly phone calls) swell the numbers of Boomerangs, as do campaigns that are narrower, more divisive or risqué. One of our clients claims he always sees negative effects in the last one or two deciles.

Summing it up: The Incremental Gains Chart

From one perspective, the Dead Certs (people who will buy whether we treat them or not) and the Lost Causes (who won't buy whatever we do) are equivalent: our action has no impact on either group. Thus if we think only in terms of our impact, a simpler segmentation is into the group we affect positively (the Persuadables), the group for whom our intervention has no effect (collectively, the Unshakables), and the group we affect negatively (the Boomerangs, or Sleeping Dogs).

If we assume that we can predict the change in purchase probability for each person, we can then plot an incremental version of a gains chart to produce the “Italian Flag” diagram, as below.

Zone 1, (the green stripe), consists of the people we can affect positively—the Persuadables. If we could identify them perfectly, this would be a straight line, that comes to an abrupt halt, but with any real model, the best we can do is identify them probabilistically, hence the curve. Obviously Zone 1 is where we spend money to make money---a reasonable proposition. Zone 2, the white stripe, is all the people who are largely unaffected by our action—a mixture of the Dead Certs and Lost Causes. Here the line would be perfectly horizontal if we could identify these groups with certainty. In Zone 2 we spend money for no appreciable return. Zone 3, red, is the group where we have a negative effect—the Boomerangs if we're selling things, and the Sleeping Dogs in a retention context. This is the disaster zone, in which spend money to drive away business. There is no rational case for targeting here.

Moving to this slightly more nuanced view, where we deal in probabilities rather than known outcomes, we can recast anyone whose probability of purchasing is increased by our action as a Persuadable; those whose purchase probability is largely unaffected as an Unshakable, and those whose probability of purchase is reduced as a Boomerang.

The trouble with conventional so-called “response” models is that, despite their name, they don't model response at all: they model purchases pure and simple: they don't look at the untreated population in the model-building process. So it's not that they simply conflate the Dead Certs with the Persuadables: they will actually also tend to recommend targeting people whose likelihood of purchase is reasonably high if treated, but even higher if left alone. Quite simply, “response” models aren't: they model the wrong thing.

In future posts, I'll discuss how we might go about segmenting people for real, and how we might model the change in response probability (the uplift) to allow us to target on that basis.

The Deceptive Simplicity of Scorecards

Statistical credit scoring is almost certainly the earliest example of what we now call CRM analytics. It was largely invented in the 1950s by Fair, Isaac, still one of the leading credit reference agencies in the world.

This post is the first of a short series that will talk about the nature of credit scorecards and explain how, behind their deceptive simplicity, there is a remarkably sophisticated modelling methodology that is competitive with just about anything else in use in mainstream predictive modelling today.

But first, a story.

Probably ten years ago, or more, I met a woman called Mary Hopper, who had worked for Fair, Isaac for many years. She told the following story, which still stands as a salutary reminder of how difficult our messages can be to get across.

Many years previously, Mary had found herself giving a presentation to the board of a bank, in which she tried to persuade them to adopt the then new-fangled statistical approach to determining lending decisions. She had done some analysis, which showed that in segment A, to which she was recommending offering credit, only one in twenty people would default. In contrast, in segment B, where she recommended refusing credit, the rate of default would be more like one in eight. She had graphs and diagrams and tables, all of which conclusively proved (so far as statistics and models ever conclusively prove anything) that segment A was the better bet.

The members of the board listened politely, as was the custom of that halcyon era, and when she had finished, feeling rather pleased with her own performance, the bank's chairman thanked her. He assured Mary that her presentation had been extremely clear, and very convincing. He had just one minor improvement to suggest. This was that rather than lending to the whole of segment A, the bank should instead lend only to the 19 out of 20 who would, in fact, pay them back.

My bet is this story has repeated itself hundreds if not thousands of times since.

The Deceptive Simplicity of Scorecards

Stories aside, I'll finish this post with a simple description of a modern scorecard. While practices vary, most credit scores today are produced using a model with a form extremely similar to that which I will describe below.

A (consumer) credit score is a number. Conventionally, the higher the number, the better an individual's credit-worthiness. They can be scaled different ways, but perhaps the most common way is to scale them so that scores mostly lie between zero and a thousand. Each score can be mapped simply, and unambiguously, to a probability of default using a simple function.

There is a fundamental distinction between so-called application scores and so-called behaviour scores. Application scores are used when a new customer applies for a credit product with a lending organization. Because the customer is new, the lender has less information available on which to make a decision, so the main factors tend to be a mixture of questions on application forms and information that can be purchased from credit reference agencies. In contrast, behaviour scores are used to estimate the credit quality of existing customers, both for day-to-day management and monitoring purposes (including allocation of capital) and also for deciding whether to extend further lines of credit to particular individuals.

The score is formed by adding up a set of component scores. Each component can be thought of as representing some fact about the customer, and is conventionally known (in terminology popularized by Fair, Isaac) as a characteristic. Stability indicators often form a major component of scorecards, so common characteristics are things like “time in job”, and “time at this address”.

For behavioural scorecards, the emphasis tends to be much more strongly on characteristics that summarize different aspects of the individual's transactional behaviour and account management. These include things like account trends (is the balance increasing or decreasing), swings (how stable is the balance), and other key indicators such as “largest single credit transaction”.

In the most common case, the possible values for each characteristic are grouped into bands (known as attributes), and each band attracts a number of points. The customer's score is then simply formed by adding up the points for each characteristic in the scorecard.

Thus a simple scorecard might look like this.

So, for example, a customer who has lived at her address for 16 months, has a 12-month swing on her account (the difference between the highest and lowest balance during that period) of $900, saw 22 credits on the account in the last 3 months and rents her house would get a score of 200 + 225 + 190 + 90 = 705.

Clearly, the scorecard is a pretty simple mechanism for coming up with a score, even if in practice there might typically be a few more characteristics, and perhaps also a few more possible values for many of them. In fact, at first glance, this might look a little too simple. Surely just adding up a bunch of component scores is a trivial way of predicting something. What about non-linearities? How could such a transparently unsophisticated system possibly compete with the subtleties of something like a neural network?

Over the next two or three posts on this thread, I'll be talking through these and other issues and showing, among other things, that beguilingly simple as it is, a state-of-the-art “numbers-in-boxes” scorecard combines extreme flexibility of modelling with a quite surprising ability to model non-linear behaviour; in fact, it is competitive with just about any other current predictive technique. Topics will include linearity (scalar multiplication and additivity) variable transformation, interactions, segmentation, binning and more.

Watch this space!

Creating Passionate Users

If you are interested in topics like customer loyalty and customer satisfaction, you might want to check out Kathy Sierra's writings at the Creating Passionate Users site. Today's on how much control is optimal for a user is excellent, yesterday's on marketing and education was great. Well, you get the pattern.

Clustering Considered Harmful: Outline

It's pretty obvious the distribution of matter in space is lumpy. Matter clumps into planets, planets orbit stars, stars clump into galaxies, galaxies group together into clusters, and―wouldn't you know it―clusters form superclusters. Thank gravity for that. There are clumps of matter, and other things, at smaller scales too. Atoms are mostly empty space, with a lot of stuff at the centre (the nucleus), and electrons like to hang around at particular distances away from the nucleus (the shells), though it's hard to pin them down. Similarly, people clump together on the Earth. London, Tokyo and Sao Paulo are pretty crowded; the Sahara, the Highlands of Scotland and central Australia mostly aren't. (People are quite hard to pin down, too.)

Cluster analysis is a set of techniques for taking the coordinates of a lot of objects (stars, particles, people…) and figuring out something about where the lumps are. There are lots of ways to do it.

Someone, deep in the mists of time, had the bright idea of applying cluster analysis to customers to figure out “where the clumps are”. The idea wasn't to use geographical coordinates (of their houses, say), but to replace coordinates with customer characteristics, like demographics (age, income etc.), behavioural measurements (spend levels, frequencies, balances etc.), and maybe attitudinal things like psychographics. That way, they thought, they might uncover the “natural groupings” of customers, which could be useful for understanding their dynamics and for segmenting them.

While it was far from a stupid idea, it turns out that it was an extremely bad idea, one that at best has wasted countless thousands of hours of analyst time, and at worst has led to baseless conclusions and highly suboptimal marketing.

There are far too many problems to do justice to in a single blog post, so I won't. Instead, I'll list some headlines here, and over the coming weeks I'll do an entry on each one. Then maybe I'll gather them into an absurdly long whole.

Here are some of the headline reasons that clustering customer characteristics isn't useful.

• There's no real evidence that customers cluster.
• Different customer characteristics are non-commensurate.
• Circularity: practitioners think they're just finding “the natural clusters”, but in fact the results are entirely dictated by decisions made up-front (often without realising it) about scaling. Different choices lead to different scalings, so clusters are unstable.
• The curse of dimensionality means that clustering doesn't really work in more than a few dimensions.
• Clustering is undirected.
• Clusters are hard to interpret. So people give them names. And then the names become the meaning.
• For (almost) every problem tackled with undirected clustering, there's a directed approach that will (almost always) work better.

For avoidance of doubt (as lawyers say), and notwithstanding the impression the title of this entry may give, the problem isn't cluster analysis per se, which is a perfectly fine collection of techniques. If you want to find the clumps in a low-dimensional space with commensurate dimensions, it's exactly what you need. It's just that that isn't a very good description of a customer base.

Here are the parts posted so far:

• Clustering Considered Harmful: I. Introduction
• Clustering Considered Harmful II: Distance and Scaling
• Clustering Considered Harmful III: Commensurability

Customer Alienation Systems

It was Herb Edelstein who, as far as I know, first argued that IVR systems ("Interactive Voice Response") should more properly be known as Customer Alienation Systems.

He's not wrong.

I Want to Give You My Money

People are bad at remembering numbers, even for short periods of time. Mostly. The most that most people seem to able to remember reliably, even for a few seconds, is four digits. I thought everyone knew this. That's why we break up telephone numbers into blocks of two, three or four digits usually. And that's why the numbers on credit cards are broken up into groups of 4.

Let's suppose you have a customer who has decided he wants to pay you some money. In fact, let's suppose it's me. You present me with a form containing a box in which to enter my 16-digit credit card number. Remember, I want to pay you money.

Clearly the box should let me type in my credit card number, as it appears on the card, with spaces, in groups of four. Of course, it should also let me type it without spaces. In fact, it should completely ignore all whitespace (and probably dashes too), and provided I enter exactly 16 digits, and nothing else except whitespace, it should go and process the number. And if I typed something else, it should highlight the problem, minimally pointing out the field I got wrong on the form, and preferably telling me something helpful like "the credit card number you entered only had 14 digits". Or whatever.

Here are some of the ways you can lose my business with a very high probability.

• Reject the number if I type spaces in it.
• For double credit, complain without telling me that the whitespace is a problem.
• For triple credit, don't even tell me that the credit card number was the problem field.
• For quadruple credit, put some text by the box saying "Enter your credit card number exactly as it appears on the card."
• Alternatively, specially cripple the form so that I can't even type whitespace into it. This will stop me entering the number with whitespace (so I have a chance of getting it right), checking that I did get it right (almost impossible without its being broken up), then deleting the whitespace while swearing profusely.
• For half credit (you'll probably still get my business but I'll be swearing under my breath), actually force me to break up the number by giving me four separate boxes to type into. (Heart's in the right place, but too fiddly.)

I'm not the first person to notice this. See, among others, Jacob Nielson (9. Overly Restrictive Form Entry", The "No Dashes Or Spaces" Hall of Shame, Don't be a Sucky Webmaster, and Simson Garfinkel.

Occasionally, I complain to a company about this (usually on when my desire to give it money is overwhelming), and it staggers me how often I am told that it is too difficult to implement technically. Here is how hard it is to strip spaces in my language of the moment (python). If the number is stored in a variable called cardNumber, you have to say

cardNumber = cardNumber.replace (' ', '')

(Removing tabs and dashes or anything else is equally simple.) I admit it might take as many as half a dozen lines in some other languages, but not many. If your systems people tell you it can't be done, you need new systems people.

Remember, all I want to do is give you my money.

The Two Controls

Everyone knows about control groups. They're the people who meet our targeting criteria, but whom we don't treat so that we can understand the incremental impact of our actions. I call these treatment controls, because they allow us to assess the effectiveness of our treatments.

Less commonly, a second kind of control group is used as well, a group call targeting controls. These are people who do not meet our criteria, but whom we treat anyway to check the effectiveness of our targeting.

The truly scientific marketer needs both.