Counting and Summing Beats Machine Learning, Most of the Time
Here is a pattern I see again and again with owners who have been sold on artificial intelligence. Someone has a perfectly ordinary business question, what should we charge, which customers are about to leave, where is the money actually leaking, and before anyone has counted a single thing the conversation jumps straight to machine learning. Let us train a model. And most of the time, and I really do mean most of the time, a careful count and a sum on the back of an envelope would have answered the question faster, at a fraction of the cost, and with an honesty that a black box will never give you. I want to show you the habit that good analysts have and almost everyone else skips. Before you reach for anything clever, you break the problem down to its simplest driving equation, and you let that equation tell you which single number is actually moving the outcome. Do that first and you will be amazed how often the model turns out to be a very expensive way of avoiding arithmetic.
The interview question that gives everyone away
There is a classic analytics interview question that I love because of how ruthlessly it sorts people. The interviewer says, quite casually, we are launching a product, what should we charge for it. And you can watch the candidate decide, in real time, what kind of analyst they are.
The show off reaches for something clever. They start talking about price elasticity models, a regression on comparable products, maybe a machine learning model trained on competitor pricing scraped from the web. It sounds impressive. It is also, at this stage, completely useless, because they have not yet written down what price even does.
The good analyst does something almost boring. They say, well, revenue is price times quantity, so let us start there and see what actually moves. That is it. That is the whole trick, and it is the habit I want to give you in this article, because it generalises to almost every data question a business will ever ask you. I have used it in pricing, in acquisition, in churn, in stock control, in staffing, and the shape is always the same. Write the outcome as a product and a sum of a few honest drivers, then go and count the driver that is doing the work.
Break it to its simplest equation
The method has a name in the trade. In The Data Analytics Handbook, the interview guide that did the rounds back in 2014, it is described as breaking a problem down to its simplest equation before you touch any data at all. You do not begin with the data. You begin with the arithmetic of the business, written as one honest line, and only then do you go looking for the numbers to fill it in.
So, what should we charge. Revenue is the thing we want to grow, and revenue is made of exactly two parts.
That looks trivial. It is not, and here is why. The moment you write it down, you have exposed the tension that the whole pricing question is really about. Push price up and, unless your customers are made of stone, quantity comes down. So the question is never what is the highest price. It is what is the price at which price times quantity is largest.
Let me put numbers on it, illustrative ones, the kind you can argue with. Say today you sell at forty pounds and you shift ten thousand units a year.
Four hundred thousand pounds. Now you are tempted to raise the price to forty four pounds, a ten percent rise. Your gut says revenue goes up ten percent. But you go and count, you actually look at what happened last time you nudged the price, and you find that a ten percent rise costs you roughly eight percent of your volume. So quantity falls to nine thousand two hundred.
Four hundred and four thousand eight hundred. It went up, but by barely one percent, not ten. And now the whole picture has changed, because you are selling eight hundred fewer units at a higher margin, which is almost certainly more profit even though revenue barely moved. The equation did not just give you an answer. It reframed the entire question from what price to what are we actually optimising, revenue or profit, because those two now point in different directions.
No model told you that. A count of what happened last time you moved the price told you that, dropped into an equation a child could read.
A HA one, the ratio that price really turns on
Let me push the pricing case one step further, because there is a second insight hiding in it that most people walk straight past. What actually decided whether that price rise was worth it was a single ratio, how much volume you lose for each percent of price you add. Analysts call it elasticity, but you do not need the word to use the idea.
An elasticity of minus zero point eight means demand is inelastic, you lose less volume than the price you gain, so raising price lifts revenue. If that ratio had come back as minus one point five, the same maths would have told you to cut the price, not raise it. So the real lever behind the pricing question is not price at all. It is one honest ratio that you can only get by counting what happened last time. That is the thing to work on, and no model is going to hand it to you at a lower cost than your own sales history already does.
The lever hides in plain sight
Let me do a second one, because the pattern is the point, not the pricing.
An owner comes to me worried about growth. We need more customers, they say, and someone has told them the answer is a propensity model that scores every visitor on how likely they are to buy. Big project. Expensive. Before we spend a penny on it, we write the equation.
New customers are just the people who show up multiplied by the fraction of them who buy. Two levers, only two. So we count. Traffic is fifty thousand visitors a month. Conversion rate is two percent.
A thousand new customers a month. Now the useful question, the only question really, is which of those two numbers is easier to move. And here is where the counting earns its keep. We look, and we find that traffic has been flat for a year despite steady ad spend, while conversion rate has quietly slipped from two point six percent to two percent over the same period, right after a checkout redesign.
There it is. The lever is conversion, and more specifically it is a checkout that got worse. Lifting conversion back to two point six percent, just undoing the damage, gets you thirteen hundred customers on the same traffic.
A thirty percent lift, for the cost of fixing a form. The propensity model would have spent three months learning to rank the very visitors who were already bouncing at a broken checkout. It would have optimised the wrong link in the chain, expensively, and produced a beautiful scored list that changed nothing.
That is the second A HA moment, and it is the one that pays for the whole article. The model does not just cost more. It actively hides the lever, because it answers the question who is most likely to convert when the question that mattered was why did conversion fall. A count answered the second question in an afternoon.
Extend the same line one more step
Watch what happens when I stretch that equation out to the thing the owner actually cares about, which is money, not customers. You just keep multiplying by the next honest driver.
Now there are three levers on one line, and you can go and count all three. Say average order value is eighty pounds.
Eighty thousand pounds a month. The beauty of the extended line is that it lets you compare levers in the same currency. A jump in conversion from two to two point six percent is worth twenty four thousand pounds a month. A rise in average order value from eighty to eighty four pounds, four percent, is worth about four thousand. Suddenly the ranking of what to work on is not a matter of opinion, it is sitting right there in the arithmetic, and you never trained a thing.
The marketing version, same shape
Once you get the habit you see the same skeleton everywhere. Here is the one I reach for whenever the conversation is about paid acquisition, and it is worth committing to memory.
Profit from acquisition is the value of a customer over their life, minus what it cost to acquire them, multiplied by how many you win. Say a customer is worth nine hundred pounds over their life, costs three hundred to acquire, and you win a thousand of them.
Six hundred thousand pounds. Now look at that bracket, because the bracket is the lever. If your CLV estimate is soft, and in most businesses it is a guess dressed as a fact, then the entire six hundred thousand is resting on a number nobody has actually counted. The most valuable analytics work here is not a model that predicts CAC to the second decimal place. It is going and counting, properly, what a customer is really worth, because a fifty pound error in CLV moves the answer by fifty thousand pounds and no amount of modelling sophistication downstream can rescue a rotten input. Count the thing the equation says matters most, and leave the clever stuff for when the arithmetic runs out.
CLV is itself an equation, so open it up
Here is a trap worth naming. People treat CLV as a single fact, a nine hundred pound label on the customer, when it is really another little equation begging to be opened. The simplest honest version is this.
Say a customer pays fifty pounds a month, you keep sixty percent of that after costs, and they stay thirty months.
There is your nine hundred pounds, but now it has seams you can pull on. Lifetime in months is just one divided by your monthly churn rate, so a customer who churns at three point three percent a month lasts about thirty months. Cut that churn to two point five percent and lifetime jumps to forty months, and CLV climbs to twelve hundred pounds without winning a single new customer or raising a single price. That is the A HA that reframes most acquisition panics. The least expensive customer to acquire is very often the one you already have and are quietly losing.
A third driver worth counting, the leak nobody watches
That last point deserves its own line, because churn is the driver I see counted least and worried about most. If you run anything on a subscription, your monthly lost revenue has a painfully simple form.
Fifteen hundred customers, a three percent monthly churn, sixty pounds each.
Two thousand seven hundred pounds walking out the door every month, thirty two thousand four hundred a year, and it compounds because those customers would have stayed and paid again. Now put that next to acquisition. To replace two thousand seven hundred pounds of lost MRR at a three hundred pound CAC and sixty pound monthly value, you need to win forty five new customers a month just to stand still. Written as one line it becomes obvious that shaving churn from three percent to two percent is worth more than almost anything you could do on the acquisition side, and you found that out by counting, not by training a churn model that would have told you who leaves without ever telling you it was less expensive to make them stay.
A worked mini case, the SaaS that wanted a churn model
Let me put the whole habit together on one realistic example, numbers illustrative as ever. A founder came to me convinced he needed a machine learning churn model. He had read that the smart SaaS companies score every account for churn risk, and he wanted one. Budget was being lined up. Before any of that, we wrote the equations.
Start with where the money actually is.
A hundred thousand pounds a month. Then the leak.
Then we did the thing the model never would have made him do. We counted the churn, but broken out by how the customer had come in. And the split was stark. Customers acquired through a discount promo churned at five and a half percent a month. Customers acquired at full price churned at one and a half percent. Same product, wildly different leak, and the blended three point three percent had been hiding it.
Nearly all of the leak, two thousand four hundred and seventy five pounds of the three thousand three hundred total, was coming from one segment that was one part discount hunters who never intended to stay. A churn model would have dutifully learned to predict exactly that and handed him a list of at risk accounts, most of them the promo cohort, and suggested he spend to retain people who were never going to pay full price anyway. The count told him something far more useful and far less flattering, that the acquisition channel itself was manufacturing churn, and that the fix was upstream, at how he was buying customers, not downstream in a retention model. He stopped the promo. That was the whole project, and it cost a whiteboard afternoon.
A little library of equations to keep in your head
Once you trust the habit it helps to carry a few of these around, because the hard part is usually just remembering that the line exists. Here is the shortlist I actually use.
| Business question | The simplest equation | The lever it exposes |
|---|---|---|
| What should we charge | Revenue = Price x Quantity | How much volume moves per percent of price |
| How do we get more customers | New customers = Traffic x Conversion rate | Whichever of the two has slipped |
| Is our acquisition profitable | Profit = (CLV minus CAC) x Customers | The honesty of the CLV number |
| What is a customer worth | CLV = ARPU x Margin x Lifetime | Lifetime, which is one over churn |
| Where is the revenue leaking | Lost MRR = Customers x Churn x ARPU | The churn rate, split by segment |
| Do we have enough staff | Capacity = People x Hours x Utilisation | Utilisation, the fraction actually billable |
None of these needs a model to compute. Every one of them needs you to go and count one number honestly, and every one of them, once written down, points at the number that is worth the counting.
So do you actually need a model, or a count
Here is the decision I walk through, out loud, before anyone is allowed to say the words machine learning in one of my projects.
Most questions never leave the left hand side. You write the equation, you count the drivers, the count answers it, you ship. A model earns its place only in the bottom right corner, where the pattern is genuinely too tangled to write as a line, and it is stable enough to be worth learning, and you already have data good enough to learn from. That is a real place. Fraud patterns, demand forecasting across thousands of items, recommendation at scale, these genuinely resist a single equation and a model is the right tool. But it is a corner, not the whole map, and the tragedy is how many businesses start in that corner for questions that never needed to leave the top.
Counting versus modelling, honestly compared
I am not against models. I build them when they are warranted. But the trade is real and worth seeing on one page.
| What you care about | Counting and summing | Machine learning model |
|---|---|---|
| Time to first answer | Hours | Weeks to months |
| Cost | Almost nothing | Data, tooling, and people |
| Can you explain it to the board | Yes, it is one line | Rarely, and not honestly |
| Can someone challenge it | Yes, every number is visible | Only the person who built it |
| Shows you the lever | Almost always | Almost never, it buries it |
| When it genuinely wins | Simple, one off, framable questions | Complex, stable, repeating patterns |
Read the row that says can someone challenge it, because that is the one owners underrate. A count is defensible. Every number in the equation is sitting there in the open for anyone to argue with, and that argument is where the real understanding gets made. A model hands you an answer with no seams, and the moment you cannot question a number is the moment it starts quietly making decisions you did not agree to.
Common mistakes I see
After enough of these projects the same handful of errors keep turning up, and they are worth naming so you can catch yourself.
The first is reaching for the model before the equation. Someone falls in love with the idea of prediction before anyone has written the one line that says what they are trying to predict and why. The model becomes a way of avoiding the harder, humbler work of counting.
The second is optimising a driver that is already near its ceiling. If your conversion rate is already excellent, squeezing another sliver out of it is brutally hard, while the traffic sitting flat beside it might double with modest effort. The equation shows you both numbers side by side, so you can pick the one with the most room, and yet people fall for the driver that feels exciting rather than the one that is actually loose.
The third is trusting a blended average that hides a split. The three percent churn that was really five and a half and one and a half. The two percent conversion that is eight percent on mobile and half a percent on desktop. Averages are where levers go to hide, so once you have the equation, always ask what happens when I break this number by segment.
The fourth is treating a soft input as if it were hard. CLV again, or a cost figure someone guessed in a meeting two years ago. The equation is only as honest as its weakest number, and the most valuable hour you can spend is often not modelling at all, it is going and counting the one input everyone has been quietly assuming.
The fifth, and the most expensive, is building something nobody can question. If the answer that comes out cannot be checked against a count, you have not reduced your uncertainty, you have only hidden it inside a machine, and hidden uncertainty is far more dangerous than the visible kind because it stops anyone arguing with it.
How to apply this on Monday morning
None of this is theory, so here is the routine, small enough to actually use. It fits on a sticky note.
Step one, write the outcome you actually care about at the top of a page, in money if you can. Step two, ask what it is made of, and keep asking until you have a line of a few drivers multiplied and added. Step three, resist the urge to gather data before the line is finished, because the line tells you which data is even worth gathering. Step four, go and count each driver, from real history, not from memory. Step five, and this is the one people skip, break every average into segments and see if the lever is really one hidden slice. Step six, pick the driver with the most room and the least effort, and move it. Only if all of that leaves the question genuinely unanswered, and the pattern is stable and repeating, do you let the word model back into the room. Nine times in ten you will already be done.
How I actually work through this with a client
When someone brings me a data question the first session almost never touches a dataset. We get a whiteboard and we write the equation. What are we really trying to move, and what is it made of, multiplied and added together into one honest line. Nine times out of ten the room goes quiet, because the equation has just made it obvious which number nobody has bothered to measure, and that missing number is the whole project. We go and count it. Often that is the entire engagement, and the client leaves with an answer they can explain to their own board without me in the room, which is exactly how it should be.
The tenth time, the arithmetic genuinely runs out. The relationship really is too knotted for a line, the data is rich and stable, and a model is the honest next step. Then we build one, gladly, but we build it knowing precisely which lever it is meant to move, because the equation told us, and we can check its answer against a count to make sure it has not wandered off into nonsense. A model you cannot sanity check against arithmetic is a model you should not trust, and the arithmetic has to come first for that check to exist at all.
If you have been quoted a big number for a machine learning project and you have a nagging feeling nobody has actually counted the simple thing yet, that is exactly the conversation I like to have. Bring the question, we will write the equation together, and more often than you would expect you will walk out without needing the model at all. That is the sort of unglamorous, money saving work my data and analytics practice is built on, and you can book a call whenever you want a second opinion before you spend.
The one habit to leave with
If you take a single thing from this, make it a reflex. The next time a business question lands on your desk, and before anyone says the word model, ask yourself what is the simplest equation that describes this. Write it as one line. Multiply the drivers, add the parts, and stare at it until it tells you which number is doing the work. Then go and count that number, really count it, and see if the question is already answered. Most of the time it will be, and you will have saved months and a great deal of money, and you will understand your own business in a way no black box was ever going to let you. The clever stuff is still there for when you truly need it. You will just need it far less often than anyone is trying to sell you.