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• Bryan Wang

# A Guide To Market Sizing

So, um, what is math doing here?

Unsurprisingly, candidates typically struggle the most with the quantitative/numerical portion of the case interview.

And, surprise surprise, math is a pretty big part of consulting. Solving problems requires data. Lots and lots of data. And as an analyst, you’re doing most of the heavy lifting when it comes to data collection and analysis, modeling, and visualization.

Quantitative questions come in 3 forms: estimation (re: market sizing), formulation (re: break-even, elasticity, etc.), and data analysis/interpretation (re: reading and analyzing graphs, which is sadly harder for most college students than one would think…).

Meanwhile, underpinning all aspects of the quantitative side of casing is mental math, which has emerged to haunt college students who have sadly reverted back into elementary school levels of math. So, before we jump straight into market sizing, let's learn some quick tips and tricks to rapidly and accurately compute mental math questions (re: the building blocks of any quantitative-based question you can get in a case interview, like a market sizing problem).

### Mental Math

Mental math, surprisingly or not, is tends to be the toughest part for candidates to overcome. I can teach you all the frameworks and structures you need to ace market sizing, break-even questions, etc. But it’s pretty hard to teach basic math… especially when you’re dealing with messy calculations and numbers in the billions and trillions.

Below are three quick tips + tricks for you to practice when doing mental math — I promise you they will make your life a LOT easier when you have to calculate on the fly. Because just like in the SAT and ACT, acing math in the case isn’t just about getting to the right answer: it’s about getting to the right answer as quickly as possible.

Your interviewer isn’t going to have all day, because the client isn’t going to have all day. They expect an answer, and they expect it now.

### A Primer on Market Sizing

There are three types of market sizing questions, and they build off each other sequentially (so expect to hit all three when tackling market sizing):

1. How many of <ABC> exist in a market? Your answer is measured as total units that exist in a market, and you should specify if you are looking for total units that exist in total (in perpetuity) / that are produced per year / etc.

2. How big is the market for <ABC>? There are 2 sub-questions for this, either stated or implied: you are either looking for the number of units sold, or for the total value of units sold. The latter sub-question involves one extra step — upon finding the total number of units, you will need to multiple volume by price. In some market sizing questions you are evaluating multiple products - and therefore multiple volumes and prices - so multiply your numbers accordingly. The ultimate answer, then is measured in dollars/currency of sales in a given year.

3. What is the opportunity if the client introduces <ABC> into the market? Upon reaching the total market size/value, this next question asks you to essentially estimate the client’s share-of-market. Multiple market size by client market share, and you will reach your answer. We will be covering how to identify a reasonable market share estimate in future sections.

Some examples of market sizing questions include:

“Our client is a national golf club manufacturer, and has observed declining profits over the past five years. They are looking to reverse their financial situation by entering new markets, and have asked you to determine whether or not they should expand to New York.”

It stands to reason that identifying the number of golf balls sold on a yearly basis in New York will help you solve this larger question. On that note, your interviewer asks:

“First, our client wants to know how big the golf club market in New York is. How do you go about solving this problem?”

Now, before you get overwhelmed, remember the fundamental principle of consulting: break larger problems into smaller and smaller, and more manageable, chunks.

As you break down these large, gargantuan problems, it’s just a matter of adding all the numbers together and reaching your conclusion. And in the next few sections, we’re going to cover exactly that.

### Before You Start Blasting…

Market sizing questions are ALWAYS ambiguous, and a strong candidate is able to collect and ask for data in order to clarify said ambiguities.

At the beginning of the case, you therefore must ask clarifying questions in order to accurately size your markets. Sometimes, this information is directly given to you. Other times, it won’t be and you’ll have to ask for it. Here are some to consider…

#### #1: Clarify The Unit Of Measurement (Volume Or Value)

Check with your interviewer if the measure you are estimating is ‘market volume’ (re: the number of units sold/year) or ‘market value’ (re: the market size in US dollars, or total revenues generated/year). If you give an estimate in dollars when your interviewer expects a market size in volume, you will fail your interview. Clarification is key!

#### #2: Clarify The Timeframe

Check if your estimate is for a specific time period. For instance, are you measuring market size by last quarter or by last year / this year?

#### #3: Clarify The Geography

It is highly unlikely you’ll have to estimate a global market. Rather, you are far likelier to estimate the size of a market for a specific region, such as the U.S., China, a state like California or New York, or a major city. Thus, if this context is not given to you, you must ask your interviewer for it.

#### #4: Clarify The Product

This is the most common question that needs clarifying, and it’s one many candidates fail to ask (and therefore fail the interview). Defining the product means thinking about product segmentation; for instance, if your interviewer is asking you to estimate the market size for smart phones, you should first be wondering if this includes all smartphones (re: iPhones, Android phones, Xiaomi, etc.) or just a particular brand / operating system. Without clarifying, you might be entirely answering the wrong question. Remember, it’s your responsibility to know what question you’re solving — a client won’t spend precious time babying you, it is your duty as a consultant to identify the key drivers, clarify the context, and solve the (right) problem.

#### #5: Clarify The Customers

Clarifying customers means identifying the target buyers of the product you are sizing. Think of segmenting customers by certain features/characteristics, such as: B2B vs B2C, age, income, gender, demographics, psychographics, etc.

#### #6: Set The Stage for Your ‘So What’ Analysis

This part may not quite make sense for you, but bear with me — when you reach the final ‘market size’, you still haven’t really answered the question. And if you just leave your interviewer with a number, you’ll have failed the interview. A number is only as valuable as its context — so what the market size is \$250M, or \$1.5B? Why does that matter for the client? In order to tell your client if the market size is a good number or a bad number, you need more data — what is the size of the market our client is currently in? What are our client’s current and historical revenues? What is their estimated share of this new market? If they can capture 33% of the new market, for instance, and that number is greater than their current/historical revenues, then entering the market - assuming the cost to enter said market isn’t ridiculously high - is very attractive. You may then propose to examine how expensive it would be to enter the new market, and evaluate if market entry is still viable (re: if cost of entry > revenues from entry, then the client should not enter the market unless over a certain period of time revenues > costs and the client will earn net profit from entry).

### Top-Down Market Sizing

If you’re choosing the top-down approach, you’ll base your hypothesis on a large overall number, such as ‘population’ or ‘household’, and drill down from there.

Another way to think about the top-down approach is to think of the issue as demand-based — you’re trying to identify the number of users/customers purchasing, say, golf balls (as per the hypothetical question above). Below is a useful framework for helping you think about how to employ a top-down approach:

Let’s start with the “baseline.” Typically, you are expected to know some basic assumptions/facts such as the population of the United States, the size of the U.S. economy, etc. You will not, however, be expected to know more niche things, such as the population of New York (unless you’re from New York, you should know the population of your state and major metropolitan areas like NYC, SF, LA, etc.) or what percentage of New Yorkers are avid golfers.

Once you’ve established your “baseline” (re: NY state’s population is ~ 20M, or roughly 6.5M households given average household sizes are 3 individuals), you need to multiply it by the “ratio,” or the portion of the “baseline” that is relevant to your market.

One of the most popular ways of generating a “ratio” is via age, though you can also do it by income, geography, consumer behavior, etc. That being said, age is the most common. I personally use age groups 0-19 (25% of population), 20-39 (25%), 40-59 (25%), and 60+ (25%) which makes for a total population of 320M. Each group is composed of 80M people, and each age is is composed of 4M unique individuals (re: # of 20 year old’s is 4M, # of 1 year old’s is 4M, vice versa). If you assume a 50-50 gender split, this means there are 2M 10 year old males, 2M 20 year old females, etc.

Using the golf example above, my goal is to multiply our baseline <New York’s population, 20M> by our ratio <% of New Yorkers that golf>. This will help us calculate the total market size for golf clubs sold in New York. Let’s assume regular golfers typically belong to an age range of 20 to +60. There are, of course, younger golfers under 20, but they are so few of them that - for simplicity’s sake - we can discount them altogether. This means our baseline is 15M individuals (e.g. 75% of 20M).

Obviously, though, not every 20 year old is a golfer, nor is every +60 year old. To further segment our population, I’m going to apply an income based “ratio.” Since golf tends to be a sport frequented by upper middle to upper class families, I’m going to make a rough assumption that only the top economic 1% are regular golfers. Our baseline of 15M has now become 150,000. If you want to be more generous, you can assume that the top 2% are regular golfers, meaning our new market is 300,000.

We have just identified the ‘Number of Customers’. Now, we must identify the ‘# of Units Purchased per Customer’, which can be found by identifying ‘frequency of purchase’ and ‘quantity per purchase’.

Frequency of purchase refers to the average number of purchases in a given time period. Typically when valuing market size, we measure size by year. To then find frequency of purchase by year, we have to make some more basic assumptions: let’s assume a golf club, on average, lasts for 1 year. This makes your analysis easier, as frequency of purchase is ‘1’. If a golf club lasts 2 years, however, then the frequency of purchase is 0.5. Depending on the utilization rate and lifetime value of a product, frequency of purchase may not be relevant. If measuring the market size for chewing gum, for instance, frequency of purchase would be much higher as chewing gum is a one-time product (re: think about it as buying one gum pack/week, or 52/year).

Next we need to find ‘quantity per purchase’. Every time a customer walks into the door, how many golf clubs do they actually buy? Again, to make things simple, we can assume that the average golfer in New York just buys one club per purchase.

Now let’s multiply ‘frequency’ by ‘quantity’. If the average golfer buys one golf club every two years, that means they buy 0.5 golf clubs per year.

150,000 golf clubs are thus sold every year in New York (e.g. 300k * 0.5). But wait — we were tasked with finding market size, not the number of golf clubs sold. We thus need to multiply 150k by the average price per golf club. We can ask our interviewer at the start of the market sizing session if they have any facts or figures on golf club prices, but if they ask us to come up with our own figure, let’s assume the average price is \$200. This results in a total market size of \$30M USD. Case closed (?).

BUT WAIT — we’re still not finished.

Just because you’ve reached the final number doesn’t mean you’re finally done with the question. A number is only as valuable as its implication; in other words, so what?

So what the market size is \$30M USD? What does this mean for our client? Why should they care? Why does this matter?

Is this a big market, or a small market? Is it attractive, or this number smaller than we expected? This is where asking for key data up-front at the beginning of the case is key — you should be asking how big your client’s current revenues are, which markets it currently operates in, and the sizes of said markets.

For instance, if the New York market is worth \$30M USD and the client currently operates in, say, Connecticut and Delaware (which separately are \$2.5M, for \$5M total), then entering New York is quite attractive. It’s also helpful to know what the competition is like in the new market — if New York is highly competitive, then the client won’t be able to reap the full benefits of the \$30M market size. If there are little to no competitors, however, then entering New York is incredibly attractive.

In order to determine if your market size is good or not, you have to be able to draw comparisons — without benchmarking your data with other data points (especially from your client’s historical records as well as their that of their competitors’), you won’t be able to impact the numbers you’ve found while market sizing.

Some people also suggest you conduct a “sanity check” — in other words, is your number too high or too low? You can offer some reasons to suggest either how your estimate is likely higher than the actual number, lower, or just about right. Don’t cover all these scenarios. Just cover one, and provide your rationale. Perhaps one of your assumptions in the ratio/frequency/quantity/etc. portion of your analysis was overly generous. Or perhaps you under-estimated the number of youth golfers.

My final note for this section is on price — in this hypothetical scenario, we assumed that all golf clubs share an average price. Some golfers might purchase premium golf clubs, however, while others may purchase cheaper, “value-based” versions. Others may just go for the discount (re: cheapest) option. To provide additional complexity and rigor in your analysis, you can segment the golfer population by price type and then make the calculations accordingly — this makes you look stronger, as you’re looking two steps ahead of most candidates, and your final answer is likely more reflective of the actual estimate than it otherwise could have been.

My personal advice is to add complexity if and only if you are comfortable with it: if you introduce more complex calculations and you quickly get lost in a sauce of your own making, you’ve just screwed yourself out of the next round. That being said, if your analysis is overly simple, even if you aced your calculations you won’t come off as more impressive. You can risk it for the biscuit, as they say, but I personally suggest avoiding needless risk. That being said, I always segment baselines by price, and you should too — practice more and more, and you’ll soon find yourself handling more difficult calculations and market sizing questions in no time.

### Bottom-Up Market Sizing

Another market sizing technique is called “Bottom-Up.” When you take the bottom-up approach, you isolate a single geography, store, unit, consumption pattern, or other micro-element of a larger population – then push the numbers up to a larger scale.

One reason to use the bottom-up method over the top-down method is if you’re asked to measure the physical distribution of a product. For instance, in order to answer the question “How many pay-phones are there in Beijing,” it would be easier for you to estimate how many pay-phones there are in a city block, then multiply by the number of blocks in the whole city. If you used a top-down approach, you’d instead have to identify how many people live in London, how often they use pay-phones, how frequently pay-phones are used daily, etc. You can see how this is pretty cumbersome.

Another tell-tale sign you should go bottom-up over top-down is if you’re measuring consumption (re: where you look at the number or amount of something “consumed” per day and then annualize it). For instance, in order to find out how many bags are lost in a year at SFO, or how much is spent on Starbucks in China, you should estimate the number of ‘occurrences daily’ (re: bags lost per day, customers served per day, etc.), and then multiply by the number of days the business is open. You may still need to factor value (re: average spend per Starbucks order), but that’s pretty easy to do.

The bottom-up approach doesn’t make much sense for the golf club question — try thinking about how you would estimate the market size for golf clubs in New York (or alternatively, just give up right now, I don’t blame you LOL).

Again, you should employ the bottom-up approach if you’re dealing with distribution and/or consumption. The top-down approach can be applied in any situation, but sometimes it’s more effective to go bottom-up (and vice versa).

Using the “How much is spent on Starbucks in China every year” question as an example, let’s start with customer/product types. Starbucks sells a number of ‘products’, from coffee/tea/drinks to snacks/pastries and even merchandise like mugs, french presses, and sunglasses. For simplicity’s sake, let’s just focus on liquid consumables (drinks) and solid consumables (pastries, sandwiches, etc.).

Now onto ‘frequency’ — how many purchases of drinks are made in an hour? How many purchases of food items are made in an hour? Let’s assume that, on average, a barista can serve 2 drinks and 1 food item every 5 minutes. This translates to 40 drinks and 20 food items every hour. Obviously, however, a barista is not constantly working — there will be periods of time where there are no customers, or at least are not serving a constant flow of customers. Let’s thus assume that, on average, a barista is only actively serving drinks/food ~75% of the time. This means that 30 drinks and 15 food items are served every hour. At this point, you should keep in mind that this is data for a single given Starbucks store — there are thousands of Starbucks in China alone, and to calculate the number of Starbucks in China would require yet another large, framework-inducing market sizing approach. Yay!

Now onto ‘price’ — obviously there are different prices for different items. If we want to be basic, we can just assume an average drink price of \$4 USD and average food item price of \$8 USD (I’m using USD even though we’re valuing the Chinese Starbucks market because it’s a currency I am more familiar with, and we can just offer to convert to RMB later if the interviewer wants us to). Note that prices in China for Starbucks are different from America, as Starbucks is seen more as a luxury good in the former than the latter. Let’s assume that drinks’ prices are split between \$2 for a small (short), \$3 for medium (tall), \$4 for a large (grande), and \$5 for an extra large (venti). A majority of customers go for the grande — let’s assume 70% do. The rest are evenly split. This means the average drink price is \$3.80 (e.g. \$2.80+\$.20+\$.30+\$.50 = \$3.80 USD). Meanwhile, let’s assume that food items prices are split between \$3 for a small pastry, \$5 for a regular pastry, and \$8 for a sandwich. 20% of customers go for a small pastry, another 20% for regular pastries, and the remaining 60% for sandwiches. This translates to an average food item price of \$6.40 (e.g. \$.60+\$1+\$4.80=\$6.40 USD).

Let’s not add prices quite yet — for now, let’s move onto ‘operation times’. If we assume Starbucks China operates 12 hours a day 7 days a week, and we assume there are 50 weeks/year (which we will assume for two reasons: first, because 50 is nicer to work with than 52, and second, because we want to account for holidays and potential sick leaves so we can afford to discount 14 days)… then Starbucks China operates 4200 hours every year (e.g. 12 * 7 * 50 = 84*50 = 4200 hours/year). Keep in mind this is for a single Starbucks — at this point, you might be gearing up for yet another market sizing odyssey, but your interviewer will likely stop you. You’ve already demonstrated your quantitative problem-solving skills and market sizing chops. They’ll likely just ask you to calculate a single Starbucks China store’s revenues, to which you’ll say:

Given a single store operates for 4200 hours/year, and 30 drinks and 15 food items are served per hour, this means 126,000 drinks and 63,000 food items (the average of 4200*10 and 4200*20, so you don’t have to multiply 4200 by 15) are served every year. With an average drink price of \$3.80 and food item price of \$6.40, we multiply the corresponding numbers to achieve our answer. Since \$3.80 and \$6.40 aren’t pretty numbers, let’s round them to \$4 and \$6. It’s not perfect, with a 20 cent net difference, so we should keep in mind that our final answer is going to be a slight under-estimate. With that said, drink spend is \$504,000 and food spend is \$378,000. Combined, total Starbucks spend in China for a single store is \$882,000 USD.

The interviewer may then tell you there are approximately 4,000 Starbucks in China. This means total spend, as you quickly do the math, is \$3,528M, or \$3.528B USD.

Sanity check time — is this number too high or too low, or just right? I personally believe this is an under-estimate — remember the 20 cent net difference in our price assumptions. Also remember that while our formula accounts for food and drinks, another bucket I previously talked about was Starbucks merchandise (re: mugs, sunglasses, etc.). We also highly simplified the Starbucks menu — perhaps there are China-only premium specialties that would have raised average customer orders, and therefore would have raised total customer spend in China.

“So What” check time — we need to know how Starbuck China stacks up to Starbucks America and any other comparable regions. If smaller than the United States, then there is opportunity for growth — Starbucks has only 4k stores in China, and we can assume it has many more in the United States (in fact, there are ~15,000 in the U.S.).