The “Flaw of Averages” Causes Havoc for Businesses

The “Flaw of Averages” Causes Havoc for Businesses

Right out of the gate, I will admit I stole the “Flaw of Averages” from Sam Savage, whose book by that name I cannot recommend highly enough if you find this topic of interest.

What is my issue with averages? They misstate what is happening in the business and cause misallocation of resources. Let’s take a hypothetical business, ABC Inc., with the following products, units sold, unit price, and gross profit per unit. Now while this examines Products, we could easily substitute Services.


Units Sold


Gross Profit/Unit



 $          100.00

 $       12.50



 $            90.00

 $       75.00



 $            80.00

 $       37.50



 $            70.00

 $       45.00



 $            60.00

 $       25.00



 $            50.00

 $       12.50



 $            40.00

 $       20.00



 $            30.00

 $       25.00

I am sure that everyone can see that ABC’s revenue is $9,575,000 and its gross profit is $3,825,000, giving it a gross margin of 39.9%. Let’s assume that this gross margin is in line with the industry to not get into the cost of goods sold issues.

If we look at products in terms of revenue and sort from largest to smallest, we get the following.

Product A is the largest seller accounting for about 40% of sales. While products B, G, H, and F together account for 35% of sales, obviously less than A. So, how should we consider this product portfolio?

Examining the product portfolio, we see that A accounts for only about 10% of gross profits. Products B, G, H, and F together account for 46% of gross profits, so they are far more critical to ABC’s profitability. Furthermore, products C, D, B, H, and G are more important than the revenue chart above would indicate. While they account for about 50% of revenue, they generate 75% of gross profit and have a gross profit margin of 61%.

If ABC were to stop selling product A, its revenue and gross profit would fall by $3MM and $300k, respectively, and its gross profit margin would increase from 40% to 52%. Increasing gross profit margin by over 10% would be fantastic! Furthermore, given product A’s high cost of goods sold, we can assume that it is consuming a large amount of raw materials and labor–in other words, working capital. If ABC were to stop selling A, its working capital situation would improve, thus improving its liquidity ratios.

Also, this simplistic assumption doesn’t provide details, but there are possibly additional costs that I have not included from the production of A, namely:

  • Factory space to produce A
  • Warehouse space to store the raw materials for A and completed inventory.
  • Staff to track orders and purchases related A
  • Shipping costs of A
  • Staff overseeing the production of A

If ABC were to stop producing A, it’s Selling, General, and Administrative Expenses could fall further, boosting profitability. Thus, by looking at average margins, we don’t see Product A’s full impact on the business. Now I realize that A might be essential to getting the other products’ sales, but undoubtedly, we can increase the price of A or put together a bundle for more effective pricing.

Many years ago, when I was working at Holiday Inn, now IHG, the company was delighted with Holiday Inn Express’s launch. Holiday Inn Express franchises were selling like proverbial “hotcakes,” compared to the sale of old Holiday Inn franchises (“Green Sign” as we referred to them then). The increase in franchises was boosting distribution dramatically. However, if we look further into this and add some data (the numbers below are indicative, not actuals, to show the effect), we see it is not as straightforward.


Holiday Inn

Holiday Inn Express

Avg No of Rooms



Average RevPAR*



Franchise Fee



Expected Hotel Revenue ($ 000’s)



Expected Franchise Income ($ 000’s)



Franchise Support Costs ($000’s)



Estimated Profit ($000’s)



RevPAR = Revenue per Available Room = Revenue / Rooms

So, while Express hotels were selling faster, IHG needed to sell two Express hotels for each Green Sign. Also, most Express hotels buyers were independent operators who had not owned franchised hotels before if they had even held a hotel. Owners of Green Sign hotels were typically experienced hotel owners who often owned multiple properties. Due to the clients’ difference, further analysis showed that each Express owner required 2.5x the Holiday Inns’ franchise service support. Thus, while Expresses were selling like hotcakes, the profitability was far lower, and it is easy to see how the adage, “We lose money on every sale but will make it up in volume,” happens.

If we add customers to the mix makes it gets more interesting. Let’s assume ABC has the following customers, who purchase the following amounts of product.

Now, if we examine the purchase and gross profits of each customer, we get:



Gross Profit




























Sorting that into the order of gross margin, we can see the following:

,Now we can see that S is our most profitable customer by a large margin, and the gross margin from its purchases is above ABC’s average. Hopefully, every company has done this analysis and know that they all want customers like S.

However, if we look across the rest of the clients, X, while not generating a lot of profit, does so at a very high margin. Y generates slightly less profit but at a margin below 20%. So, ABC wants more customers like X and fewer like Y. Also, given that our average gross margin was 40%, nearly all customers except Y, W & U are buying combinations to generate gross margins above 40%.

Therefore, this analysis shows that while ABC’s gross margin is nearly 40% and its gross profit is $3.8MM, if it were to lose customer S, sales and gross profits would fall to $7,675,110 and $3,333,828 respectively, providing a gross margin of 38.5%. However, if ABC were to lose client U, sales and gross profits would fall to $7,976,570 and $3,410,400, respectively, while gross margin would increase to 42.8%. Increasing gross margin by even 300 basis points would be significant for many companies.

As with products, we don’t see which clients to seek or replace by looking at the average gross margin. If ABC were to extend the analysis to clients that were done product A by looking at the time taken to service each client, it might find more that are not worth having.

(An old client of mine had a business doing about $4MM in revenue and generating $200k in EBITDA. His original client, say XYZ, was his largest, accounting for 40% of his sales, and it was time for the contract renewal. As we looked at it, we noticed that XYZ was like Product A, generating meager gross profit. We then analyzed what would be the impact on the business if he were to lose XYZ. My client realized he could cut his workforce by 50%, reduce his vehicle fleet by 55%, and cut energy consumption and floor space. As a result, he held firm on his proposed price increase with XYZ during the contract renewal, and XYZ refused to renew the contract. So, he cut the expenses we had identified, and the following year, his revenue fell to about $2.4MM, but his EBITDA increased to $450k.)

Finally, for company ABC, when we determine that we want to make a gross profit of “X%”, focusing on each product to ensure it meets that criteria will help. By focusing on each customer to ensure that their purchases don’t drive gross profits down, we can raise ABC’s profitability.

I hope you do this work for all your products/services and clients regularly and focus on those that improve margin and profitability. Using data properly can really help your business.

As I mentioned above, if you are interested in this area, I would recommend the following books The Flaw of Averages: Why We Underestimate Risk in the Face of Uncertainty, by Sam Savage and Why Can’t You Just Give Me The Number?: An Executive’s Guide to Using Probabilistic Thinking to Manage Risk and to Make Better Decisions, by Patrick Leach.


Copyright (c) 2021, Marc A. Borrelli

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