Ode to Weighted Averages

Several years ago, in the essay Average is the Enemy, I wrote about the “false shortcuts offered by averages” for making decisions. Averages give a sense for where the middle lies within a group. They offer a starting point for understanding a situation but, like stereotypes, are incomplete and can mislead. 

Mathematically, averages specify the arithmetic mean. Calculating an average represents one of many approaches for profiling data when conducting analysis. In fact, averages themselves come in different forms. When conducting forest industry research, my team at Forisk often uses rolling and weighted averages to address different issues and better leverage underlying data. 

Rolling Averages

A rolling, or “moving,” average provides a way to measure trends over time. This can be useful when studying the status of a situation from daily, weekly, or monthly data, such as housing starts, health trends, and the economics of different businesses. For example, in the forest industry, the COVID-19 pandemic initiated two years of extreme volatility with softwood lumber prices. Indexed monthly prices increased 71% in mid-2020 before resetting and spiking to an all-time high in mid-2021 and resetting and cycling steeply again in 2022 before, relatively speaking, stabilizing.

When evaluating product margins over time, we want to avoid over-exposure to outliers or random spot prices, such as when lumber exceeded $1,500 per thousand board feet (MBF) in mid-2021. A rolling average cuts a path through the cycle to “smooth out” reported prices while still including the most recent data. In this way, we might apply the last three, six or twelve-month average lumber price to fairly assess the break-even and potential profitability of a business or sector.

Overall, a rolling average provides a practical way to readily communicate insights from simple data series. The Economist calls them, “Among the unsung heroes of statistical methods…” I agree.

Weighted Averages

A weighted average accounts for the relative importance of certain aspects of the data. This differs from a simple average, which treats all observations in a data set equally. In this way, and depending on the question asked, a weighted average can improve our use of available data.

Consider another forest industry example. In 2022 in the U.S. South, the four-quarter rolling average price of pine sawtimber, the logs bought by sawmills to produce the softwood lumber used for homebuilding, was $27.79 per ton according to data from TimberMart-South. This number is a simple average of 11 state-level prices, from Texas to Virginia and down to Florida. However, when we weight those prices by log use (volume) by state, we get $28.59 per ton. 

The difference reflects how higher volume states with more sawmills and higher lumber production levels reported higher log prices and vice versa. For example, Georgia, with a 2022 average price of $33.43, consumed around 13 million tons of pine sawtimber in 2022, while Virginia reported a price of $21.17 while using around 3 million tons of sawtimber over the same period. 

We can also combine approaches to calculate a rolling weighted average. This will better reflect the state of the sawtimber market and the value of wood delivered regionally over time.


Systematic exploration of a situation benefits greatly from the proper, context-appropriate application of available tools and methods. The calculation of an average is, of itself, an agnostic act. However, its ability to clarify depends on the underlying data and question being asked. Rolling and weighted averages, and their combination, offer ways to improve our understanding of a given situation.

Learn from Others and Tie Your Camel

After watching then New England Patriot quarterback Tom Brady at practice, former Indiana basketball coach Tom Crean, in a 2018 Sports Illustrated article, observed: 

“Everything Brady does, he does with purpose… bag drills, footwork drills, the dropping back, throwing to one receiver …the great ones… don’t waste any reps…the great ones never think they’re beyond improvement…”

The story reminds us how leaders, whether formally appointed executives and team captains or informal mentors, set the tone and example for any group. In this post, I revisit lessons that continue to help me and my team improve and make better decisions.

We Learn by Watching Others

We learn what is acceptable and okay based on what our leaders and role models do [see “We All Lead by Example”]. This applies both to productive habits and less desirable ones. For example, while I learned much about leadership and integrity from my Dad, I also picked up choice four-letter words when listening to him on the phone in the other room when I was a kid. (I fear my daughters learned the same words from me the same way…)

People always watch and learn from others. Kids watch parents. Players watch coaches. Students watch teachers. Citizens watch their elected leaders. The actions and behaviors of others serve as models and permissions. If the goal is to become a better leader, manager, and person, then embrace the idea that, first, we can learn by watching others – especially “the best” – go about their work and, second, that we serve and lead as examples for others, as well.

Trust in Allah but Tie Your Camel

How do you decide on who to trust? By comparing a person’s words to their actions. Does the person do what they say they’re going to do when they say they’re going to do it? Do they answer questions simply and directly? Long rambling answers and failures to follow-through increase doubt and decrease trust. 

Years ago, partners at another consulting firm expressed interest on three separate occasions to explore a potential joint venture with Forisk and promised to follow up for a demo and details. They never did. To this day, I view those individuals and their work as unreliable. 

A manager or business owner cannot put up with the warm smelly mess of excuses, missed deadlines, bashful apologies, and inconsiderate tardiness that leave tracks through the office and get carried home. If someone fails to do their job or what they say they are going to do, you have a right and obligation to communicate and reinforce the expectation, to make a change if required, and to move on. 


If you think in terms of absolutes relative to your values and priorities, then decisions related to hiring and firing and improvement are easier [see Notes on Managing a Business]. Stop rationalizing. Say no to choices, offers, and performance counter to your values and goals. Don’t wait for the manure to hit the fan. Determine what is important, before the divorce, heart attack, kid failing a class, or upset client. Look at how the best perform. Then move forward, do your best, and have some fun.

Clean Over Current

As leaders, parents, investors, and coaches, we often make decisions with imperfect and incomplete information. Therefore, we benefit by having an approach or philosophy for dealing with uncertainty. When screening and evaluating analysis, I start by confirming that what we have in hand is clean and accurate. Building a history of clean, error-free, detail-oriented work builds trust and puts you in a better position to influence decisions and lead the room.

Errors Inject Doubt

For strategic questions and market projections, I prefer clean data and analysis over rushed, subjective intel. Ideally, we have both, but if given the choice, I want things clean, with an “as of” date, over speculation on today’s unconfirmed events. It’s how we report things at Forisk, since we, like many market analysts, rely on government data and other sources that often lag actuals by weeks, months, or quarters, and this data often gets revised in future months. 

If the report I have has multiple errors, then I doubt everything it contains. If it’s clean but a little behind, we can still make decisions and assess performance. We can also evaluate the likelihood and implications of the most recent market intel when it comes in. Without a clean, verified understanding of historical events, we are poorly positioned to evaluate new theses or announcements. However, with a clean dataset and framework, we can develop intuition and scenarios on how changes affect the market and our clients.

Understand How Things Work on the Ground

When conducting forest industry analysis, teams I work with are mindful of the fact that “operations come first” to truly understanding how things function on the ground. If our analysis and understanding is inconsistent with what mill managers or procurement foresters see, then we have something to reconcile. In our role, we add value by connecting information across markets and over time, which prioritizes clean analysis to make our work credible for clients who need to make decisions. 

If we hear a piece of market intel that could change our thinking, we call local contacts working in the field and ask, “is this true? How could this affect you?” As with many things, news is often a rumor, and the impact is regularly overstated. 


There are situations and occupations where the most recent intel has more value, such as on the battlefield, in the operating room, or at the trading desk. However, for strategic questions and projections, and given the choice, I’ll take clean over current.

Errors are Opportunities*

My baseball coach at MIT, Fran O’Brien, reminded us that we will all make errors. The ball will go between our legs. A pop fly will get lost in the sun and fall safely to the ground. But he did not tolerate mental errors. If you missed a sign or failed to hustle, you received a stern look and quick reprimand, and, at times, a hard seat on the bench.

Coach O’Brien’s message of personal responsibility still resonates powerfully with me when working with customers and clients. Sometimes we make mistakes. However, our success depends more on how we handle these errors and complaints then on the errors themselves. In a way, errors and slights, even if imagined or perceived, are gifts. They provide opportunities to build trust and exceed expectations. 

Years ago, I had my oil changed by a local firm in Athens, Georgia. At the end, the young technician reviewed the list of completed services, which included checking and correcting the tire pressure. I had been nearby throughout and had not seen them check the tires, so I asked to confirm if they had done this. No, they had not. It was checked on the list, but they had not actually completed this task.  

They backed my car into the service bay once again and checked the tire pressure. It was low. However, the air compressor on site did not work. I asked if they had another compressor near-by. The technician said no. I asked if he had a suggestion as to where I could fill my tires. He said, “no, but if you just drive down the road here for a while, I’m sure you will find another tire and oil change place that could do it for you.”  

So that is what I did—never to return.

I pulled into a place on Broad Street called University Car Wash. A young guy came up to my window with a clipboard. I said, “I don’t need a car wash or oil change, but may I check and adjust my tire pressure?”  

He said, “Sure” and directed me over to the service bays. He checked and adjusted each tire himself. At the end, he said, “Thank you for stopping in. Just so you know, we are having an oil change and car wash special for the rest of the summer. Next time you need an oil change, please consider us.”

This young man earned my trust, and his firm earned my business for years (until they closed 🙁 ).  I wrote his manager a note to relate this story and commend his employee.

I wrote another note, this one to the owner of the first business, to share with him my experience with his firm. Compressors break. Mistakes happen. But his firm lost my trust by misleading me, and it lost my business by failing to help me solve a simple, practical problem.

What could have happened differently? Any of several responses could have kept me loyal to that firm.

  • “I am so sorry about this. Let me help you find a service station near-by with a working compressor.”
  • “I am sorry. Perhaps my colleague or manager can help us with this.”
  • “Sir, please accept my apologies. No excuses. And please let us pay for this oil change.”

At the end of the day, customers and clients will cut you slack if you are responsive and respectful.  Customers will continue to work with you if you apologize and demonstrate awareness, humility, and ownership. Ultimately, customers can become ambassadors for your business if you help them solve their problems, even if they relate to mistakes made by your firm.

*Part of this post appeared in an “At the Office” column I published in the Athens Banner Herald in 2008.

Four Ways to Strengthen Non-Fiction Writing

This post introduces an essay on improving the clarity and power of blogs, essays, and articles. 

My go-to resources for writing advice include books such as The Elements of Style by Strunk and White and On Writing by Steven King. (My two-phrase summary of The Elements of Style would be “Omit needless words; let every word tell!”)

In this 700-word essay, I summarize years of reading, writing, revising, and editing into four guidelines intended to help you strengthen the sharing of your ideas and analysis, through the written word, with others. The ultimate aim is to dispense with the garnish and deliver the meat. Clear writing communicates clarified thinking. 

Click here to read the essay.