Never design a product without explicit metrics and tracking tools.

Imagine driving cross-country without a dashboard. How do you know your school zone speed? Low gas? Without a dashboard, you can't monitor your car. You can't improve what you don't measure, as Peter Drucker said. Product managers must constantly enhance their understanding of their users, how they use their product, and how to improve it for optimum value. Customers will only pay if they consistently acquire value from your product.

I’m Solomon Ayanlakin. I’m a product manager at CredPal, a financial business that offers credit cards and Buy Now Pay Later services. Before falling into product management (like most PMs lol), I self-trained as a data analyst, using Alex the Analyst's YouTube playlists and DannyMas' virtual data internship. This article aims to help product managers, owners, and CXOs understand product metrics, give a methodology for creating them, and execute product experiments to enhance them.

☝🏽Introduction

Product metrics assist companies track product performance from the user's perspective. Metrics help firms decide what to construct (feature priority), how to build it, and the outcome's success or failure. To give the best value to new and existing users, track product metrics.

Why should a product manager monitor metrics?

• to assist your users in having a "aha" moment

• To inform you of which features are frequently used by users and which are not

• To assess the effectiveness of a product feature

• To aid in enhancing client onboarding and retention

• To assist you in identifying areas throughout the user journey where customers are satisfied or dissatisfied

• to determine the percentage of returning users and determine the reasons for their return

📈 What Metrics Ought a Product Manager to Monitor?

What indicators should a product manager watch to monitor product health? The metrics to follow change based on the industry, business stage (early, growth, late), consumer needs, and company goals. A startup should focus more on conversion, activation, and active user engagement than revenue growth and retention. The company hasn't found product-market fit or discovered what features drive customer value.

Depending on your use case, company goals, or business stage, here are some important product metric buckets:

All measurements shouldn't be used simultaneously. It depends on your business goals and what value means for your users, then selecting what metrics to track to see if they get it.

Some KPIs are more beneficial to track, independent of industry or customer type. To prevent recording vanity metrics, product managers must clearly specify the types of metrics they should track. Here's how to segment metrics:

1. The North Star Metric, also known as the Focus Metric, is the indicator and aid in keeping track of the top value you provide to users.

2. Primary/Level 1 Metrics: These metrics should either add to the north star metric or be used to determine whether it is moving in the appropriate direction. They are metrics that support the north star metric.

3. These measures serve as leading indications for your north star and Level 2 metrics. You ought to have been aware of certain problems with your L2 measurements prior to the North star metric modifications.

North Star Metric

This is the key metric. A good north star metric measures customer value. It emphasizes your product's longevity. Many organizations fail to grow because they confuse north star measures with other indicators. A good focus metric should touch all company teams and be tracked forever. If a company gives its customers outstanding value, growth and success are inevitable. How do we measure this value?

A north star metric has these benefits:

• Customer Obsession: It promotes a culture of customer value throughout the entire organization.

• Consensus: Everyone can quickly understand where the business is at and can promptly make improvements, according to consensus.

• Growth: It provides a tool to measure the company's long-term success. Do you think your company will last for a long time?

How can I pick a reliable North Star Metric?

Some fear a single metric. Ensure product leaders can objectively determine a north star metric. Your company's focus metric should meet certain conditions. Here are a few:

1. A good focus metric should reflect value and, as such, should be closely related to the point at which customers obtain the desired value from your product. For instance, the quick delivery to your home is a value proposition of UberEats. The value received from a delivery would be a suitable focal metric to use. While counting orders is alluring, the quantity of successfully completed positive review orders would make a superior north star statistic. This is due to the fact that a client who placed an order but received a defective or erratic delivery is not benefiting from Uber Eats. By tracking core value gain, which is the number of purchases that resulted in satisfied customers, we are able to track not only the total number of orders placed during a specific time period but also the core value proposition.
   

2. Focus metrics need to be quantifiable; they shouldn't only be feelings or states; they need to be actionable. A smart place to start is by counting how many times an activity has been completed.
   

3. A great focus metric is one that can be measured within predetermined time limits; otherwise, you are not measuring at all. The company can improve that measure more quickly by having time-bound focus metrics. Measuring and accounting for progress over set time periods is the only method to determine whether or not you are moving in the right path. You can then evaluate your metrics for today and yesterday. It's generally not a good idea to use a year as a time frame. Ideally, depending on the nature of your organization and the measure you are focusing on, you want to take into account on a daily, weekly, or monthly basis.
   

4. Everyone in the firm has the potential to affect it: A short glance at the well-known AAARRR funnel, also known as the Pirate Metrics, reveals that various teams inside the organization have an impact on the funnel. Ideally, the NSM should be impacted if changes are made to one portion of the funnel. Consider how the growth team in your firm is enhancing customer retention. This would have a good effect on the north star indicator because at this stage, a repeat client is probably being satisfied on a regular basis. Additionally, if the opposite were true and a client churned, it would have a negative effect on the focus metric.
   

5. It ought to be connected to the business's long-term success: The direction of sustainability would be indicated by a good north star metric. A company's lifeblood is product demand and revenue, so it's critical that your NSM points in the direction of sustainability. If UberEats can effectively increase the monthly total of happy client orders, it will remain in operation indefinitely.

Many product teams make the mistake of focusing on revenue. When the bottom line is emphasized, a company's goal moves from giving value to extracting money from customers. A happy consumer will stay and pay for your service. Customer lifetime value always exceeds initial daily, monthly, or weekly revenue.

Great North Star Metrics Examples

🥇 Basic/L1 Metrics:

The NSM is broad and focuses on providing value for users, while the primary metric is product/feature focused and utilized to drive the focus metric or signal its health. The primary statistic is team-specific, whereas the north star metric is company-wide. For UberEats' NSM, the marketing team may measure the amount of quality food vendors who sign up using email marketing. With quality vendors, more orders will be satisfied. Shorter feedback loops and unambiguous team assignments make L1 metrics more actionable and significant in the immediate term.

🥈 Supporting L2 metrics:

These are supporting metrics to the L1 and focus metrics. Location, demographics, or features are examples of L1 metrics. UberEats' supporting metrics might be the number of sales emails sent to food vendors, the number of opens, and the click-through rate. Secondary metrics are low-level and evident, and they relate into primary and north star measurements. UberEats needs a high email open rate to attract high-quality food vendors. L2 is a leading sign for L1.

Where can I find product metrics?

How can I measure in-app usage and activity now that I know what metrics to track? Enter product analytics. Product analytics tools evaluate and improve product management parameters that indicate a product's health from a user's perspective.

Various analytics tools on the market supply product insight. From page views and user flows through A/B testing, in-app walkthroughs, and surveys. Depending on your use case and necessity, you may combine tools to see how users engage with your product. Gainsight, MixPanel, Amplitude, Google Analytics, FullStory, Heap, and Pendo are product tools.

This article isn't sponsored and doesn't market product analytics tools. When choosing an analytics tool, consider the following:

• Tools for tracking your Focus, L1, and L2 measurements

• Pricing

• Adaptations to include external data sources and other products

• Usability and the interface

• Scalability

• Security

An investment in the appropriate tool pays off. To choose the correct metrics to track, you must first understand your business need and what value means to your users. Metrics and analytics are crucial for any tech product's growth. It shows how your business is doing and how to best serve users.

Managers spend much time in 1:1s. Most team members meet with supervisors regularly. 1:1s can help create relationships and tackle tough topics. Few appreciate the 1:1 format's potential. Most of the time, that potential is spent on small talk, surface-level updates, and ranting (Ugh, the marketing team isn’t stepping up the way I want them to).

What if you used that time to have deeper conversations and important insights? What if change was easy?

This post introduces a new 1:1 format to help you dive deeper, faster, and develop genuine relationships without losing impact.

A 1:1 is a chat, you would assume. Why use structure to talk to a coworker? Go! I know how to talk to people. I can write. I've always written. Also, This article was edited by Zoe.

Before you discard something, ask yourself if there's a good reason not to try anything new. Is the 1:1 only a talk, or do you want extra benefits? Try the steps below to discover more.

I. Reflection (5 minutes)

Context-free, broad comments waste time and are useless. Instead, give team members 5 minutes to write these 3 prompts.

1. What's effective?

2. What is decent but could be improved?

3. What is broken or missing?

Why these? They encourage people to be honest about all their experiences. Answering these questions helps people realize something isn't working. These prompts let people consider what's working.

Why take notes? Because you get more in less time. Will you feel awkward sitting quietly while your coworker writes? Probably. Persevere. Multi-task. Take a break from your afternoon meeting marathon. Any awkwardness will pay off.

What happens? After a few minutes of light conversation, create a template like the one given here and have team members fill in their replies. You can pre-share the template (with the caveat that this isn’t meant to take much prep time). Do this with your coworker: Answer the prompts. Everyone can benefit from pondering and obtaining guidance.

This step's output.

Part II: Talk (10-20 minutes)

Most individuals can explain what they see but not what's behind an answer. You don't like a meeting. Why not? Marketing partnership is difficult. What makes working with them difficult? I don't recommend slandering coworkers. Consider how your meetings, decisions, and priorities make work harder. The excellent stuff too. You want to know what's humming so you can reproduce the magic.

First, recognize some facts.

• Real power dynamics exist. To encourage individuals to be honest, you must provide a safe environment and extend clear invites. Even then, it may take a few 1:1s for someone to feel secure enough to go there in person. It is part of your responsibility to admit that it is normal.

• Curiosity and self-disclosure are crucial. Most leaders have received training to present themselves as the authorities. However, you will both benefit more from the dialogue if you can be open and honest about your personal experience, ask questions out of real curiosity, and acknowledge the pertinent sacrifices you're making as a leader.

• Honesty without bias is difficult and important. Due to concern for the feelings of others, people frequently hold back. Or if they do point anything out, they do so in a critical manner. The key is to be open and unapologetic about what you observe while not presuming that your viewpoint is correct and that of the other person is incorrect.

Let's go into some prompts (based on genuine conversations):

• “What do you notice across your answers?”

• “What about the way you/we/they do X, Y, or Z is working well?”

• “ Will you say more about item X in ‘What’s not working?’”

• “I’m surprised there isn’t anything about Z. Why is that?”

• “All of us tend to play some role in maintaining certain patterns. How might you/we be playing a role in this pattern persisting?”

• “How might the way we meet, make decisions, or collaborate play a role in what’s currently happening?”

Consider the preceding example. What about the Monday meeting isn't working? Why? or What about the way we work with marketing makes collaboration harder? Remember to share your honest observations!

Third section: observe patterns (10-15 minutes)

Leaders desire to empower their people but don't know how. We also have many preconceptions about what empowerment means to us and how it works. The next phase in this 1:1 format will assist you and your team member comprehend team power and empowerment. This understanding can help you support and shift your team member's behavior, especially where you disagree.

How to? After discussing the stated responses, ask each team member what they can control, influence, and not control. Mark their replies. You can do the same, adding colors where you disagree.

This step's output.

Next, consider the color constellation. Discuss these questions:

• Is one color much more prevalent than the other? Why, if so?

• Are the colors for the "what's working," "what's fine," and "what's not working" categories clearly distinct? Why, if so?

• Do you have any disagreements? If yes, specifically where does your viewpoint differ? What activities do you object to? (Remember, there is no right or wrong in this. Give explicit details and ask questions with curiosity.)

Example: Based on the colors, you can ask, Is the marketing meeting's quality beyond your control? Were our marketing partners consulted? Are there any parts of team decisions we can control? We can't control people, but have we explored another decision-making method? How can we collaborate and generate governance-related information to reduce work, even if the requirement for prep can't be eliminated?

Consider the top one or two topics for this conversation. No 1:1 can cover everything, and that's OK. Focus on the present.

Part IV: Determine the next step (5 minutes)

Last, examine what this conversation means for you and your team member. It's easy to think we know the next moves when we don't.

Like what? You and your teammate answer these questions.

1. What does this signify moving ahead for me? What can I do to change this? Make requests, for instance, and see how people respond before thinking they won't be responsive.

2. What demands do I have on other people or my partners? What should I do first? E.g. Make a suggestion to marketing that we hold a monthly retrospective so we can address problems and exchange input more frequently. Include it on the meeting's agenda for next Monday.

Close the 1:1 by sharing what you noticed about the chat. Observations? Learn anything?

Yourself, you, and the 1:1

As a leader, you either reinforce or disrupt habits. Try this template if you desire greater ownership, empowerment, or creativity. Consider how you affect surrounding dynamics. How can you expect others to try something new in high-stakes scenarios, like meetings with cross-functional partners or senior stakeholders, if you won't? How can you expect deep thought and relationship if you don't encourage it in 1:1s? What pattern could this new format disrupt or reinforce?

Fight reluctance. First attempts won't be ideal, and that's OK. You'll only learn by trying.

10-sketch explanation

Choosing Tasks

Bringing News

carrying out 1:1s

providing critique

Managing Turbulence

900K impressions, 8K clicks, and $$$ orders…

I recently started dropshipping. Now that I own my business and can charge it as a business expense, it feels less like money wasted if it doesn't work. I also made t-shirts to sell. I intended to open a t-shirt store and had many designs on a hard drive. I read that Tiktok advertising had a high conversion rate and low cost because they were new. According to many, the advertising' cost/efficiency ratio would plummet and become as bad as Google or Facebook Ads. Now felt like the moment to try Tiktok marketing and dropshipping. I work in marketing for a SaaS firm and have seen how poorly ads perform. I wanted to try it alone.

I set up $250 and ran advertising for a week. Before that, I made my own products, store, and marketing. In this post, I'll show you my process and results.

Setting up the store

Dropshipping is a sort of retail business in which the manufacturer ships the product directly to the client through an online platform maintained by a seller. The seller takes orders but has no stock. The manufacturer handles all orders. This no-stock concept increases profitability and flexibility.

In my situation, I used previous t-shirt designs to make my own product. I didn't want to handle order fulfillment logistics, so I looked for a way to print my designs on demand, ship them, and handle order tracking/returns automatically. So I found Printful.

I needed to connect my backend and supplier to a storefront so visitors could buy. 99% of dropshippers use Shopify, but I didn't want to master the difficult application. I wanted a one-day project. I'd previously worked with Big Cartel, so I chose them.

Big Cartel doesn't collect commissions on sales, simply a monthly flat price ($9.99 to $19.99 depending on your plan).

After opening a Big Cartel account, I uploaded 21 designs and product shots, then synced each product with Printful.

Developing the ads

I mocked up my designs on cool people photographs from placeit.net, a great tool for creating product visuals when you don't have a studio, camera gear, or models to wear your t-shirts.

I opened an account on the website and had advertising visuals within 2 hours.

Because my designs are simple (black design on white t-shirt), I chose happy, stylish people on plain-colored backdrops. After that, I had to develop an animated slideshow.

Because I'm a graphic designer, I chose to use Adobe Premiere to create animated Tiktok advertising.

Premiere is a fancy video editing application used for more than advertisements. Premiere is used to edit movies, not social media marketing. I wanted this experiment to be quick, so I got 3 social media ad templates from motionarray.com and threw my visuals in. All the transitions and animations were pre-made in the files, so it only took a few hours to compile. The result:

I downloaded 3 different soundtracks for the videos to determine which would convert best.

After that, I opened a Tiktok business account, uploaded my films, and inserted ad info. They went live within one hour.

The (poor) outcomes

As a European company, I couldn't deliver ads in the US. All of my advertisements' material (title, description, and call to action) was in English, hence they continued getting rejected in Europe for countries that didn't speak English. There are a lot of them:

I lost a lot of quality traffic, but I felt that if the images were engaging, people would check out the store and buy my t-shirts. I was wrong.

• 51,071 impressions on Day 1. 0 orders after 411 clicks

• 114,053 impressions on Day 2. 1.004 clicks and no orders

• Day 3: 987 clicks, 103,685 impressions, and 0 orders

• 101,437 impressions on Day 4. 0 orders after 963 clicks

• 115,053 impressions on Day 5. 1,050 clicks and no purchases

• 125,799 impressions on day 6. 1,184 clicks, no purchases

• 115,547 impressions on Day 7. 1,050 clicks and no purchases

• 121,456 impressions on day 8. 1,083 clicks, no purchases

• 47,586 impressions on Day 9. 419 Clicks. No orders

My overall conversion rate for video advertisements was 0.9%. TikTok's paid ad formats all result in strong engagement rates (ads average 3% to 12% CTR to site), therefore a 1 to 2% CTR should have been doable.

My one-week experiment yielded 8,151 ad clicks but no sales. Even if 0.1% of those clicks converted, I should have made 8 sales. Even companies with horrible web marketing would get one download or trial sign-up for every 8,151 clicks. I knew that because my advertising were in English, I had no impressions in the main EU markets (France, Spain, Italy, Germany), and that this impacted my conversion potential. I still couldn't believe my numbers.

I dug into the statistics and found that Tiktok's stats didn't match my store traffic data.

Looking more closely at the numbers

My ads were approved on April 26 but didn't appear until April 27. My store dashboard showed 440 visitors but 1,004 clicks on Tiktok. This happens often while tracking campaign results since different platforms handle comparable user activities (click, view) differently. In online marketing, residual data won't always match across tools.

My data gap was too large. Even if half of the 1,004 persons who clicked closed their browser or left before the store site loaded, I would have gained 502 visitors. The significant difference between Tiktok clicks and Big Cartel store visits made me suspicious. It happened all week:

• Day 1: 440 store visits and 1004 ad clicks

• Day 2: 482 store visits, 987 ad clicks

• 3rd day: 963 hits on ads, 452 store visits

• 443 store visits and 1,050 ad clicks on day 4.

• Day 5: 459 store visits and 1,184 ad clicks

• Day 6: 430 store visits and 1,050 ad clicks

• Day 7: 409 store visits and 1,031 ad clicks

• Day 8: 166 store visits and 418 ad clicks

The disparity wasn't related to residual data or data processing. The disparity between visits and clicks looked regular, but I couldn't explain it.

After the campaign concluded, I discovered all my creative assets (the videos) had a 0% CTR and a $0 expenditure in a separate dashboard. Whether it's a dashboard reporting issue or a budget allocation bug, online marketers shouldn't see this.

Tiktok can present any stats they want on their dashboard, just like any other platform that runs advertisements to promote content to its users. I can't verify that 895,687 individuals saw and clicked on my ad. I invested $200 for what appears to be around 900K impressions, which is an excellent ROI. No one bought a t-shirt, even an unattractive one, out of 900K people?

Would I do it again?

Nope. Whether I didn't make sales because Tiktok inflated the dashboard numbers or because I'm horrible at producing advertising and items that sell, I’ll stick to writing content and making videos. If setting up a business and ads in a few days was all it took to make money online, everyone would do it.

Video advertisements and dropshipping aren't dead. As long as the internet exists, people will click ads and buy stuff. Converting ads and selling stuff takes a lot of work, and I want to focus on other things.

I had always wanted to try dropshipping and I’m happy I did, I just won’t stick to it because that’s not something I’m interested in getting better at.

If I want to sell t-shirts again, I'll avoid Tiktok advertisements and find another route.

We've fought for humanity's sake. We need equilibrium.

We live in a world of opposites (black/white, up/down, love/hate), thus life is a game of achieving equilibrium. We have a universe of paradoxes within ourselves, not just in physics.

Individually, you balance your intellect and heart, but as a species, we're full of polarities. They might be gentle and compassionate, then ruthless and unsympathetic.

We desire for connection so much that we personify non-human beings and objects while turning to violence and hatred toward others. These contrasts baffle me. Will we find balance?

Anthropomorphization

Assigning human-like features or bonding with objects is common throughout childhood. Cartoons often give non-humans human traits. Adults still anthropomorphize this trait. Researchers agree we start doing it as infants and continue throughout life.

Humans of all ages are good at humanizing stuff. We build emotional attachments to weather events, inanimate objects, animals, plants, and locales. Gods, goddesses, and fictitious figures are anthropomorphized.

Cast Away, starring Tom Hanks, features anthropization. Hanks is left on an island, where he builds an emotional bond with a volleyball he calls Wilson.

We became emotionally invested in Wilson, including myself.

Why do we do it, though?

Our instincts and traits helped us survive and thrive. Our brain is alert to other people's thoughts, feelings, and intentions to assist us to determine who is safe or hazardous. We can think about others and our own mental states, or about thinking. This is the Theory of Mind.

Neurologically, specialists believe the Theory of Mind has to do with our mirror neurons, which exhibit the same activity while executing or witnessing an action.

Mirror neurons may contribute to anthropization, but they're not the only ones. In 2021, Harvard Medical School researchers at MGH and MIT colleagues published a study on the brain's notion of mind.

“Our study provides evidence to support theory of mind by individual neurons. Until now, it wasn’t clear whether or how neurons were able to perform these social cognitive computations.”

Neurons have particular functions, researchers found. Others encode information that differentiates one person's beliefs from another's. Some neurons reflect tale pieces, whereas others aren't directly involved in social reasoning but may multitask contributing factors.

Combining neuronal data gives a precise portrait of another's beliefs and comprehension. The theory of mind describes how we judge and understand each other in our species, and it likely led to anthropomorphism. Neuroscience indicates identical brain regions react to human or non-human behavior, like mirror neurons.

Some academics believe we're wired for connection, which explains why we anthropomorphize. When we're alone, we may anthropomorphize non-humans.

Humanizing non-human entities may make them deserving of moral care, according to another theory. Animamorphizing something makes it responsible for its actions and deserves punishments or rewards. This mental shift is typically apparent in our connections with pets and leads to deanthropomorphization.

Dehumanization

Dehumanizing involves denying someone or anything ethical regard, the opposite of anthropomorphizing.

Dehumanization occurs throughout history. We do it to everything in nature, including ourselves. We experiment on and torture animals. We enslave, hate, and harm other groups of people.

Race, immigrant status, dress choices, sexual orientation, social class, religion, gender, politics, need I go on? Our degrading behavior is promoting fascism and division everywhere.

Dehumanizing someone or anything reduces their agency and value. Many assume they're immune to this feature, but tests disagree.

It's inevitable. Humans are wired to have knee-jerk reactions to differences. We are programmed to dehumanize others, and it's easier than we'd like to admit.

Why do we do it, though?

Dehumanizing others is simpler than humanizing things for several reasons. First, we consider everything unusual as harmful, which has helped our species survive for hundreds of millions of years. Our propensity to be distrustful of others, like our fear of the unknown, promotes an us-vs.-them mentality.

Since WWII, various studies have been done to explain how or why the holocaust happened. How did so many individuals become radicalized to commit such awful actions and feel morally justified? Researchers quickly showed how easily the mind can turn gloomy.

Stanley Milgram's 1960s electroshock experiment highlighted how quickly people bow to authority to injure others. Philip Zimbardo's 1971 Stanford Prison Experiment revealed how power may be abused.

The us-versus-them attitude is natural and even young toddlers act on it. Without a relationship, empathy is more difficult.

It's terrifying how quickly dehumanizing behavior becomes commonplace. The current pandemic is an example. Most countries no longer count deaths. Long Covid is a major issue, with predictions of a handicapped tsunami in the future years. Mostly, we shrug.

In 2020, we panicked. Remember everyone's caution? Now Long Covid is ruining more lives, threatening to disable an insane amount of our population for months or their entire lives.

There's little research. Experts can't even classify or cure it. The people should be outraged, but most have ceased caring. They're over covid.

We're encouraged to find a method to live with a terrible pandemic that will cause years of damage. People aren't worried about infection anymore. They shrug and say, "We'll all get it eventually," then hope they're not one of the 30% who develops Long Covid.

We can correct course before further damage. Because we can recognize our urges and biases, we're not captives to them. We can think critically about our thoughts and behaviors, then attempt to improve. We can recognize our deficiencies and work to attain balance.

Changing perspectives

We're currently attempting to find equilibrium between opposites. It's superficial to defend extremes by stating we're only human or wired this way because both imply we have no control.

Being human involves having self-awareness, and by being careful of our thoughts and acts, we can find balance and recognize opposites' purpose.

Extreme anthropomorphizing and dehumanizing isolate and imperil us. We anthropomorphize because we desire connection and dehumanize because we're terrified, frequently of the connection we crave. Will we find balance?

Katrina Paulson ponders humanity, unanswered questions, and discoveries. Please check out her newsletters, Curious Adventure and Curious Life.

DATA MINING WITH SUPERALGORES

Old pots produce the best soup.

Science has always inspired indicator design. From physics to signal processing, many indicators use concepts from mechanical engineering, electronics, and probability. In Superalgos' Data Mining section, we've explored using thermodynamics and information theory to construct indicators and using statistical and probabilistic techniques like reduced normal law to take advantage of low probability events.

An asset's price is like a mechanical object revolving around its moving average. Using this approach, we could design an indicator using the oscillator's Total Energy. An oscillator's energy is finite and constant. Since we don't expect the price to follow the harmonic oscillator, this energy should deviate from the perfect situation, and the maximum of divergence may provide us valuable information on the price's moving average.

Definition of the Harmonic Oscillator in Few Words

Sinusoidal function describes a harmonic oscillator. The time-constant energy equation for a harmonic oscillator is:

With

Time saves energy.

In a mechanical harmonic oscillator, total energy equals kinetic energy plus potential energy. The formula for energy is the same for every kind of harmonic oscillator; only the terms of total energy must be adapted to fit the relevant units. Each oscillator has a velocity component (kinetic energy) and a position to equilibrium component (potential energy).

The Price Oscillator and the Energy Formula

Considering the harmonic oscillator definition, we must specify kinetic and potential components for our price oscillator. We define oscillator velocity as the rate of change and equilibrium position as the price's distance from its moving average.

Price kinetic energy:

It's like:

With

and

L is the number of periods for the rate of change calculation and P for the close price EMA calculation.

Total price oscillator energy =

Given that an asset's price can theoretically vary at a limitless speed and be endlessly far from its moving average, we don't expect this formula's outcome to be constrained. We'll normalize it using Z-Score for convenience of usage and readability, which also allows probabilistic interpretation.

Over 20 periods, we'll calculate E's moving average and standard deviation.

We calculated Z on BTC/USDT with L = 10 and P = 21 using Knime Analytics.

The graph is detrended. We added two horizontal lines at +/- 1.6 to construct a 94.5% probability zone based on reduced normal law tables. Price cycles to its moving average oscillate clearly. Red and green arrows illustrate where the oscillator crosses the top and lower limits, corresponding to the maximum/minimum price oscillation. Since the results seem noisy, we may apply a non-lagging low-pass or multipole filter like Butterworth or Laguerre filters and employ dynamic bands at a multiple of Z's standard deviation instead of fixed levels.

Kinetic Detrender Implementation in Superalgos

The Superalgos Kinetic detrender features fixed upper and lower levels and dynamic volatility bands.

The code is pretty basic and does not require a huge amount of code lines.

It starts with the standard definitions of the candle pointer and the constant declaration :

let candle = record.current
let len = 10
let P = 21
let T = 20
let up = 1.6
let low = 1.6

Upper and lower dynamic volatility band constants are up and low.

We proceed to the initialization of the previous value for EMA :

if (variable.prevEMA === undefined) {
    variable.prevEMA = candle.close
}

And the calculation of EMA with a function (it is worth noticing the function is declared at the end of the code snippet in Superalgos) :

variable.ema = calculateEMA(P, candle.close, variable.prevEMA)
//EMA calculation
function calculateEMA(periods, price, previousEMA) {
    let k = 2 / (periods + 1)
    return price * k + previousEMA * (1 - k)
}

The rate of change is calculated by first storing the right amount of close price values and proceeding to the calculation by dividing the current close price by the first member of the close price array:

variable.allClose.push(candle.close)
if (variable.allClose.length > len) {
    variable.allClose.splice(0, 1)
}
if (variable.allClose.length === len) {
    variable.roc = candle.close / variable.allClose[0]
} else {
    variable.roc = 1
}

Finally, we get energy with a single line:

variable.E = 1 / 2 * len * variable.roc + 1 / 2 * P * candle.close / variable.ema

The Z calculation reuses code from Z-Normalization-based indicators:

variable.allE.push(variable.E)
if (variable.allE.length > T) {
    variable.allE.splice(0, 1)
}
variable.sum = 0
variable.SQ = 0
if (variable.allE.length === T) {
    for (var i = 0; i < T; i++) {
        variable.sum += variable.allE[i]
    }
    variable.MA = variable.sum / T
for (var i = 0; i < T; i++) {
        variable.SQ += Math.pow(variable.allE[i] - variable.MA, 2)
    }
    variable.sigma = Math.sqrt(variable.SQ / T)
variable.Z = (variable.E - variable.MA) / variable.sigma
} else {
    variable.Z = 0
}
variable.allZ.push(variable.Z)
if (variable.allZ.length > T) {
    variable.allZ.splice(0, 1)
}
variable.sum = 0
variable.SQ = 0
if (variable.allZ.length === T) {
    for (var i = 0; i < T; i++) {
        variable.sum += variable.allZ[i]
    }
    variable.MAZ = variable.sum / T
for (var i = 0; i < T; i++) {
        variable.SQ += Math.pow(variable.allZ[i] - variable.MAZ, 2)
    }
    variable.sigZ = Math.sqrt(variable.SQ / T)
} else {
    variable.MAZ = variable.Z
    variable.sigZ = variable.MAZ * 0.02
}
variable.upper = variable.MAZ + up * variable.sigZ
variable.lower = variable.MAZ - low * variable.sigZ

We also update the EMA value.

variable.prevEMA = variable.EMA

Conclusion

We showed how to build a detrended oscillator using simple harmonic oscillator theory. Kinetic detrender's main line oscillates between 2 fixed levels framing 95% of the values and 2 dynamic levels, leading to auto-adaptive mean reversion zones.

Superalgos' Normalized Momentum data mine has the Kinetic detrender indication.

All the material here can be reused and integrated freely by linking to this article and Superalgos.

This post is informative and not financial advice. Seek expert counsel before trading. Risk using this material.