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Will Lockett

Will Lockett

3 years ago

Tesla recently disclosed its greatest secret.

More on Leadership

Solomon Ayanlakin

Solomon Ayanlakin

3 years ago

Metrics for product management and being a good leader

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.

Product Management Metrics — Measuring the right metrics as a Product Leader by Solomon Ayanlakin

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:

Popular Product Metric Buckets for Product Teams

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

Notable companies and their North star metrics

🥇 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.

Product Metrics for UberEats

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.

Sammy Abdullah

Sammy Abdullah

3 years ago

Payouts to founders at IPO

How much do startup founders make after an IPO? We looked at 2018's major tech IPOs. Paydays aren't what founders took home at the IPO (shares are normally locked up for 6 months), but what they were worth at the IPO price on the day the firm went public. It's not cash, but it's nice. Here's the data.

Several points are noteworthy.

Huge payoffs. Median and average pay were $399m and $918m. Average and median homeownership were 9% and 12%.

Coinbase, Uber, UI Path. Uber, Zoom, Spotify, UI Path, and Coinbase founders raised billions. Zoom's founder owned 19% and Spotify's 28% and 13%. Brian Armstrong controlled 20% of Coinbase at IPO and was worth $15bn. Preserving as much equity as possible by staying cash-efficient or raising at high valuations also helps.

The smallest was Ping. Ping's compensation was the smallest. Andre Duand owned 2% but was worth $20m at IPO. That's less than some billion-dollar paydays, but still good.

IPOs can be lucrative, as you can see. Preserving equity could be the difference between a $20mm and $15bln payday (Coinbase).

Trevor Stark

Trevor Stark

3 years ago

Peter Thiels's Multi-Billion Dollar Net Worth's Unknown Philosopher

Peter Thiel studied philosophy as an undergraduate.

Peter Thiel and Elon Musk, Co-Founders of PayPal

Peter Thiel has $7.36 billion.

Peter is a world-ranked chess player, has a legal degree, and has written profitable novels.

In 1999, he co-founded PayPal with Max Levchin, which merged with X.com.

Peter Thiel made $55 million after selling the company to eBay for $1.5 billion in 2002.

You may be wondering…

How did Peter turn $55 million into his now multi-billion dollar net worth?

One amazing investment?

Facebook.

Thiel was Facebook's first external investor. He bought 10% of the company for $500,000 in 2004.

This investment returned 159% annually, 200x in 8 years.

By 2012, Thiel sold almost all his Facebook shares, becoming a billionaire.

What was the investment thesis of Peter?

This investment appeared ridiculous. Facebook was an innovative startup.

Thiel's $500,000 contribution transformed Facebook.

Screenshot of Facebook in 2004 (Source)

Harvard students have access to Facebook's 8 features and 1 photo per profile.

How did Peter determine that this would be a wise investment, then?

Facebook is a mimetic desire machine.

Social media's popularity is odd. Why peek at strangers' images on a computer?

Peter Thiel studied under French thinker Rene Girard at Stanford.

Mimetic Desire explains social media's success.

Mimetic Desire is the idea that humans desire things simply because other people do.

If nobody wanted it, would you?

Would you desire a family, a luxury car, or expensive clothes if no one else did? Girard says no.

People we admire affect our aspirations because we're social animals. Every person has a role model.

Our nonreligious culture implies role models are increasingly other humans, not God.

The idea explains why social media influencers are so powerful.

Why would Andrew Tate or Kim Kardashian matter if people weren't mimetic?

Humanity is fundamentally motivated by social comparison.

Facebook takes advantage of this need for social comparison, and puts it on a global scale.

It aggregates photographs and updates from millions of individuals.

Facebook mobile allows 24/7 social comparison.

Thiel studied mimetic desire with Girard and realized Facebook exploits the urge for social comparison to gain money.

Social media is more significant and influential than ever, despite Facebook's decline.

Thiel and Girard show that applied philosophy (particularly in business) can be immensely profitable.

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Ivona Hirschi

Ivona Hirschi

3 years ago

7 LinkedIn Tips That Will Help in Audience Growth

In 8 months, I doubled my audience with them.

LinkedIn's buzz isn't over.

People dream of social proof every day. They want clients, interesting jobs, and field recognition.

LinkedIn coaches will benefit greatly. Sell learning? Probably. Can you use it?

Consistency has been key in my eight-month study of LinkedIn. However, I'll share seven of my tips. 700 to 4500 people followed me.

1. Communication, communication, communication

LinkedIn is a social network. I like to think of it as a cafe. Here, you can share your thoughts, meet friends, and discuss life and work.

Do not treat LinkedIn as if it were a board for your post-its.

More socializing improves relationships. It's about people, like any network.

Consider interactions. Three main areas:

  • Respond to criticism left on your posts.

  • Comment on other people's posts

  • Start and maintain conversations through direct messages.

Engage people. You spend too much time on Facebook if you only read your wall. Keeping in touch and having meaningful conversations helps build your network.

Every day, start a new conversation to make new friends.

2. Stick with those you admire

Interact thoughtfully.

Choose your contacts. Build your tribe is a term. Respectful networking.

I only had past colleagues, family, and friends in my network at the start of this year. Not business-friendly. Since then, I've sought out people I admire or can learn from.

Finding a few will help you. As they connect you to their networks. Friendships can lead to clients.

Don't underestimate network power. Cafe-style. Meet people at each table. But avoid people who sell SEO, web redesign, VAs, mysterious job opportunities, etc.

3. Share eye-catching infographics

Daily infographics flood LinkedIn. Visuals are popular. Use Canva's free templates if you can't draw them.

Last week's:

Screenshot of Ivona Hirshi’s post.

It's a fun way to visualize your topic.

You can repost and comment on infographics. Involve your network. I prefer making my own because I build my brand around certain designs.

My friend posted infographics consistently for four months and grew his network to 30,000.

If you start, credit the authors. As you steal someone's work.

4. Invite some friends over.

LinkedIn alone can be lonely. Having a few friends who support your work daily will boost your growth.

I was lucky to be invited to a group of networkers. We share knowledge and advice.

Having a few regulars who can discuss your posts is helpful. It's artificial, but it works and engages others.

Consider who you'd support if they were in your shoes.

You can pay for an engagement group, but you risk supporting unrelated people with rubbish posts.

Help each other out.

5. Don't let your feed or algorithm divert you.

LinkedIn's algorithm is magical.

Which time is best? How fast do you need to comment? Which days are best?

Overemphasize algorithms. Consider the user. No need to worry about the best time.

Remember to spend time on LinkedIn actively. Not passively. That is what Facebook is for.

Surely someone would find a LinkedIn recipe. Don't beat the algorithm yet. Consider your audience.

6. The more personal, the better

Personalization isn't limited to selfies. Share your successes and failures.

The more personality you show, the better.

People relate to others, not theories or quotes. Why should they follow you? Everyone posts the same content?

Consider your friends. What's their appeal?

Because they show their work and identity. It's simple. Medium and Linkedin are your platforms. Find out what works.

You can copy others' hooks and structures. You decide how simple to make it, though.

7. Have fun with those who have various post structures.

I like writing, infographics, videos, and carousels. Because you can:

Repurpose your content!

Out of one blog post I make:

  • Newsletter

  • Infographics (positive and negative points of view)

  • Carousel

  • Personal stories

  • Listicle

Create less but more variety. Since LinkedIn posts last 24 hours, you can rotate the same topics for weeks without anyone noticing.

Effective!

The final LI snippet to think about

LinkedIn is about consistency. Some say 15 minutes. If you're serious about networking, spend more time there.

The good news is that it is worth it. The bad news is that it takes time.

Pen Magnet

Pen Magnet

3 years ago

Why Google Staff Doesn't Work

Photo by Rajeshwar Bachu on Unsplash

Sundar Pichai unveiled Simplicity Sprint at Google's latest all-hands conference.

To boost employee efficiency.

Not surprising. Few envisioned Google declaring a productivity drive.

Sunder Pichai's speech:

“There are real concerns that our productivity as a whole is not where it needs to be for the head count we have. Help me create a culture that is more mission-focused, more focused on our products, more customer focused. We should think about how we can minimize distractions and really raise the bar on both product excellence and productivity.”

The primary driver driving Google's efficiency push is:

Google's efficiency push follows 13% quarterly revenue increase. Last year in the same quarter, it was 62%.

Market newcomers may argue that the previous year's figure was fuelled by post-Covid reopening and growing consumer spending. Investors aren't convinced. A promising company like Google can't afford to drop so quickly.

Google’s quarterly revenue growth stood at 13%, against 62% in last year same quarter.

Google isn't alone. In my recent essay regarding 2025 programmers, I warned about the economic downturn's effects on FAAMG's workforce. Facebook had suspended hiring, and Microsoft had promised hefty bonuses for loyal staff.

In the same article, I predicted Google's troubles. Online advertising, especially the way Google and Facebook sell it using user data, is over.

FAAMG and 2nd rung IT companies could be the first to fall without Post-COVID revival and uncertain global geopolitics.

Google has hardly ever discussed effectiveness:

Apparently openly.

Amazon treats its employees like robots, even in software positions. It has significant turnover and a terrible reputation as a result. Because of this, it rarely loses money due to staff productivity.

Amazon trumps Google. In reality, it treats its employees poorly.

Google was the founding father of the modern-day open culture.

Larry and Sergey Google founded the IT industry's Open Culture. Silicon Valley called Google's internal democracy and transparency near anarchy. Management rarely slammed decisions on employees. Surveys and internal polls ensured everyone knew the company's direction and had a vote.

20% project allotment (weekly free time to build own project) was Google's open-secret innovation component.

After Larry and Sergey's exit in 2019, this is Google's first profitability hurdle. Only Google insiders can answer these questions.

  • Would Google's investors compel the company's management to adopt an Amazon-style culture where the developers are treated like circus performers?

  • If so, would Google follow suit?

  • If so, how does Google go about doing it?

Before discussing Google's likely plan, let's examine programming productivity.

What determines a programmer's productivity is simple:

How would we answer Google's questions?

As a programmer, I'm more concerned about Simplicity Sprint's aftermath than its economic catalysts.

Large organizations don't care much about quarterly and annual productivity metrics. They have 10-year product-launch plans. If something seems horrible today, it's likely due to someone's lousy judgment 5 years ago who is no longer in the blame game.

Deconstruct our main question.

  • How exactly do you change the culture of the firm so that productivity increases?

  • How can you accomplish that without affecting your capacity to profit? There are countless ways to increase output without decreasing profit.

  • How can you accomplish this with little to no effect on employee motivation? (While not all employers care about it, in this case we are discussing the father of the open company culture.)

  • How do you do it for a 10-developer IT firm that is losing money versus a 1,70,000-developer organization with a trillion-dollar valuation?

When implementing a large-scale organizational change, success must be carefully measured.

The fastest way to do something is to do it right, no matter how long it takes.

You require clearly-defined group/team/role segregation and solid pass/fail matrices to:

  • You can give performers rewards.

  • Ones that are average can be inspired to improve

  • Underachievers may receive assistance or, in the worst-case scenario, rehabilitation

As a 20-year programmer, I associate productivity with greatness.

Doing something well, no matter how long it takes, is the fastest way to do it.

Let's discuss a programmer's productivity.

Why productivity is a strange term in programming:

Productivity is work per unit of time.

Money=time This is an economic proverb. More hours worked, more pay. Longer projects cost more.

As a buyer, you desire a quick supply. As a business owner, you want employees who perform at full capacity, creating more products to transport and boosting your profits.

All economic matrices encourage production because of our obsession with it. Productivity is the only organic way a nation may increase its GDP.

Time is money — is not just a proverb, but an economical fact.

Applying the same productivity theory to programming gets problematic. An automating computer. Its capacity depends on the software its master writes.

Today, a sophisticated program can process a billion records in a few hours. Creating one takes a competent coder and the necessary infrastructure. Learning, designing, coding, testing, and iterations take time.

Programming productivity isn't linear, unlike manufacturing and maintenance.

Average programmers produce code every day yet miss deadlines. Expert programmers go days without coding. End of sprint, they often surprise themselves by delivering fully working solutions.

Reversing the programming duties has no effect. Experts aren't needed for productivity.

These patterns remind me of an XKCD comic.

Source: XKCD

Programming productivity depends on two factors:

  • The capacity of the programmer and his or her command of the principles of computer science

  • His or her productive bursts, how often they occur, and how long they last as they engineer the answer

At some point, productivity measurement becomes Schrödinger’s cat.

Product companies measure productivity using use cases, classes, functions, or LOCs (lines of code). In days of data-rich source control systems, programmers' merge requests and/or commits are the most preferred yardstick. Companies assess productivity by tickets closed.

Every organization eventually has trouble measuring productivity. Finer measurements create more chaos. Every measure compares apples to oranges (or worse, apples with aircraft.) On top of the measuring overhead, the endeavor causes tremendous and unnecessary stress on teams, lowering their productivity and defeating its purpose.

Macro productivity measurements make sense. Amazon's factory-era management has done it, but at great cost.

Google can pull it off if it wants to.

What Google meant in reality when it said that employee productivity has decreased:

When Google considers its employees unproductive, it doesn't mean they don't complete enough work in the allotted period.

They can't multiply their work's influence over time.

  • Programmers who produce excellent modules or products are unsure on how to use them.

  • The best data scientists are unable to add the proper parameters in their models.

  • Despite having a great product backlog, managers struggle to recruit resources with the necessary skills.

  • Product designers who frequently develop and A/B test newer designs are unaware of why measures are inaccurate or whether they have already reached the saturation point.

  • Most ignorant: All of the aforementioned positions are aware of what to do with their deliverables, but neither their supervisors nor Google itself have given them sufficient authority.

So, Google employees aren't productive.

How to fix it?

  • Business analysis: White suits introducing novel items can interact with customers from all regions. Track analytics events proactively, especially the infrequent ones.

  • SOLID, DRY, TEST, and AUTOMATION: Do less + reuse. Use boilerplate code creation. If something already exists, don't implement it yourself.

  • Build features-building capabilities: N features are created by average programmers in N hours. An endless number of features can be built by average programmers thanks to the fact that expert programmers can produce 1 capability in N hours.

  • Work on projects that will have a positive impact: Use the same algorithm to search for images on YouTube rather than the Mars surface.

  • Avoid tasks that can only be measured in terms of time linearity at all costs (if a task can be completed in N minutes, then M copies of the same task would cost M*N minutes).

In conclusion:

Software development isn't linear. Why should the makers be measured?

Notation for The Big O

I'm discussing a new way to quantify programmer productivity. (It applies to other professions, but that's another subject)

The Big O notation expresses the paradigm (the algorithmic performance concept programmers rot to ace their Google interview)

Google (or any large corporation) can do this.

  1. Sort organizational roles into categories and specify their impact vs. time objectives. A CXO role's time vs. effect function, for instance, has a complexity of O(log N), meaning that if a CEO raises his or her work time by 8x, the result only increases by 3x.

  2. Plot the influence of each employee over time using the X and Y axes, respectively.

  3. Add a multiplier for Y-axis values to the productivity equation to make business objectives matter. (Example values: Support = 5, Utility = 7, and Innovation = 10).

  4. Compare employee scores in comparable categories (developers vs. devs, CXOs vs. CXOs, etc.) and reward or help employees based on whether they are ahead of or behind the pack.

After measuring every employee's inventiveness, it's straightforward to help underachievers and praise achievers.

Example of a Big(O) Category:

If I ran Google (God forbid, its worst days are far off), here's how I'd classify it. You can categorize Google employees whichever you choose.

The Google interview truth:

O(1) < O(log n) < O(n) < O(n log n) < O(n^x) where all logarithmic bases are < n.

O(1): Customer service workers' hours have no impact on firm profitability or customer pleasure.

CXOs Most of their time is spent on travel, strategic meetings, parties, and/or meetings with minimal floor-level influence. They're good at launching new products but bad at pivoting without disaster. Their directions are being followed.

Devops, UX designers, testers Agile projects revolve around deployment. DevOps controls the levers. Their automation secures results in subsequent cycles.

UX/UI Designers must still prototype UI elements despite improved design tools.

All test cases are proportional to use cases/functional units, hence testers' work is O(N).

Architects Their effort improves code quality. Their right/wrong interference affects product quality and rollout decisions even after the design is set.

Core Developers Only core developers can write code and own requirements. When people understand and own their labor, the output improves dramatically. A single character error can spread undetected throughout the SDLC and cost millions.

Core devs introduce/eliminate 1000x bugs, refactoring attempts, and regression. Following our earlier hypothesis.

The fastest way to do something is to do it right, no matter how long it takes.

Conclusion:

Google is at the liberal extreme of the employee-handling spectrum

Microsoft faced an existential crisis after 2000. It didn't choose Amazon's data-driven people management to revitalize itself.

Instead, it entrusted developers. It welcomed emerging technologies and opened up to open source, something it previously opposed.

Google is too lax in its employee-handling practices. With that foundation, it can only follow Amazon, no matter how carefully.

Any attempt to redefine people's measurements will affect the organization emotionally.

The more Google compares apples to apples, the higher its chances for future rebirth.

Vitalik

Vitalik

4 years ago

An approximate introduction to how zk-SNARKs are possible (part 1)

You can make a proof for the statement "I know a secret number such that if you take the word ‘cow', add the number to the end, and SHA256 hash it 100 million times, the output starts with 0x57d00485aa". The verifier can verify the proof far more quickly than it would take for them to run 100 million hashes themselves, and the proof would also not reveal what the secret number is.

In the context of blockchains, this has 2 very powerful applications: Perhaps the most powerful cryptographic technology to come out of the last decade is general-purpose succinct zero knowledge proofs, usually called zk-SNARKs ("zero knowledge succinct arguments of knowledge"). A zk-SNARK allows you to generate a proof that some computation has some particular output, in such a way that the proof can be verified extremely quickly even if the underlying computation takes a very long time to run. The "ZK" part adds an additional feature: the proof can keep some of the inputs to the computation hidden.

You can make a proof for the statement "I know a secret number such that if you take the word ‘cow', add the number to the end, and SHA256 hash it 100 million times, the output starts with 0x57d00485aa". The verifier can verify the proof far more quickly than it would take for them to run 100 million hashes themselves, and the proof would also not reveal what the secret number is.

In the context of blockchains, this has two very powerful applications:

  1. Scalability: if a block takes a long time to verify, one person can verify it and generate a proof, and everyone else can just quickly verify the proof instead
  2. Privacy: you can prove that you have the right to transfer some asset (you received it, and you didn't already transfer it) without revealing the link to which asset you received. This ensures security without unduly leaking information about who is transacting with whom to the public.

But zk-SNARKs are quite complex; indeed, as recently as in 2014-17 they were still frequently called "moon math". The good news is that since then, the protocols have become simpler and our understanding of them has become much better. This post will try to explain how ZK-SNARKs work, in a way that should be understandable to someone with a medium level of understanding of mathematics.

Why ZK-SNARKs "should" be hard

Let us take the example that we started with: we have a number (we can encode "cow" followed by the secret input as an integer), we take the SHA256 hash of that number, then we do that again another 99,999,999 times, we get the output, and we check what its starting digits are. This is a huge computation.

A "succinct" proof is one where both the size of the proof and the time required to verify it grow much more slowly than the computation to be verified. If we want a "succinct" proof, we cannot require the verifier to do some work per round of hashing (because then the verification time would be proportional to the computation). Instead, the verifier must somehow check the whole computation without peeking into each individual piece of the computation.

One natural technique is random sampling: how about we just have the verifier peek into the computation in 500 different places, check that those parts are correct, and if all 500 checks pass then assume that the rest of the computation must with high probability be fine, too?

Such a procedure could even be turned into a non-interactive proof using the Fiat-Shamir heuristic: the prover computes a Merkle root of the computation, uses the Merkle root to pseudorandomly choose 500 indices, and provides the 500 corresponding Merkle branches of the data. The key idea is that the prover does not know which branches they will need to reveal until they have already "committed to" the data. If a malicious prover tries to fudge the data after learning which indices are going to be checked, that would change the Merkle root, which would result in a new set of random indices, which would require fudging the data again... trapping the malicious prover in an endless cycle.

But unfortunately there is a fatal flaw in naively applying random sampling to spot-check a computation in this way: computation is inherently fragile. If a malicious prover flips one bit somewhere in the middle of a computation, they can make it give a completely different result, and a random sampling verifier would almost never find out.


It only takes one deliberately inserted error, that a random check would almost never catch, to make a computation give a completely incorrect result.

If tasked with the problem of coming up with a zk-SNARK protocol, many people would make their way to this point and then get stuck and give up. How can a verifier possibly check every single piece of the computation, without looking at each piece of the computation individually? There is a clever solution.

see part 2