© Bowtie and Revenue Architecture - credit Winning by Design
Welcome back to our Revenue Architecture series on the Force & Friction Podcast, where we break down what really moves the needle in GTM, RevOps, AI, partnerships, and SaaS growth.
Today, we have an exceptionally special guest for a deep dive into the Mathematical Model and revenue architecture as a whole with Derek Sather.
What makes Derek's story compelling is his transformation from watching brilliant companies fail because revenue was treated like magic, not science, to becoming an MIT-educated systems thinker who co-created the framework that makes revenue predictable.
Derek's track record speaks for itself: helping companies scale from 25 million to a billion ARR, again and again, using mathematical precision instead of guesswork.
In our conversation, we explore why small changes create massive impacts while large investments yield minimal results, the counterintuitive nature of nonlinear systems, and how the Mathematical Model enables companies to engineer growth rather than hope for it.
Derek Sather
Derek is now the Chief Revenue Officer at KKR-backed Education Perfect, but spent nearly 6 years with Winning by Design in a C-level executive role.
Derek gives us fantastic insight into the Revenue Architecture models from the people who actually designed them.
For context, Winning by Design's revenue architecture framework is trusted by over 600 companies worldwide, including SpaceX, Meta, and Amazon.
Watch the Episode:
What is The Mathmatical Model
The Mathematical Model in Revenue Architecture reveals the nonlinear relationships that govern recurring revenue businesses, operating in two distinct domains: acquisition and retention/expansion.
Unlike traditional linear thinking that focuses on adding more resources (more reps, more leads, more budget), the Mathematical Model demonstrates how small, systematic improvements compound to create exponential growth.
Core Mathematical Principles:
1. Acquisition Side:
Polynomial Growth Through Compound Multiplication The left side of the bowtie operates as a "one-round game" where conversion rates multiply across the customer journey (CR1 × CR2 × CR3 × CR4). Small improvements in each conversion rate compound dramatically because of this multiplication effect.
Polynomial Growth Through Compound Multiplication The left side of the bowtie operates as a "one-round game" where conversion rates multiply across the customer journey (CR1 × CR2 × CR3 × CR4). Small improvements in each conversion rate compound dramatically because of this multiplication effect.
2. Retention Side:
Exponential Growth Through Accumulation Over Time The right side operates through summation of revenue over the customer lifetime, where time is measured in months and years rather than days and weeks. This creates the opportunity for infinite optimization as you can improve the same customer relationship multiple times.
Exponential Growth Through Accumulation Over Time The right side operates through summation of revenue over the customer lifetime, where time is measured in months and years rather than days and weeks. This creates the opportunity for infinite optimization as you can improve the same customer relationship multiple times.
3. The Compound Effect Formula
A 10% improvement across 7 different conversion rates doesn't yield 70% growth, it doubles revenue. This counterintuitive math is why marginal gains across multiple conversion points outperform big bets on single variables.
A 10% improvement across 7 different conversion rates doesn't yield 70% growth, it doubles revenue. This counterintuitive math is why marginal gains across multiple conversion points outperform big bets on single variables.
The Real Job of the Mathematical Model
The Mathematical Model doesn't just predict revenue, it reveals:
•Which micro-improvements will create exponential results
•Why acquisition and retention require fundamentally different optimization strategies
•How to allocate resources between acquisition and expansion for maximum ROI
•Where traditional linear thinking fails in recurring revenue businesses
It transforms revenue from an art based on intuition into a science based on mathematical relationships, enabling leaders to engineer growth with precision rather than hope for it with activity.
Here are the core areas we discuss in today's episode:
1: From Linear Thinking Addiction to Systems Engineering
Derek opens by explaining how his MIT education in complex systems theory revealed why most revenue leaders fail, they're addicted to linear thinking.
"Most revenue leaders have been trained to think linearly for their entire careers. So if you look at a sales leader, they'll say, hey, Derek, I need more leads, not more math. They're used to solving problems by just adding resources, so it's more reps, more leads, more budget, and the idea that reducing any of that just seems counterintuitive."
This insight reveals why doubling marketing spend often yields marginal improvements while tiny conversion rate improvements create exponential growth. The breakthrough comes from understanding that recurring revenue businesses operate as nonlinear systems where small changes can make massive impacts.
2: The Compound Multiplication Magic: Why 10% Becomes 100%
Derek demonstrates the counterintuitive math that makes revenue architecture so powerful, using real examples of how micro-improvements compound.
"If you're able to increase the conversion rate... 10% across 7 different conversion rates. Seems like something that is very attainable... But if you're able to actually do that, in your examples, you're maybe moving from that $2 million, you actually double revenue. So you're actually moving to $4 million. And that idea of compounding effects is truly some of the magic of that non-linear system."
This mathematical reality explains why companies can achieve 40%+ growth rates while others plateau at 10%—it's the difference between hoping for growth and engineering growth through systematic optimization.
3: The One-Round Game vs. Infinite Game Dynamic
Derek reveals the fundamental difference between acquisition and retention optimization that most leaders miss entirely.
"If you look at the acquisition side... it is a one-round game. You only have opportunity to improve those metrics once during acquisition. However, on the right side of the bow tie, it's about expansion and retention... it is the lifetime, so hopefully you're going to be able to play that multiple times."
This insight transforms resource allocation strategy. While acquisition operates through compound multiplication measured in days and weeks, retention operates through accumulation over months and years, creating dramatically different optimization opportunities.
4: The Segmentation Imperative: Why Averages Kill Insights
Derek explains why most companies fail to see their mathematical relationships—they're looking at blended data instead of segmented motions.
"If you have multiple go-to-market motions, you cannot combine them all... really getting micro-segmentation, if you will, so you can understand where things step out. Because if you look at the system as a whole, in some cases, you're going to miss, some of those conversion rates, because everything kind of gets blended and muted. The law of averages starts to be reflected, and then everything just looks gray."
This principle prevents the common mistake of optimizing for average performance instead of understanding the specific mathematical relationships within each GTM motion, region, or product line.
5: Beauty in Simplicity: Why Complex Systems Need Simple Visuals
Derek addresses the counterintuitive design philosophy behind Winning by Design's deliberately simple visual framework.
"The beauty is in the simplicity... he has an incredible superpower, where he's a fantastic graphic designer, he is a fantastic engineered systems thinker, and deeply understands go-to-market. But he can design and build something that I would never be able to do... So, and you've really simplified something that is incredibly complex."
This design philosophy ensures that complex mathematical relationships become accessible to entire revenue teams, enabling cross-functional alignment around systematic optimization rather than departmental silos.
Final Thoughts
Derek leaves us with a powerful insight about the resource allocation mistake that kills growth potential.
"Most software organizations, from a go-to-market standpoint, significantly overfund acquisition, and significantly underfund expansion... keeping your existing customer and expanding is so much more efficient. Of course it is, but let's actually get the right resources there... we really want to look at recurring revenue equals recurring impact."
His final message emphasizes that mathematical precision isn't just about optimization—it's about understanding where to invest for maximum return, recognizing that the infinite game of retention and expansion often delivers better ROI than the one-round game of acquisition.
The Mathematical Model transforms revenue from guesswork into engineering, from hoping for growth to systematically creating it. As Derek demonstrates, when you understand the nonlinear relationships that govern recurring revenue businesses, you can achieve exponential results through marginal gains rather than massive investments.
The future belongs to leaders who can think in systems, optimize for compound effects, and engineer growth with mathematical precision rather than linear intuition.
The Revenue Architecture Series
Watch more episodes from the Revenue Architecture Series - get started with the founder of Winning By Design Jacco van der Kooij's interview - watch that here:
The Revenue Architecture Textbook
Order you text workbook on Revenue Architecture - more than a 'read' this is a comprehensive workbook to ensure you up skill your knowledge.
Learn more about Derek's team at Education Perfect here:
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A little about Mike who hosts the show. Please connect with me on LinkedIn I'd love to have you as part of our professional network.
Mike Midgley runs a portfolio career, a dynamic digital entrepreneur, NXD, strategist, public speaker, Winning by Design certified Revenue Architect and Host at The Force & Friction Podcast.
Mike has achieved successful six and seven-figure exits over a 30+ year career, raised in excess of £1.6m [$2.5m] in Venture Capital and franchised his businesses 68 times.
