Explaining Funding Round Momentum With Complexity Theory

The tech start-up world often resorts to post-hoc justifications for funding round outcomes. The typical narrative is that funding amounts are determined by the tech's uniqueness or the founder's track record. While there's truth here, it doesn't paint the whole picture. Many founders speak of "momentum" during their rounds. But what the hell is momentum? My aim here is to demystify this term using a mathematical lens, highlighting how positive feedback loops are at the heart of successful, oversubscribed funding rounds.

The Mean Is Not the Entire Story

If your feet are in an oven and your head in a freezer, your average temperature is just fine.

I find this example compelling because it vividly emphasizes a key mathematical distinction: the distribution of data points, or the  "measures of dispersion", sometimes play a more important role in determining the outcome than the average, or "measures of central tendency". 

In other words, extreme conditions - a hot oven and a cold freezer - could prove lethal, irrespective of what the average temperature suggests. If both extremes simultaneously escalate - the oven getting hotter, and the freezer colder - the average remains unchanged, yet clearly this should be a cause of worry.

Complexity theory introduces the concept of feedback loops, escape velocities and thresholds which are yet other explanations of why averages are not so important. I borrowed the following example from Scott E. Page's insightful lectures at the University of Michigan.

Picture yourself in a mall, when suddenly one person sprints towards the exit. Would you follow suit? Maybe Elon Musk is outside, or perhaps there's a fire this person is fleeing from. Then again, that person might just be late for their bus. No reason to run. Would you react differently if two people were running? Or twenty? Everyone has a unique threshold, but eventually, everyone would likely join the crowd.

Such feedback chains aren't just theoretical; they reflect real-world scenarios. 

Suppose that there are 100 people in the mall with an average running threshold of 50 people, in this case one might conclude that starting a mass dash would be difficult. 

However, in such situations, the average is often less relevant than the unique distribution of thresholds. Let's say the distribution is as follows:

Person 1 runs if 1 other person runs

Person 2 runs if 2 people run

Person 3 runs if 3 people run

…

Person 98 runs if 98 people run

Person 99 runs if 99 people run

Person 100 runs if 100 people run

Here, the average and median are around 50, meaning half of the individuals would start running if more than 50 others are running. 

Yet, what if a random person (not Person 1) begins to run? This triggers Person 1, and now two people are running, prompting Person 2 to join in. As a third person starts running, Person 3 follows suit, creating a domino effect until everyone is running. 

This domino effect is not triggered by the average threshold of the group; it is triggered by the unique distribution of individual thresholds.

What Does This Mean for Founders and Their Fundraising Strategy?

The same principle behind complexity theory applies to funding rounds. Consider this scenario: 

An average angel investor expects to see a €500K commitment before they decide to invest. While daunting for many founders, the average isn't the key determinant. 

What if a sizable number of investors are willing to commit their funds upon seeing commitments of €50K, or €150K, and so forth, and what if you could identify these investors and approach them first?

Targeting these early investors can kickstart momentum, leading to rounds being oversubscribed, often securing funds beyond initial targets - sometimes even securing 3–4 times the required capital. 

I believe that without these positive feedback loops, in a context where only the venture's objective potential is considered, the extent of oversubscription we observe in funding rounds would be significantly less.

As early-stage founders, we can learn from this predictably unconventional behaviour:

Timing Matters

It is pretty much impossible to trigger a positive feedback loop if you go fundraising for an entire year. Contacting all investors at roughly the same time, let’s say within 2 to 3 weeks, will make it far more likely to create positive momentum. A great example of this is the Y-Combinator Demo Day or EWOR Grand Pitch, which creates exactly this dynamic. 

Order Matters

Start with easily approachable investors before aiming for the big fish. If you contact the conservative, hard-to-get investors first, they’ll probably decline given that you don’t have any fundraising traction. Start with the low-hanging fruit and make sure you raise enough “easy money”. Especially if you plan to raise from VCs - who definitely have a higher threshold for first-time founders. 

Also, start approaching the investors with low thresholds first. There are angel investors that are happy to make a first commitment and then get involved in contacting further investors. Those will have a much higher impact if contacted first than any other type of investor. 

Storytelling Matters

The mall example might seem oversimplified, as it only takes one person to initiate the running. In reality, the distribution is not as perfect and you’ll have to get a couple people to commit simultaneously. It often makes strategic sense to engage with multiple potential investors simultaneously, informing them that you're in talks with others, then leverage that momentum to secure the first commitment.

When I was 19, I used a similar approach to organize an event with top-tier speakers. I extended invitations to five incredible individuals, informing each that the other four had also been invited. While I didn't state that they had confirmed their participation, the indication of their potential involvement was enough to get the first speaker's commitment. That enabled me to secure the participation of two more top-tier speakers. Eventually, everyone of the top tier guys was happy as other top-tier speakers were also there. Fundraising operates on a similar principle.

Round Sizes Matter

Turning an oversubscribed €500K funding round into a €1 million round is often simpler than securing the latter half of a €1 million round that has only €500K in commitments. The facts remain the same in both scenarios: you've got €500K committed. Yet, the framing is dramatically different. In the first case, you're not actively looking for more funding and you seem to have high interest for what you offer, thus creating a sense of FOMO. The second scenario suggests you're only halfway done with the task. That makes your startup much less “sexy”.

The psychological power of scarcity is well documented across various studies. One of my favourite studies conducted with 200 female college students offers some intriguing insights that entrepreneurs can leverage. The study revolved around the perceived value of cookies.

The researchers manipulated the availability of cookies, creating scenarios where the cookies were either in abundant supply, scarce, or fluctuating between the two. They also added a twist, attributing changes in cookie supply to either an accident or shifts in demand. To top it off, they made the participants believe that the number of future participants in the study was either high or low.

Here's what they found:

1. Scarcity is a powerful tool: Cookies that were in short supply were seen as more desirable than those readily available. When something is hard to get, people want it more.
2. The illusion of loss enhances value: Cookies that went from being abundant to scarce were perceived as more valuable than those that were always scarce. This suggests that the perceived loss of availability can boost appeal.
3. The reason for scarcity matters: Cookies that were scarce due to high demand were rated higher than those scarce because of an accident. This shows that consumers value items more when they believe others also want them.

I will leave the transfer to entrepreneurship to you, but can tell from experience that the analogy is almost perfect. You can use these principles to make your startup more desirable, as, unfortunately, these irrational parameters matter even for the world’s best product. I always recommend creating an aura of scarcity whenever possible. Begin with a modest round that's ambitious enough to demonstrate your visionary thinking but modest enough to swiftly introduce the FOMO factor.

My conclusion

Keep in mind, funding rounds for tech startups often involve more than just technology and a strong team. Momentum plays a key role in oversubscribed rounds, driven by positive feedback loops. Complexity theory provides insights into how the distribution of thresholds, rather than the average, can trigger cascading effects. 

Founders can leverage this by identifying early investors with lower commitment thresholds to ignite positive feedback loops and exceed funding targets. Timing, order of engagement, storytelling, and round sizes are crucial factors in leveraging momentum and creating a sense of scarcity.