Attempting to untangle the messy math behind the "Power Law"

Or, how venture funding rounds often leave companies in a valuation trap

I was lucky enough to begin my career in the later stage investing world (private equity), before moving into the early stage investing world (venture capital). At first, this resulted in a fair number of growing pains: while the industries can be similar, I have found that the way investors think about making investments in each category can be rather different. As a result there is a little bit of re-wiring needed to be done in order to approach each space differently.

One of the first concepts that I had to wrap my arms around in the early stage world was the VC community’s obsession with the concept of the “Power Law” (no, not the book by Sebastien Mallaby, which I would highly recommend), which effectively declares that venture fund returns do not follow a normal distribution and instead are driven by a small number of home run hits. I have found the below image from ULU Ventures helpful in visualizing the math:

This concept is treated as gospel in the VC community and has been written about ad nauseum so I will not rehash it, but I think that it’s fairly safe to say that it has indeed been proven to be true in practice. What fascinates me more, however, is why this seems to be the case. As any high school statistics teacher would point out, the vast majority of statistical distributions follow a normal distribution (bell curve), but for some reason venture stage investing does not. I have never really gotten a satisfactory answer to this question, but when I’ve inquired I typically bump into a few common hand-wavey explanations:

1. Startups are “really hard” and therefore usually fail (vague and unhelpful)

2. Asset selection is “really hard” and only the very smartest people in the world can do it properly (cue eye roll)

3. Early stage investments have an asymmetric return profile, meaning that you can only lose 1x the money you invested, but you have “unbounded upside” if things go right (technically correct, but this would also apply to buying lottery tickets and I’m not sure I’d ever call that investing)

I have always found the above answers to be unsatisfactory. Maybe #3 explains the distribution of the biggest winners, but what about the “missing middle” of the curve? Shouldn’t the distribution look something like a bell curve with one really long tail? I had always been puzzled about by why there aren’t more “really good” venture outcomes (maybe 3-5x deals) and instead there are more often outstanding outcomes (10x+) and bad ones (0-1x). After spending the last few years noodling on this, I think the answer is at least partially explained by the funding mechanics of early stage companies.

The fuzzy math of venture valuation

To begin, let’s consider how businesses are valued:

For mature businesses, assigning a valuation to a Company is fairly formulaic. The investment banker in me would say that you lean on “trading multiples, precedent transactions, and a discounted cash flow (DCF) analysis”. The private equity investor would note that public comps and precedents can often be nonsensical (particularly at the top of a business cycle), so you should really take a perspective on what the steady-state (“pro forma”) profitability of the business will be. In other words, what is the free cash flow yield of my investment over the hold period (FCF / dollars in), and how does this compare to the amount of risk I’m expecting to carry over the hold period. It’s important to note that the inverse of free cash flow yield is the free cash flow multiple (which is more commonly quoted): if a Company is trading at 10x Free Cash Flow, that means it’s generating a 10% (unlevered) free cash flow yield.

Eventually investors get to a place where they make a decision on whether they think the potential yield on an investment is worth taking on the inherent business risk (often referred to as the “risk-reward profile” of an investment). Lower risk businesses (high growth, contracted revenues, etc.) are typically bought and sold for high multiples of free cash flow, and higher risk businesses trade for lower multiples of free cash flow.

While businesses should be evaluated on multiples of free cash flow, in practice these figures can be cumbersome to properly scrub from financial documents so lazy investors tend to use EBITDA as a proxy. EBITDA is not free cash flow (it notably ignores the capex requirements of a business), but it’s generally close enough to draw some conclusions. Unfortunately, in the world of technology where many businesses are not profitable, investors have simplified even further and review businesses on a multiple of revenue. The belief here is that these business will eventually become profitable, and so revenue is a good enough proxy for now. At this point, we’re already a very far ways away from free cash flow (notably, comparing revenue multiples imply that all businesses will have the same cost structure / profitability in the long run, which is definitively false).

As if that weren’t enough, in the world of startups / growth equity investing, most investments today are quoted on the basis of annualized recurring revenue (ARR), which gives credit to the most recent month / quarter of sales growth as if you had that revenue for the full year. Yes, in hypergrowth scenarios this does mean that a Company’s recent growth is properly captured in its valuation, but you’re now a really far ways away from free cash flow yield. Unfortunately, this is what it is and is really the closest way to measure the intrinsic value of a high growth, but money losing business. Clearly, we’re getting into a realm where investors are taking on a ton of risk about what will happen to a business in the future if they want to participate in this asset class (we’ll come back to this outsized risk point later on). In summary:

For those of you who have survived the valuation 101 review and are for some reason still with me, we now find ourselves looking at true, early stage VC investing where companies have usually have no real revenue or financials to speak of. If you want to invest in these companies, how do you value them? In practice, I’ve found this tends to be a triangulation exercise around a few points:

1. How much money does the team need to reach their next funding milestone? (often VC’s and Founders will disagree on what this number actually is)

2. How much dilution is acceptable at this stage to keep the Founders motivated while leaving enough of the cap table for future hires and future investors? (in practice, most early stage investment rounds seem to acquire 20-25% of the Company)

3. What is the implied valuation based on the first two points (e.g., if a Company is looking to raise $5M, the Company would be valued at a $15-20M pre-money valuation)?

From here this tends to be a take it or leave it exercise: i) do you really believe in the Founding team and expect them to succeed?; ii) if so, do you think this is a big enough idea / market that this could become a giant company if successful?; and iii) if so, do you generally like the idea / approach they’re taking to solve the problem? If a VC believes all three of the above points to be true, they typically will be inclined to proceed with an investment. If the situation become competitive, the round size may increase (e.g., raising $10M instead of $5M), or the dilution may decrease (20% instead of 25%), and a VC might have to re-evaluate on whether or not they feel like the deal is now “too expensive”. In general, however, I think most VC’s seem to just pay the market clearing price and assume the math will sort itself out later (and will often mumble something about the power law making the math irrelevant anyways).

For those who come from the later stage investing world, I’ve found it helpful to think of early stage investment rounds as closer to purchasing call options on a future business that might emerge, as opposed to investing on the basis of financial metrics or business fundamentals. In this analogy, the “cost” of the call option is the invested capital in a venture financing, and the “payoff” of the call option is the ownership you received in a future business (furthermore, the “expiration” of the instrument would be the date in which the business runs out of money). As businesses startups mature (and are less likely to go to zero), those financing rounds begin to look more and more like a traditional valuation exercise (image taken from Investopedia and annotated by yours truly):

The implications of selling rocket fuel

There is a long standing VC-ism that venture funding isn’t gasoline, it’s rocket fuel. While this analogy is also hand wavey, I think it does point to some of the truth: Cars (and companies) cannot run on rocket fuel. It kills them, regardless of whether or not they’re an entry level sedan or an F-1 racecar (note to reader: I have never actually tested this analogy, so if you have video of cars trying to drive on literal rocket fuel, I’d love to see it).

The problem with the valuation exercise from the above example is that eventually, someone is going to care about the math. When a Company raises money at a valuation that is not tied to the underlying business metrics, it has to “outgrow” or at least “grow into” that valuation at the next stage. Let’s look at an example. Consider a good outcome scenario in which a Company performs well (for simplicity’s sake, lets consider this to be a traditional SaaS business):

Scenario A

This Company is performing exceptionally well: it generated $1M of ARR within 12 months of launching, tripled YoY in year two, and doubled thereafter. By the end of Year 6, this company would probably be valued as a unicorn. It may not be abundantly clear in the formatting, but the pre-money valuation flips from being a function of fundraising needs at the Seed and Series A stages, to becoming tied to a multiple of ARR by Series B (which is typically when I see ARR metrics start to be taken seriously, particularly for SaaS businesses). As of writing this, Public SaaS companies growing greater than 50% YoY are trading at 9-10x NTM revenue, so you’d better be growing faster than that if you want to command a premium ARR multiple.

Now let’s consider a different financing scenario in which the very same Company convinces VC’s that it actually requires more capital to achieve its goals, and is able to raise a Seed and Series A at higher valuations:

Scenario B

In this scenario, a Series B investor would require the Company to take a down round to proceed with an investment: something that can be particularly painful for a Company when employees are often heavily compensated in stock, as nobody wants to tell their staff that their equity is now underwater. Even if Founders are open to a down round, if the Company has been undisciplined with their spending and is running out of money, there may not even be any new investors at the table who are interested in investing in a Company that has burnt close to $75M to get to $6M of ARR.

Finally, if we consider a third scenario in which the Company raises at somewhat reasonable valuations, but isn’t able to execute at venture speed (i.e., this is a good/great Company, but not an exceptional one), we end up in the same place as scenario B:

Scenario C

In either scenario B or C, the only option a cash burning Company can turn to at this point is to facilitate a sale, which can be challenging in short order. Even if we assume that a buyer is comfortable that they can mitigate the burn rate of a Company they likely won’t be willing to pay a premium multiple. If we assume they want to pay something in-line with market comps (at the time of this writing, lets say 10x ARR), that might actually end up in a scenario in which the purchase price is less than preferred equity the VC’s have paid into the Company:

In both Scenarios B and C, the money invested by VC’s (preferred equity), is greater than the sale price. As preferred equity typically has a liquidation preference (VC’s get their money back first), this means that the Founders and employees would get nothing in a sale, despite building a multi-million dollar business in just three years. Given this dynamic, founders are not incentivized to facilitate a sale below the value of the pref stack, and instead are incentivized to use every last drop of runway to try to drive an inflection in growth in the business. The end result is that many of these businesses end up going to zero, or being sold in a fire sale for pennies on the dollar.

How does this all explain the power law distribution?

In short, I think the above examples help to explain why venture returns tend to follow a power law distribution: the VC funding itself tends to kill many of the good/great businesses.

Given ownership dynamics / incentives and the general costs of running a startup, businesses need to initially raise money at a valuation that is completely disjointed from any real business fundamentals or financials (given that at t=0, there are no fundamentals). From there, the clock is on to see if they can grow into their valuation. On a distribution curve, this means companies often end up falling into four broad categories:

1. Bucket One: The very best businesses can grow at such a pace that they can grow into lofty valuation expectations over the long run (i.e., significantly outgrow the broader market). This is the magic of exponential growth at work

2. Bucket Two: Great businesses that get overcapitalized and are never able to grow into their valuations, despite good fundamentals. This outcome can be blamed on VC’s themselves who get too divorced from the underlying math and kill companies

3. Bucket Three: Good businesses with solid fundamentals are never really able to take off and scale. These businesses probably would’ve been successful with a different funding mechanism (e.g., bootstrapping, debt financing, etc.), but aren’t venture scalable and can’t grow into a VC-funded valuation.

4. Bucket Four: Bad businesses. These were never going to work regardless of funding source. No need to run the math on this one.

What I’ve described as “buckets” two & three above would represent the “missing middle”, from the normal distribution curve, ultimately resulting in a power law distribution. While it’s extremely hard to know exactly which “bucket” a Company is going to fall into at the time of a Seed investment, I do think investors could be more prudent about financing in the early stages to at least salvage bucket two (yes, this is much easier said than done).

A brief note on down rounds

I think the obvious private equity response to the above problem would be something along the lines of “well, these Companies will just have to take a down round”. While this is true in theory, it’s I’ve discovered in practice that this is actually much easier said than done in the world of venture.

Given the dependency on exponential growth and compounding returns, startup success is tightly intertwined with the concept of momentum. Given the risk profile associated with backing unprofitable businesses based on ARR, investors have to believe in the potential for breakout growth in order to accept the risk-reward tradeoff. Employees have to believe that the embedded value of their equity in the future will outweigh the pay cuts they’re taking on today. Perhaps most importantly, customers have to believe that this business will be around for the long haul if they want to depend on a startup as a vendor. As soon as this narrative is challenged, all three of the above parties get spooked. I have been surprised to learn that in practice, startups are as much about storytelling and narrative building as they are about execution. Unfortunately, when a Company is recapped and a datapoint emerges that the Company’s trajectory may have flattened, investors, employees, and customers can jump ship, making a down round a self-fulfilling prophecy.

There are a few gigantic private businesses that have been able to successfully stomach hefty down rounds (e.g., Klarna), but many of these have already been proven to have a repeatable and sustainable business model. For younger startups with less of a track record, a down round early in their life cycle can ultimately mean death. We’ve actually already seen this play out in the data: the Nasdaq finished 2022 down 33%, but in the same year only 11% of private company financings indicated a a down round. This is surprisingly far less than the historical average (data per MorningStar / Pitchbook), as more and more companies instead opted for structured financing rounds or worse, fire sales / bankruptcies (speculation: not included in below data):

So what does it all mean?

In my research for this piece I came across this blog post from Fred Wilson back from 2007. I think it still has valuable lessons for us today, particularly about Bucket Two companies:

“So it’s pretty clear to me that most venture backed investments don’t fail because the business plan was flawed. In my experience at least 2/3 of all business plans we back are flawed.

Most venture backed investments fail because the venture capital is used to scale the business before the correct business plan is discovered. That scale/burn rate becomes the cancer that kills the business.”

I maybe could’ve just read that blog post without getting into all of the (extremely oversimplified) math, but I do think that it’s been a helpful exercise. As I think about what this means for venture investors and founders, a few thoughts pop into my head:

1. Eventually, the math is going to matter. If a Company can raise less in early funding rounds and reduce their burn rate as much as possible, they have a better chance of surviving longer and ultimately becoming a breakout success (yes, this obviously benefits early stage investors. But that doesn’t make it wrong)

2. For businesses that are clearly not able to grow at venture scale, the Board and the Founders should make the decision early to drive towards a sale (this may require creating a management incentive pool if the sale price is going to be lower than the value of the pref stack)

3. Capital efficiency is always critical, for all types of businesses. In the last few years, companies have gotten away with overspending, but the music is going to stop. The more chances that a Company has to pivot and clearly demonstrate product-market-fit and compelling unit economics, the better

4. If a Company does choose to raise a large funding round, they had better deploy that capital effectively to drive efficient growth and create competitive advantage, or stockpile it to extend runway beyond a typical two-year horizon

As a final teaser, I do think that some of the above rules of thumb differ for AI-first businesses, which typically require more investment up front but benefit from greater economies of scale and growth in the long run. In practice, this means that AI-first Companies typically raise at least one more pre revenue financing round than SaaS companies do, but tend to benefit from greater exponential growth once they take off. That being said, this post is already too long as is so I’ll save that one for another day