Your fund has twenty-two positions. In the model, each one returns a respectable multiple and the arithmetic works.
That is not how the result will arrive. One or two positions will produce almost all of it, and every projection built on the typical case is describing an outcome that does not occur.
Why these three models
The decision is how to size a portfolio and what to promise about it, and for founders on the other side of the table, what your investor actually needs from you. The features that fire are outcomes concentrated in a small number of positions, a forecasting habit that builds each case from its own details, and a frequency question that the details cannot answer.
Three lenses. Heavy tails produce a random answer about where the result comes from. The inside view produces an equilibrium answer about why your model looks reasonable and is wrong in a predictable direction. Base rates produce a cycle answer about the only quantity that transfers between deals. The first is widely repeated and badly understood. The other two are what make it operational.
1. The result lives in the tail, and the label is often overclaimed
Start with the part that is solid. In venture returns, in customer revenue, in city sizes and in firm sizes, outcomes are not distributed around a typical value. A small number of cases account for a large share of the total, so the mean sits far above the median and the average case describes almost nobody.1
The practical consequences are direct. A portfolio’s outcome is decided by its best one or two positions, which means the cost of missing the best position dominates the cost of including several bad ones. That flips the usual instinct about selectivity: past a point, tightening your filter removes more upside than downside, because the filter cannot identify the tail case reliably and the tail case is the entire result.
Now the part that is routinely overstated, and it matters because the overstatement is what makes people trust the maths too far. The specific claim that these distributions are power laws, with the exact functional form and the tidy properties that come with it, is much weaker than the general claim that they are heavy-tailed. A systematic examination of nearly one thousand real-world network datasets found that only about four percent showed the strongest evidence of scale-free structure, and that a majority were at best weakly consistent with it.2
Take the operational implication and leave the functional form. Concentration is real and you should build for it. Precise tail exponents, and any calculation that depends on them, are a level of confidence the data does not support. Build for the tail and refuse to price it.
Building for the tail has a consequence that gets skipped, and it decides more results than selection does. A fund of fixed size that takes more shots is writing smaller cheques, and a smaller cheque in the one position that works is a smaller share of the only outcome that pays. Ten million dollars across twenty-two first cheques with nothing held back is a different instrument from the same ten million across twelve positions with half the capital reserved. The first buys more chances at finding the tail. The second buys more of the tail once it appears. You cannot have both, and the fund you already raised has chosen one.
The failure mode of the more-shots argument is visible in advance. Watch for the round in which your best position raises and you cannot participate. That is the moment the portfolio’s shape costs you money, and it is the only real test of a reserve policy. If that has already happened once, the correction is not more positions.
2. Your model is written from inside the deal
Everyone in this business knows the tail exists. The models still get built around the median case, and the reason is a specific and well-documented habit.
When you forecast a particular investment, you reason from its own particulars: this team, this market, this pipeline, this quarter’s traction. That is the inside view. The alternative is to ask what happened to the class of things this belongs to, which is the outside view, and it is systematically more accurate while feeling much less informative because it discards everything specific you know.3
The failure is not that the inside view is uninformative. It is that it produces confident forecasts clustered around a plausible middle, and a portfolio of plausible middles is exactly the object that heavy tails say cannot happen. Twenty-two positions each modelled to return three times will not return three times; a few will return far more and most will return nothing, and the difference between those two pictures is the difference between a fund that works and one that does not.
You are not being optimistic, you are being specific, and specificity is what removes the tail from the model.
The correction is procedural rather than attitudinal. Before the deal-specific analysis, write the reference class and its historical distribution. Not the average outcome. The shape: what fraction returned nothing, what fraction returned the fund. Then let the specifics move you off that shape, and record by how much and why. Most investors have never written the shape down, which means the inside view has nothing to be corrected against.
Expect an objection from your own team, and it is a fair one. Reasoning from the specifics is what they are paid for, and the outside view feels like it throws that work away. It does not replace the work. It fixes where the work starts. Write the class shape first and the deal analysis second, on the same page, in that order. The order is the method: a reference class written after the memo is written to agree with it.
Where the class is too thin to write, borrow the structure rather than the number. Take the twenty companies you have already backed, at the stage you back them, and write what happened: how many are gone, how many are alive and flat, how many returned real money, how many are undecided. It is a small sample and it is genuinely yours. Set it against the memos you wrote at the time and you learn whether your specifics have ever predicted anything, which is the only thing this exercise is for.
3. The base rate is the only number that transfers
The third model is the one that decides whether the second is doing anything.
Under a weak or noisy signal, the sensible estimate stays close to the underlying frequency and moves away from it only in proportion to how diagnostic the new information is. Substituting a compelling specific case for the frequency is the standard error, and it is stable enough to be treated as the default rather than as an occasional lapse.4
In practice this is the difference between two sentences that sound similar. This company could be a fund-returner is a statement about possibility and carries no information. In this stage and geography, roughly this fraction of companies reach that outcome, and here is what is different about this one is a statement with a base rate in it, and it can be wrong in a way you can later check.
The uncomfortable version for African early-stage investing specifically is that the base rates are thin. There are not decades of exit data at the sample sizes that would make a confident frequency claim honest. That is a real limitation and the correct response is not to substitute a global base rate as though it applied, nor to abandon the discipline. It is to state the frequency you are assuming, mark it as an assumption rather than as a finding, and record what would revise it. An assumption you have written down is auditable. A feeling is not.
State the outcome as well as the frequency, because in this market the two are usually mismatched. A fund modelling a fund-returner is often implicitly modelling an exit route that does not exist locally: a listing, or an acquisition by a global buyer at a global multiple. The exits that clear in East Africa are trade sales to regional groups, secondaries to a later fund, and occasionally a buyout financed out of cash flow. Underwrite the outcome your market produces, at the multiple that outcome produces, and the tail you are building for becomes something you can name.
Then write the revision trigger beside it, in one line. Something of the form: if fewer than two of the next ten positions raise a priced round within eighteen months, the assumed frequency was too high and the cheque size comes down. A base rate with a trigger attached is a decision rule. A base rate without one is a sentence in a memo that nobody will ever be able to say was wrong.
What the three say together
- Write the shape of the reference class before you write the deal memo. Fraction to zero, fraction to a modest outcome, fraction to a fund-returner.
- Size the portfolio for the tail, not the median. The binding question is how many independent chances at the tail you can afford, not how good your average position looks.
- State your base rate explicitly and label it as an assumption where the data is thin. Then record what evidence would move it.
- Reserve deliberately. If the result comes from one or two positions, capital held back to follow them is not caution, it is where the return is captured.
Where they disagree
The tail argument and the base-rate argument conflict on selectivity, and the conflict is sharp.
The tail view says take more shots, because the cost of missing the exceptional case exceeds the cost of several failures and no filter reliably identifies it in advance. The base-rate view says that if the frequency of the exceptional outcome is genuinely low in your market, more shots at a low frequency is a slow way to lose the fund, and discipline is what protects you.
Both are right under different frequencies, and neither is a philosophy you get to pick. The number that decides it is the base rate you claimed in step three, which is exactly the number that is weakest in emerging markets. That is an honest finding rather than a gap in the article: in a market with thin outcome data, the portfolio-construction question does not have a defensible analytical answer, and anyone offering one with confidence is extrapolating from somewhere else. What you can do is state which regime you believe you are in and size accordingly, so that the assumption is visible to your investors rather than buried in a spreadsheet.
What none of them contain
None of the three contains your ability to help. All of them treat outcomes as drawn from a distribution that you observe rather than influence. An investor who materially improves a company’s odds is changing the distribution, and none of this arithmetic will tell you whether you are that investor. The honest test is whether founders who have other options choose you, which is evidence you can collect and most funds do not.
None of them handles correlation between positions. Heavy-tail reasoning about a portfolio assumes the draws are roughly independent. Twenty-two companies selling to the same three banks in the same country are not independent draws, and the diversification you believe you have is smaller than the position count suggests.
And for founders reading this from the other side: none of these models says anything about whether your company is good. They say what your investor needs, which is different. A business that will produce a solid, unspectacular return is a good business and a poor fit for a fund that requires a tail outcome to work. Knowing which conversation you are in is worth more than a better deck.
The one action that survives the ignorance: before your next investment committee, write one line stating the fraction of companies in this reference class that you believe reach the outcome you are underwriting, and mark it as data or as assumption. If every line in the memo is assumption, that is the finding, and it should change the size of the cheque rather than the confidence of the argument.
Who has to move
This belongs to whoever sets portfolio construction, not to the person sourcing deals, because the failure is in the shape of the fund rather than in any single decision. The instinct after a run of write-offs is to raise the bar on new investments, which reduces the number of chances at the tail and feels like discipline. The cheapest first test is retrospective: take your last twenty positions, write down the reference-class shape you would have used at the time, and compare it to what actually happened. It costs a morning, it uses only data you own, and it tells you whether your selection is adding anything to the base rate.
Sources and notes
- Albert-László Barabási, Network Science, Cambridge University Press. Heavy-tailed and scale-free degree distributions, the divergence between mean and median, and the mechanisms that generate concentration, including growth with preferential attachment, are developed in the chapters on the scale-free property and the Barabási-Albert model. Used in section 1 for the general property of concentration, not for any claim about a specific exponent.
- Anna D. Broido and Aaron Clauset, Scale-free networks are rare, Nature Communications 10, 2019, article 1017. Open access: https://www.nature.com/articles/s41467-019-08746-5. Applying statistical tests to a corpus of nearly one thousand network datasets, the authors report that scale-free structure is not universal, that only a small minority of datasets show the strongest evidence for it, and that most are at best weakly consistent with the scale-free hypothesis. Cited in section 1 for the caution about the label. Note the scope: this is a result about networks, and it is used here as a general warning against over-precise tail claims rather than as a direct measurement of venture returns, for which no comparable corpus exists.
- Sanjit S. Dhami, The Foundations of Behavioral Economic Analysis, Oxford University Press. The distinction between inside and outside views, and the associated tendency to underestimate durations and overestimate success when forecasting from case-specific detail, sit in the part on bounded rationality alongside the planning fallacy. The original framing is due to Kahneman and Lovallo. Used in section 2 for the direction of the error only.
- Sanjit S. Dhami, The Foundations of Behavioral Economic Analysis, Oxford University Press. Base rate neglect and its treatment within the judgement-heuristics literature. Used in section 3 for the direction of the effect. Magnitudes in this literature are sensitive to how the problem is presented and none is claimed here.
A note on a number this article does not give. It would be easy to state what fraction of early-stage African companies reach a fund-returning outcome. The exit data at that sample size does not exist, and any figure offered would be a global number wearing local clothes. The method survives the missing number: state your assumed frequency, label it, and record what would revise it.
Joshua Agonya Pi’Rwot, Founder.