A probability tree from seed to exit, the expected multiple it implies, and why a 30-company fund with the right average can still return less than half its money.
Multiply the graduation rates down the tree, weight each stopping point by its multiple, and add. With illustrative rates of 40 per cent from seed to Series A, then 50, 50 and 40 per cent, only 4.0 per cent of seed companies reach a 40x exit, yet that branch supplies 80.0 per cent of an expected 2.00x gross multiple. The same tree says a 30-company fund has a 29.4 per cent chance of finding no such company at all.
Worked in full in Venture Capital by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Graduation rates, the share of companies that raise the next round, are the one portfolio statistic a seed manager can observe years before exits arrive. They are also the cleanest way to see the power law as arithmetic rather than anecdote: a few conditional probabilities, multiplied together, produce a distribution in which almost all of the value sits in a branch almost nobody reaches.
| Stage | Graduation rate | If the company stops here | Multiple |
|---|---|---|---|
| Seed to Series A | 40% | Shut down at seed | 0.0x |
| Series A to Series B | 50% | Sold or wound down after the A | 0.3x |
| Series B to Series C | 50% | Modest sale after the B | 1.0x |
| Series C to large exit | 40% | Good sale after the C | 4.0x |
| Large exit | The fund-returner | 40.0x |
None of these figures is a market statistic. They are round numbers chosen to make the mechanism visible; replace them with your own portfolio's history before drawing conclusions about it.
P(stops at seed) = 1 − 40% = 60.0%
P(stops after A) = 40% × (1 − 50%) = 20.0%
P(stops after B) = 40% × 50% × (1 − 50%) = 10.0%
P(stops after C) = 40% × 50% × 50% × (1 − 40%) = 6.0%
P(large exit) = 40% × 50% × 50% × 40% = 4.0%
In Excel, the reach probability of stage n: =PRODUCT($B$2:Bn); the expected multiple: =SUMPRODUCT(Probabilities,Multiples).
| Ending | Probability | Multiple | Contribution | Share of value |
|---|---|---|---|---|
| Stops at seed | 60.0% | 0.0x | 0.00x | 0.0% |
| Stops after A | 20.0% | 0.3x | 0.06x | 3.0% |
| Stops after B | 10.0% | 1.0x | 0.10x | 5.0% |
| Stops after C | 6.0% | 4.0x | 0.24x | 12.0% |
| Large exit | 4.0% | 40.0x | 1.60x | 80.0% |
| Expected multiple | 100.0% | 2.00x | 100.0% |
Eighty per cent of companies lose money, and the portfolio is still worth 2.00x on average. Strip out the large-exit branch and the other 96 per cent of companies are worth 0.42x each. This is the same shape that makes the median venture investment return less than 1x, here derived from four rates instead of observed after the fact.
An expected value describes the average over many draws. A fund gets 30 draws. With a 4.0 per cent chance per company, it expects 1.2 large exits, and the binomial arithmetic gives:
P(no large exit in 30) = (1 − 4.0%)^30 = 29.4%, fund multiple about 0.42x
One large exit: (40.0 + 29 × 0.42) ÷ 30 = 1.74x
Two large exits: 3.06x
The fund's outcome is a lottery over a handful of draws, and the 2.00x average is a result almost no fund actually reports. That is why portfolio size is a decision about the odds of drawing the branch, worked in how many companies a VC fund should invest in.
| Seed to Series A | C to exit 30% | C to exit 40% | C to exit 50% |
|---|---|---|---|
| 30% | 1.23x | 1.50x | 1.77x |
| 40% | 1.64x | 2.00x | 2.36x |
| 50% | 2.05x | 2.50x | 2.95x |
The first rate multiplies every outcome after it, so the expected multiple is exactly proportional to it: 0.050x per point, 25.0 per cent of the total for each ten points. One point on the last step is worth 0.036x, because it only converts a 4.0x outcome into a 40.0x one for the 10.0 per cent of companies that reach Series C. Ten points on either middle stage move the result by 18.8 and 17.4 per cent. To reach 3.0x expected on seed selection alone, the seed to Series A rate would have to be 60.0 per cent.
Reading your own portfolio: graduation rates are visible in year two or three, exits in year eight or later. The tree turns the early signal into an expected multiple, provided the multiples at each stopping point are your own and not borrowed from a better vintage.
The common mistake is to judge a seed portfolio by its later-stage graduation rates alone, which look healthy because they are conditional on survival, or to average the rates rather than multiply them. Four respectable-looking rates averaging 45 per cent compound to a 4.0 per cent chance of the outcome that pays for the fund. The second mistake is to read the expected multiple as the fund's likely result. With a 29.4 per cent chance of no large exit, the distribution of fund outcomes is wide, and the manager's real lever is the number of draws and the size of the best branch, not the average.
Graduation rates compound: 40, 50, 50 and 40 per cent leave 4.0 per cent of companies at the exit that carries 80.0 per cent of the value. The expected multiple is 2.00x; the fund you actually run returns about 0.42x, 1.74x or 3.06x if it draws zero, one or two of them, and only rarely more. The book's 28-position fund, ranked by proceeds with a tick box on every line, is in the free workbook for this case.
There is no single benchmark, and published rates vary by vintage and source. What the arithmetic shows is the sensitivity: in this illustrative tree the expected multiple is exactly proportional to the seed to Series A rate, 0.050x per point. At 40 per cent the portfolio is worth 2.00x gross; it needs 60.0 per cent for 3.0x if nothing else improves, and falls to 1.0x at 20.0 per cent.
Because 80.0 per cent of the expected value sits in a branch with a 4.0 per cent probability. Across 30 equal seed cheques the fund expects 1.2 big exits, but has a 29.4 per cent chance of none, and then returns about 0.42x. One big exit gives 1.74x and two give 3.06x. The average describes many funds, not yours.
In points, the earliest, because it multiplies every later outcome. Here one point of seed to Series A graduation is worth 0.050x of expected multiple, against 0.036x for one point of the last step to a large exit. Ten points on the seed rate moves the expected multiple by 25.0 per cent, from 2.00x to 2.50x.
This article is one calculation from Venture Capital. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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