Non-Ergodic Power Law Investing (Slugging Percentage)
Play for slugging percentage, not batting average — your outcome is not the average outcome.
- Difficulty
- Advanced
- Time to result
- ~ongoing to results
- Steps
- 5
- Confidence
- 85%
Traditional risk models assume returns are normally distributed, but NZS argues markets — like earthquakes or word frequency in Moby Dick — actually follow power laws, so tail events happen far more often than Gaussian math predicts. Worse, portfolio theory relies on 'ensemble averages' across many hypothetical investors, but any individual investor only experiences their own 'time average,' and in games with multiplicative, power-law payoffs (illustrated by a coin-flip contest with positive expected value where most players still go bankrupt), the time average can be ruinous even when the ensemble average looks great — a property called non-ergodicity. The practical response is to size individual optionality bets small, accept being wrong roughly 70% of the time, and optimize for slugging percentage (a few enormous winners) rather than batting average (being right most of the time).
Origin
Drawn from economist Ole Peters' work on ergodicity economics and NZS's own study of power-law distributions in nature (earthquakes, language) and markets.
Core principles
- 01Markets are power-law, not normally, distributed
- 02Your personal outcome (time average) can differ drastically from the theoretical average (ensemble average)
- 03Rare 'tail' events happen far more often than Gaussian models predict
- 04Optimize for magnitude of wins (slugging percentage), not frequency of being right (batting average)
- 05Size bets so that being wrong most of the time doesn't destroy the portfolio
How to run it
- 1
Reject Gaussian risk assumptions
Recognize that standard risk models (based on normal distributions) systematically underestimate the frequency of extreme events in markets.
Pro tip Remember: 'risk models are like airbags that go off at stop signs but not when you get in a crash.'
- 2
Understand ergodicity
Distinguish the 'ensemble average' (the average outcome across many hypothetical parallel investors) from the 'time average' (the actual sequential outcome you personally experience) — in non-ergodic systems these diverge.
- 3
Stress-test with the coin-flip example
Model a game with positive expected value (e.g., +50%/-40% coin flip) played repeatedly; observe that most individual players go bankrupt despite a favorable average.
- 4
Look for power laws in your domain
Check whether the distribution of outcomes in your market resembles a power law (a few huge winners, many small ones) rather than a bell curve.
Pro tip Power laws show up broadly in nature — earthquake magnitude/frequency, word frequency in text — reinforcing that they're the default, not the exception.
- 5
Size bets for slugging, not batting average
Accept a lower 'win rate' (e.g., ~30%) in exchange for occasional multi-bagger winners, sizing each bet small enough that repeated losses don't sink the portfolio.
Watch out Don't judge a strategy's soundness only by how often it's 'right' day to day — value creation concentrates in rare outlier events.
In the wild
In a hypothetical game where winning pays +50% and losing costs -40%, the expected value per flip is positive, so naive analysis suggests everyone should play.
→ Simulated over time, nearly all individual players go bankrupt while a tiny few become massively wealthy, illustrating why time-average outcomes diverge from ensemble-average expectations.
NZS notes that both earthquake magnitude/frequency and word frequency in Moby Dick naturally form power-law curves rather than bell curves.
→ Reinforces that power-law, not normal, distributions are the default pattern in complex systems, including markets.
Common mistakes
Trusting Gaussian Risk Models
Treating market moves as normally distributed causes investors to badly underestimate the frequency of extreme ('three-sigma') events, which occur far more often than the math suggests.
Optimizing for Batting Average
Demanding a high win-rate on every position ignores that most durable value creation comes from a small number of huge, asymmetric winners, not from being right most of the time.
Is it for you?
Best for
Investors constructing diversified portfolios of asymmetric bets who want a rigorous alternative to normal-distribution risk models.
Not ideal for
Investors who need consistent, low-variance quarterly returns or who rely on standard mean-variance optimization.
From the transcript
“when the time average does not equal the ensemble average that is called a non-ergodic system.”
“we're playing for slugging percentage, where even if only one out of three work, but you know, those are are multi-baggers and can really create…”
From the episode
Complexity Investing & Semiconductors (with NZS Capital)