an Oxford statistician exposed the probability error that helped send a mother to prison.
the number nobody challenged: 1 in 73 million.
Sally Clark had two babies who died suddenly. they were initially thought to have died from sudden infant death syndrome. during Clark’s murder trial, an expert told the court that the chance of two natural deaths in a professional, non-smoking family like hers was 1 in 73 million.
the calculation reached the jury without being challenged. Clark was convicted. her convictions were later overturned on a second appeal.
Oxford statistician Peter Donnelly used the case to show where the math broke. the expert started with a reported risk of 1 in 8,500 for one death, assumed the two deaths were independent, then squared it:
8,500 × 8,500 ≈ 73 millionbut the first death was new information.
shared genetic or environmental factors could place the same family in a higher-risk group. treating event two as if nothing changed meant discarding what event one revealed.
after the conviction, a newspaper misread the number again. it turned the stated probability of two natural deaths if Clark was innocent into the probability that Clark was innocent after two deaths.
those are different questions.
the same error appears in portfolios that look diversified across 20 positions while every position depends on the same rates, liquidity or counterparty. one failure can change the odds for the rest.
before multiplying probabilities, ask whether event one changed what you know about event two.
the official TED talk is free. the Clark case begins at 13:24
the article below shows how base rates and Bayesian updates keep the same error out of your decisions
Team Spirit made it through the lower bracket without dropping a single map
i still backed the team that sent them there in the first place
Team Vision to win The International
Vision already beat Spirit 2-1 in the upper bracket
then Spirit came back and destroyed:
- Team Liquid 2-0
- BOOMBOYS 2-0
- Team Yandex 2-0
now map 1 of the grand final is live and more than $6M has already traded on the rematch
i bought Team Vision through @thefireflyapp at around 59.5¢
ofc they can still lose
one bad draft
one lost fight
one stupid buyback
and the whole calculation gets cooked
but thats the point
a good bet can lose
a terrible bet can win
the result only shows what happened once
the price, logic and size show if the decision was worth making
i sized the position so one BO5 cant kill my bankroll and left the receipt inside Firefly
no deleting the prediction if Spirit wins
no “i knew it” if Vision wins
the article below has the full 6-part system behind this decision
read it while my thesis is getting stress-tested live
after the final everyone becomes a genius
Warren Buffett lost $2,000 on a gas station.
by 2001, he priced that mistake at $6 billion.
he was about 20 when he bought half of a Sinclair filling station with a friend. Buffett had roughly $10,000 at the time, put in $2,000, and lost it all.
that was 20% of everything he had.
about five decades later, he told University of Georgia students that the opportunity cost had grown to $6 billion.
that was his own counterfactual estimate, not a booked $6 billion loss. the cash loss was $2,000. the larger number measured what the same capital could have become elsewhere.
then Buffett went further: his biggest mistakes were omissions.
he estimated that Berkshire could have made about $5 billion from Fannie Mae, a business he understood but did not buy. conventional accounting recorded nothing because no purchase ever happened.
one practical extension of Buffett’s story is to keep two ledgers: one for completed trades, and one for serious opportunities you understood but rejected.
for every serious pass, record:
- the opportunity you rejected
- why you rejected it
- the capital it required
- what evidence would reopen the decision
review only opportunities that were understandable and actionable at the time. otherwise hindsight turns every winner you missed into a fake mistake.
the complete Warren Buffett talk is attached. after removing the university introduction, the gas-station story begins at 24:42.
Buffett’s story shows where the ledger is incomplete. the quoted Article supplies the underlying tools: EV, base rates, sunk costs and Bayesian updates for improving the next decision before its outcome is known.
THE MOST DANGEROUS ASSUMPTION IN FINANCE IS THAT YOUR RISKS ARE INDEPENDENT.
In a Yale lecture on probability, Robert Shiller explains why diversification can look mathematically safe right until a crisis begins.
If you own 100 independent risks, one bad outcome barely matters. Spread the exposure wide enough and the law of large numbers starts working in your favor. This basic idea sits underneath insurance, portfolios and much of modern risk management.
But 2008 exposed the problem.
Risks that looked separate weren't actually separate. Housing prices fell, mortgage defaults increased, securities backed by those mortgages lost value and institutions exposed to the same system started failing together.
The individual probabilities weren't the whole problem.
The relationships between them were.
Shiller spends the first part of the lecture building probability from scratch. Later he explains independence and why its failure matters during financial crises. Near the end, he attacks another comfortable assumption: that extreme market moves behave like a normal bell curve. Real financial markets produce extreme events more often than that model would suggest.
That's the part worth understanding.
You can calculate expected value, update probabilities and size every position correctly.
But if the risks you thought were separate all become the same risk at the worst possible moment, the model protecting you can become the thing that blinds you.
The dangerous question isn't only:
“What are the odds I'm wrong?”
It's:
“What else becomes wrong at the same time?”
Warren Buffett lost $2,000 on a gas station.
by 2001, he priced that mistake at $6 billion.
he was about 20 when he bought half of a Sinclair filling station with a friend. Buffett had roughly $10,000 at the time, put in $2,000, and lost it all.
that was 20% of everything he had.
about five decades later, he told University of Georgia students that the opportunity cost had grown to $6 billion.
that was his own counterfactual estimate, not a booked $6 billion loss. the cash loss was $2,000. the larger number measured what the same capital could have become elsewhere.
then Buffett went further: his biggest mistakes were omissions.
he estimated that Berkshire could have made about $5 billion from Fannie Mae, a business he understood but did not buy. conventional accounting recorded nothing because no purchase ever happened.
one practical extension of Buffett’s story is to keep two ledgers: one for completed trades, and one for serious opportunities you understood but rejected.
for every serious pass, record:
- the opportunity you rejected
- why you rejected it
- the capital it required
- what evidence would reopen the decision
review only opportunities that were understandable and actionable at the time. otherwise hindsight turns every winner you missed into a fake mistake.
the complete Warren Buffett talk is attached. after removing the university introduction, the gas-station story begins at 24:42.
Buffett’s story shows where the ledger is incomplete. the quoted Article supplies the underlying tools: EV, base rates, sunk costs and Bayesian updates for improving the next decision before its outcome is known.