P03 ยท Lesson 2 of 10 ยท 12 min ยท 4 hands-on tasks
Expected Value: The Manager's Superpower
Weigh every possible outcome by how likely it is, add them up, and you can compare any two risky choices on one number. Then check you can survive the bad draws.
๐ฅ Watch it (3 min)
๐ฌ Situation
A big garden trade fair is coming. A stall costs $1,200. Some years shops land huge wholesale deals; some years they sell nothing.
Nina's gut says "too risky". Her friend's gut says "go for it". Guts disagree. Let's put a number on it.
๐ฎ Play
Run the trade fair many times. Each run is one possible fair, drawn using Nina's guesses. Watch the average settle, and see how often she actually loses money.
Nothing yet. Press a button to run some fairs.
A 30% chance of losing money, yet clearly worth it on average. Now change the guesses and see when it stops being worth it.
Positive expected value: worth going, if Nina can afford a bad year.
๐ท๏ธ Name it
Expected value = ฮฃ (probability ร payoff)
| Outcome | Probability | Payoff (after stall) | Probability ร payoff |
|---|---|---|---|
| Big deal | 20% | +$6,800 | +$1,360 |
| A few sales | 50% | +$300 | +$150 |
| Nothing | 30% | โ$1,200 | โ$360 |
| Expected value | 100% | +$1,150 |
| Term | Meaning |
|---|---|
| Expected value (EV) | The average result if you could repeat the choice many times |
| Break-even probability | The chance at which EV = 0 |
| Downside | The worst realistic outcome; check you can survive it |
| Decision vs outcome | A good decision can have a bad result, and the reverse |
๐๏ธ Like you're five: a game costs 1 sticker. Half the time you win 3 stickers, half the time nothing. Play it 10 times: you'll win about 5 times (15 stickers) and pay 10. You come out 5 ahead. One game could still leave you a sticker down.
Real life: insurers, venture capitalists, oil explorers and drug companies live on expected value. A venture fund expects most startups to fail, but a few huge wins make the average great. Insurers do the reverse: they collect a little from many people and pay big amounts to a few. Both work because they make the same kind of bet many, many times.
๐จ Do it: 4 tasks
0 / 4 doneTask 1 of 4 ยท The trade fair
A garden trade fair stall costs $1,200. Nina's guesses:
- 20% chance of a big wholesale deal: +$8,000
- 50% chance of a few sales: +$1,500
- 30% chance of nothing: $0
What's the expected value of going, after the stall cost?
Task 2 of 4 ยท Break-even chance
Ignore the small sales. A stall costs $1,200 and a big deal is worth $8,000. What chance of a big deal makes going break even?
Task 3 of 4 ยท Free shipping
Offering free shipping costs $6 per order. Nina expects it to lift the chance a visitor buys from 3% to 3.5%. Each order makes $20 profit before shipping.
What's the change in expected profit per visitor? (Two decimals.)
Task 4 of 4 ยท Can you survive it?
Option A: a sure +$2,000. Option B: 50% chance of +$10,000, 50% chance of โ$4,000 (EV +$3,000). Nina has $3,000 in the bank. Which is wiser?
๐งฉ Case: Two ways to spend $5,000
โญ VIPNina has $5,000 for marketing this quarter. Option 1: Instagram ads, which reliably bring about $7,000 of profit. Option 2: a booth at a big home show: 25% chance of a retail chain deal worth $30,000, otherwise about $2,000 of sales profit. Sprout Box has $40,000 in the bank.
Which has the higher expected value?
What would you do? VIP members make the call, see what happens next across 2 decisions, and get the expert debrief.
๐ Remember it
A raffle ticket costs $5. There's a 1 in 1,000 chance of winning $2,000. Expected value of buying?
When does expected value work best as a guide?
A good decision turned out badly. What should you conclude?
Expected value = ฮฃ (probability ร payoff). Choose the higher expected value when you'll face the bet many times, but only if you can survive the bad outcomes along the way.
๐ Use it Monday
Pick a decision with uncertain results. List 2 or 3 possible outcomes, give each a rough probability and a value, and work out the expected value. Then ask: what's the worst case, and can we live with it?
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