Expected Value (EV)

Expected Value is a concept from probability theory that helps you make rational decisions when outcomes are uncertain. Instead of asking "What's the best case?" or "What's the worst case?", EV asks: "If I made this decision many times, what would the average outcome be?" It forces you to consider both the magnitude and the likelihood of each possible outcome.

1. List all possible outcomes — For a given decision, what could happen? Include both good and bad outcomes.
2. Estimate the probability of each — How likely is each outcome? Probabilities should sum to 100%.
3. Assign a value to each outcome — What is each outcome worth? Use dollars, impact points, or any consistent unit.
4. Calculate EV — Multiply each outcome's value by its probability, then sum:

• EV = Σ (probability × value)

1. Compare options — The option with the highest EV is the mathematically rational choice.
2. Consider variance — Two options can have the same EV but very different risk profiles. A high-variance option might be inappropriate even if its EV is slightly better (e.g., betting the company).

• Repeated decisions (hiring, feature prioritization)
• When you can afford occasional losses
• Portfolio decisions (not single all-or-nothing bets)

• 70% chance of +$500K revenue → 0.7 × $500K = $350K
• 20% chance of +$100K revenue → 0.2 × $100K = $20K
• 10% chance of -$200K (flop + opportunity cost) → 0.1 × -$200K = -$20K
• EV = $350K

• 30% chance of +$2M revenue → 0.3 × $2M = $600K
• 40% chance of +$100K revenue → 0.4 × $100K = $40K
• 30% chance of -$500K → 0.3 × -$500K = -$150K
• EV = $490K

Expected Value helps you make rational decisions under uncertainty by weighing all outcomes by their probability. It's the antidote to both unwarranted optimism and paralyzing risk aversion.