Expected value

The average outcome of a decision if you could repeat it many times: each possible result multiplied by its probability, all added together.

Example

A bet paying $10 with 30% probability and losing $2 with 70% probability has an expected value of (0.30 x $10) + (0.70 x -$2) = $3.00 - $1.40 = $1.60.

Important

A positive expected value does not mean you will make money on any single attempt - it describes the average of many attempts, which is why how much you commit to each one matters as much as the calculation.

Related terms

  • Base rate — How often an outcome occurs across the whole population of similar cases, before you know anything specific about the one in front of you.
  • Variance — How widely actual outcomes spread around their average. High variance means individual results routinely land far from the expected value, in both directions.
  • Risk — The chance that an investment's actual outcome differs from what you expected, in either direction.

Lessons that explain it

  • One investment can decide the return of twenty — Venture portfolio returns follow a power law: most of the money comes from very few companies. Working through a portfolio's arithmetic shows why missing the best company matters more than avoiding the worst. (11 min)
  • A follow-on buys the same company at a higher price, so it needs its own maths — Exercising pro rata rights maintains ownership, but the new money earns a lower multiple than the original investment. Modelling follow-ons across scenarios shows when they add value. (11 min)
  • Model the rounds between now and the exit, or your ownership estimate is fiction — Today's percentage is not what you will hold at an exit. Projecting future rounds and pool top-ups gives a realistic ownership figure and a much better sense of what an outcome would return. (12 min)
  • Would you invest in this round if you had never met the company? — A follow-on decision should be judged as a new investment at today's price and today's evidence. What you already invested is gone either way and should not decide what you do next. (9 min)
  • Adding to winners at higher prices often beats rescuing losers at lower ones — Follow-on capital usually has a better expected result in companies with strong evidence, even at higher prices, than in struggling companies at lower prices - though the right choice always depends on the specific evidence. (11 min)
  • Write the follow-on policy before the requests arrive — Deciding in advance what would earn more capital removes the pressure, relationships and urgency that distort follow-on decisions when a request is already on the table. (10 min)

All 578 terms in the Investing glossary