What it means
The concept came from gambling mathematics and moved into business because most commercial decisions are bets of one kind or another. Whether to sue, to bid, to launch or to insure all involve outcomes that are uncertain, and expected value gives a single comparable number for each option.
Its greatest practical use is in decisions where the outcomes are lopsided. A choice with a 10% chance of making $9,000,000 and a 90% chance of losing $500,000 has a positive expected value of $450,000, which is not obvious from the headline odds and is exactly the kind of judgement people get wrong intuitively.
Working it out forces three things into the open: the full list of outcomes, an honest probability for each, and the money attached to each. Teams often discover that the argument in the room was never about the numbers but about wildly different unstated beliefs on one of those three inputs.
The limitation is that expected value assumes you can repeat the bet. A positive expected value is small comfort if the losing branch bankrupts the company, which is why insurers happily write policies with negative expected value from the customer's point of view and customers happily buy them.
A useful extension is the expected value of information, which asks what you would pay to remove some of the uncertainty. If a $60,000 market study could move a decision worth $2,000,000 either way, buying the study is usually the highest-return action available.
In practice
Real-world examples.
Example
A software firm is offered a settlement of $600,000 to end a contract dispute. Its lawyers estimate a 55% chance of winning $1,800,000 and a 45% chance of losing and paying $400,000 in costs, giving an expected value of $810,000, so the company rejects the offer and continues.
Example
A construction contractor decides how much to spend preparing a competitive tender. Winning is worth $2,500,000 in margin, the estimated chance of winning is 20% and the bid costs $180,000 to prepare, so the expected value is $500,000 against a certain $180,000 cost and the bid proceeds.
Example
An airline chooses whether to hedge its fuel purchases. Hedging has a slightly negative expected value because the counterparty charges a margin, but the airline buys it anyway to make its costs predictable, which is a deliberate decision to pay for certainty.
Think of it
“Expected value is the average outcome when you account for all possibilities and their chances.
Formula
Calculation
Expected Value = Sum of (Probability of each outcome x Monetary value of that outcome)
A consumer goods company is deciding whether to launch a new range. It sees three outcomes over the first three years: a 30% chance of a strong launch worth $4,000,000 in cumulative profit, a 50% chance of a modest launch worth $1,000,000, and a 20% chance of failure costing $2,000,000.
Strong: 0.30 x $4,000,000 = $1,200,000
Modest: 0.50 x $1,000,000 = $500,000
Failure: 0.20 x -$2,000,000 = -$400,000
Expected Value = $1,200,000 + $500,000 - $400,000 = $1,300,000
Against a required upfront investment of $900,000, the launch has a positive expected value of $1,300,000 - $900,000 = $400,000, so on this basis it goes ahead.Case study
Seen in the real world.
What follows is an illustrative, fictional example. Merrow Diagnostics had to decide whether to pursue regulatory approval for a second use of an existing test. Approval would be worth $18,000,000 over the product's life, the internal estimate of success was 25%, and the submission programme would cost $2,600,000 spread over 20 months.
The expected value calculation was 0.25 x $18,000,000 = $4,500,000 against a cost of $2,600,000, leaving $1,900,000 of positive expected value. The chief executive nearly approved it on the spot, until the head of regulatory affairs pointed out that the 25% figure was really two questions stacked together: a 50% chance the trial data would be strong enough to submit, and a 50% chance of approval if it were.
In this fictional case the company restructured the programme into two stages, spending $700,000 to reach the data readout and holding back the remaining $1,900,000 until the first question was answered. The expected value of the staged plan was higher than the single-shot plan, because the company only paid for the second stage in the worlds where it was worth paying for.
Watch out
Common mistakes.
- Using expected value for a one-off decision that could ruin the business, when the average across many repetitions is irrelevant if you only get one attempt.
- Estimating probabilities to look precise, such as 37%, when the underlying judgement is really no better than "roughly a third".
- Leaving out the do-nothing option, so a proposal is compared against zero rather than against what the money and effort would earn elsewhere.
Questions
People also ask.
How is expected value different from expected return?
Expected value is measured in currency and expected return in percentage terms, so the two are the same calculation applied to different units.
Should I always choose the option with the highest expected value?
Not always, because the size of the downside and your ability to absorb it matter, and a slightly lower expected value with a survivable worst case is often the better choice.
What if I genuinely cannot estimate the probabilities?
Work backwards and ask what probability would be needed to make the decision break even, then judge whether the real chance is above or below that threshold.
From the founder's library
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