expected value
Low frequency in general discourse; high frequency in mathematics, statistics, finance, gambling, and certain scientific/engineering fields.Formal, Technical, Academic. Rare in informal or colloquial speech unless discussing probability or decision-making in a technical sense.
Definition
Meaning
The predicted average outcome of a random variable over many trials, calculated as the probability-weighted sum of all possible values.
In broader, non-technical contexts, the outcome or benefit that is anticipated or considered most likely based on current knowledge or assumptions.
Linguistics
Semantic Notes
Primarily a technical term. Its lay usage often conflates with simple expectation or prediction, losing the precise mathematical meaning of a probability-weighted average.
Dialectal Variation
British vs American Usage
Differences
No significant differences in definition or usage. Spelling and pronunciation follow standard BrE/AmE patterns for the constituent words.
Connotations
Identical technical connotations. In business contexts, both regions use it similarly in risk assessment and financial modelling.
Frequency
Equally frequent in academic and professional technical contexts in both regions.
Vocabulary
Collocations
Grammar
Valency Patterns
The expected value of [NOUN PHRASE] is [NUMBER].To calculate/find/determine the expected value.[Someone] evaluated the expected value.Vocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Phrases
Idioms & Phrases
- “A positive expected value bet”
- “Playing with negative expected value (often shortened to -EV in gaming communities)”
Usage
Context Usage
Business
Used in decision theory, investment analysis, and project valuation to quantify the average return of a risky venture.
Academic
A foundational concept in probability theory, statistics, and quantitative fields like economics and engineering.
Everyday
Rare. Might be used when discussing the average payoff of a repeated activity like a lottery ticket or a casino game.
Technical
Precise mathematical definition: E[X] = Σ x_i * p_i for discrete variables, or ∫ x f(x) dx for continuous variables.
Examples
By Part of Speech
verb
British English
- We need to value the asset.
- They are expecting a delivery.
American English
- We need to value the asset.
- They are expecting a delivery.
adverb
British English
- Unexpectedly, the value fell.
- He predictably chose the safest option.
American English
- Unexpectedly, the value fell.
- He predictably chose the safest option.
adjective
British English
- The expected outcome is favourable.
- She received the expected results.
American English
- The expected outcome is favorable.
- She received the expected results.
Examples
By CEFR Level
- I expect the value of my gift to be about twenty pounds.
- The expected time of arrival is 5 PM.
- The expected value of the prize in the raffle is low because so many tickets are sold.
- In the long run, a game with a negative expected value will lose you money.
- To make a rational decision, an investor should compare the expected values of different portfolios.
- The insurance premium is based on the expected value of claims the company will have to pay.
- Although the start-up carries significant risk, its high potential payoff gives it a positive expected value, making it an attractive investment on paper.
- The researcher used the law of large numbers to demonstrate how the sample mean converges to the population's expected value.
Learning
Memory Aids
Mnemonic
Think of it as the average result you'd get if you could repeat a chance-based experiment (like rolling dice) an infinite number of times.
Conceptual Metaphor
THE MEAN IS THE CENTRE OF GRAVITY (the expected value is the balance point of a probability distribution).
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Do not translate as "ожидаемая ценность". The correct direct equivalent is "математическое ожидание" (матожидание). Translating as "среднее значение" is acceptable only if the probabilistic context is clear.
Common Mistakes
- Using 'expected value' to mean simply what one hopes for ('I expect a high value').
- Confusing 'expected value' with 'most likely value' (mode).
Practice
Quiz
In probability theory, the 'expected value' is best described as:
FAQ
Frequently Asked Questions
In probability, it is the theoretical average (mean) of a random variable over an infinite number of trials. For a finite data set, the calculated average (sample mean) is an estimate of this true expected value.
Yes, absolutely. The expected value of rolling a standard die is 3.5, but you can never roll a 3.5. It represents the long-run average, not a possible single outcome.
No. Expected value is a long-term statistical average. In the short term, due to variance, you can lose money on a +EV bet or win on a -EV bet. It indicates a favourable or unfavourable proposition over many repetitions.
Expected value is purely monetary or numerical. Expected utility incorporates a person's subjective preferences and risk tolerance, modeling the anticipated satisfaction or benefit from an outcome, not just its numerical value.