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Expected Value

Expected value (EV) is a fundamental concept in probabilistic thinking and decision-making. It involves quantifying the potential outcomes of various decisions by multiplying each outcome by its probability of occurring, then summing those results. By using expected value, you assess choices more systematically, focusing not just on potential rewards or risks individually, but on their weighted long-term outcomes.

Formally, the expected value is calculated as:

EV=∑Probability of outcome×Value of outcomeEV = \sum \text{Probability of outcome} \times \text{Value of outcome}

Why Use Expected Value Thinking?​

Expected value thinking allows decisions to be made objectively, especially when uncertainty is high. Rather than relying solely on intuition or immediate outcomes, this method helps you consistently maximize long-term results by considering probabilities and impacts simultaneously.

Examples of Expected Value in Action​

Investing​

Suppose you have an investment with a 50% chance of gaining $200 and a 50% chance of losing $100:

  • EV=(0.5×200)+(0.5×−100)=100−50=50EV = (0.5 \times 200) + (0.5 \times -100) = 100 - 50 = 50

The positive EV of $50 indicates that, despite the risk, repeatedly making similar investments would likely be profitable over time.

Product Development​

Imagine a feature with a 30% chance of significantly boosting revenue by $500,000, and a 70% chance it generates no return:

  • EV=(0.3×500,000)+(0.7×0)=150,000EV = (0.3 \times 500,000) + (0.7 \times 0) = 150,000

Despite its lower probability of success, the high potential return makes pursuing the feature worthwhile from an expected value standpoint.

Insurance​

Purchasing insurance generally has a negative expected value in purely financial terms. You typically pay premiums exceeding the expected payout to protect against losses. Yet insurance may still be rational due to the enormous potential downside of certain risks.

For a deeper philosophical/mathematical exploration of when insurance is worthwhile, this is the best article I've read on this topic: When is Insurance Worth It?

When Expected Value is Not Enough​

While expected value thinking is powerful, it doesn't account fully for non-financial factors such as emotional well-being, ethics, or personal preferences. Decisions involving safety, happiness, or moral judgments often require a more nuanced approach beyond strictly probabilistic calculations.

To incorporate these, it may require consideration of the expected utility.