expected value
Expected Value is the average outcome you would get if you repeated a bet or investment many times, considering each possible result by its chance of happening.
In plain English
"So if I put ₦100,000 into this thing and it doubles, I am happy. But if it crashes, I lose everything. How do I even decide?" Tunde asked his cousin Ada, who had just finished a finance course in Leeds.
"You do not decide by hoping," Ada said. "You decide by working out expected value. You take every possible outcome, multiply it by how likely it is, and add them all up. That number tells you what you should really expect on average, not what you wish would happen."
Say there is a seventy percent chance the investment stays flat, a twenty percent chance it doubles, and a ten percent chance it goes to zero. Ada worked it out on a napkin. Seventy percent of ₦100,000 is ₦70,000. Twenty percent of ₦200,000 is ₦40,000. Ten percent of ₦0 is ₦0. Add those together and the expected value is ₦110,000.
That does not mean Tunde will get exactly ₦110,000. Nobody gets the average in one try. It means if he faced this same choice a hundred times, ₦110,000 is roughly what he would land on per attempt, and that beats leaving the money in a savings account earning almost nothing.
This is the calm arithmetic behind every serious investing decision, from a trader in Lagos choosing between two stocks, to a fund manager in London pricing a risky bond, to someone abroad deciding whether to send money home now or wait for a better exchange rate. Expected value will not tell you the future. It tells you which bet is smarter to keep making.
An investment has a sixty percent chance of returning ₦150,000 and a forty percent chance of returning ₦20,000 on a ₦100,000 stake. Expected value equals (0.6 times ₦150,000) plus (0.4 times ₦20,000), which is ₦90,000 plus ₦8,000, giving ₦98,000. Slightly below the ₦100,000 stake, so on average this bet loses money over time even though a win feels good in the moment.
Questions people ask
Does expected value guarantee that outcome will happen?
No. It is an average over many repeated attempts, not a promise for a single try. You could still lose money on one investment even if its expected value is positive, because real life gives you one roll of the dice at a time, not a hundred.
Why does expected value matter if I only invest once?
Because even a single decision is better made with clear odds in mind. Choosing the option with the higher expected value simply means you are consistently choosing the smarter side of the bet, which adds up nicely if you keep investing over years.
How do I estimate the probabilities if nobody tells me the odds?
You will not get exact numbers, but you can make honest estimates using history, research, and common sense, the way a stock analyst studies past earnings before guessing future ones. Rough odds thoughtfully applied beat no odds at all.
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