Probability and Basic Statistics

Losing more often than you win doesn't mean you're losing money.

• Calculate the expected value of a repeated decision by weighing the probability of each outcome against its size, and interpret whether the result is truly profitable.
• Distinguish frequency (how often an outcome happens) from magnitude (how much it's worth) as two separate factors that must both be checked before judging a repeated decision.
• Explain why a strategy with a win rate below 50% can still be profitable, and why a strategy with a win rate above 50% can still lose money.

Here's the number that matters: a strategy can lose 60 out of every 100 trades and still make you richer. That sounds wrong, but it's only wrong if you're asking one question when you need to ask two.

The first question is frequency: how often does something happen? A 40% win rate answers this. The second question is magnitude: how much is each result worth? A ₹3,000 win and a ₹1,000 loss answer this. Most people stop at the first question, because it's the easier one to count. But the real worth of a repeated decision comes from both questions combined — that combination is called Expected Value.

The formula is simple arithmetic: take each outcome's probability (how likely it is), multiply it by its size, and add up all the results.

For this strategy: 0.40 × ₹3,000 (the win side) + 0.60 × −₹1,000 (the loss side) = ₹1,200 − ₹600 = ₹600.

Judging by win rate alone treats every win and every loss as equal in size.

That ₹600 is the expected value per trade — the average amount this strategy earns each time it's run, once you weigh in both how often it wins and how much each win or loss is worth. Multiply that by 100 trades and you get roughly ₹60,000 in expected profit, even though the strategy is "wrong" — meaning it loses — three out of every five times.

The win rate (40%) only ever told you the frequency half of the story. It never mentioned that each win is three times bigger than each loss. Once you multiply frequency by magnitude, the picture flips completely: the strategy isn't unreliable, it's profitable by design.

Judging by win rate alone treats every win and every loss as equal in size — which is rarely true in real life.

This is why expected value, not win rate, is the honest number. It doesn't ask "which happens more?" It asks "which side, once you multiply out how often and how much, actually weighs more?" That's a completely different question — and often a completely different answer.

Take the same strategy, run over 100 trades, and lay out exactly what happened. It won 40 times. Each of those wins brought in ₹3,000, so the wins alone total 40 × ₹3,000 = ₹1,20,000. It lost the other 60 times. Each of those losses cost ₹1,000, so the losses alone total 60 × ₹1,000 = ₹60,000.

Now put both sides together: ₹1,20,000 in wins minus ₹60,000 in losses leaves a net result of ₹60,000 across all 100 trades. Divide that by 100 trades and you get the expected value per trade: ₹600.

Written as the formula: Expected Value = (0.40 × ₹3,000) + (0.60 × −₹1,000) = ₹1,200 − ₹600 = ₹600 per trade.

Notice what just happened. If someone only heard "this strategy wins 40% of the time," they'd likely walk away from it, assuming it loses more than it makes. But the actual money tells a different story — a net gain of roughly ₹60,000 over those same 100 trades. The strategy isn't good despite losing 60% of the time. It's good because each win is worth three times each loss, and that size difference more than makes up for losing more often.

Point: Expected value combines frequency and magnitude into one honest number; a strategy can lose most of the time and still be reliably profitable if its wins are large enough relative to its losses.

Flip the same numbers around and the danger becomes even clearer. Imagine a second strategy that wins 70 out of 100 trades — a win rate most people would call excellent. But suppose each win only makes ₹300, while each loss costs ₹1,000. Expected value = (0.70 × ₹300) + (0.30 × −₹1,000) = ₹210 − ₹300 = −₹90 per trade. This strategy wins most of the time and still loses money overall, because its rare losses are far bigger than its frequent wins. Set side by side with the 40%-win-rate strategy from the Core Concept, the lesson sharpens: win rate by itself tells you almost nothing about whether a repeated decision is worth continuing. Only expected value — frequency multiplied by magnitude, added up — tells you the truth.

• Assuming a strategy that loses more often than it wins must be unprofitable. — Win rate is the easiest number to notice and count, so it feels like the whole answer, even though it only measures frequency. Fix: Always ask about the size of wins and losses too, then calculate expected value before deciding if a strategy is good or bad.
• Treating a positive expected value as a promise that the next trade will be a win. — A single clean number like ₹600 per trade feels like a prediction rather than an average spread across many repetitions. Fix: Remember expected value describes what tends to happen over many repeats — any single trade can still lose money, so never bet more than you can afford to lose on one outcome.
• Believing expected value requires advanced math or a statistics background to use. — The term sounds technical, which makes it feel out of reach for someone without formal training. Fix: Remember it's just multiplying probability by size for each outcome and adding the results — arithmetic anyone can do once they know to ask both questions.

• Expected value = (probability of each outcome × its size), added together across all outcomes.
• Frequency (how often) and magnitude (how much) are two separate questions — you need both to judge a repeated decision.
• A strategy can lose more often than it wins and still be profitable, if its wins are big enough relative to its losses.
• Expected value is a long-run average across many repeats, not a guarantee for any single trade.
• Before trusting a gut feeling about 'mostly wins' or 'mostly loses,' do the multiply-and-add — the real answer often surprises you.

Q1. What is the correct formula for calculating expected value of a repeated decision with two possible outcomes?

• (Probability of outcome 1 × its size) + (Probability of outcome 2 × its size)
• Just the win rate expressed as a percentage
• The average of the win amount and the loss amount
• The total number of wins minus the total number of losses Answer: (Probability of outcome 1 × its size) + (Probability of outcome 2 × its size) — Expected value combines both outcomes by multiplying each one's probability by its size, then adding the results — that's what makes it different from just counting wins or losses.

Q2. A strategy wins only 40% of the time but still has a positive expected value. What does this tell you?

• The win rate number must be wrong somewhere
• The size of each win is large enough relative to the size of each loss to offset losing more often
• The strategy will win on the very next trade for certain
• Expected value only applies when win rate is above 50% Answer: The size of each win is large enough relative to the size of each loss to offset losing more often — Frequency and magnitude are separate questions. Even though this strategy loses more often, its wins are big enough compared to its losses that the overall weighted result is still positive.

Q3. If a strategy has a positive expected value per trade, it is guaranteed that every single trade will make money. Answer: False — Expected value is a long-run average across many repetitions, not a promise for any one trade. A single trade can still lose money even when the expected value is positive.

Q4. A different strategy wins 30 out of 100 trades. Each win earns ₹5,000, and each loss costs ₹1,000. What is the expected value per trade, and is this strategy profitable overall? Answer: Expected value = (0.30 × ₹5,000) + (0.70 × −₹1,000) = ₹1,500 − ₹700 = ₹800 per trade. Yes, it is profitable, since the expected value per trade is positive. — Multiplying each outcome's probability by its size and adding the results gives ₹800 per trade — a clearly profitable strategy, even though it loses 70% of the time.

Q5. A trading strategy has a 70% win rate. Someone says: "A 70% win rate means this strategy is clearly profitable." Does a high win rate alone confirm the strategy is profitable? Reveal: Weak: yes, winning 70% of the time means it's a good, profitable strategy. Strong: win rate only measures how often an outcome happens, saying nothing about how much each win or loss is worth — a strategy can win 70% of the time with tiny wins and still lose money overall if its rare losses are large enough.