The Maths Every Day Trader Should Know
Do I need to win most of my trades?
Explore how win rate, average reward, losses, and costs work together—and why a high win rate alone cannot tell you whether trading pays.
By ContextChart Research · 4 min
Published
Look beyond the winning percentage
Try it yourself
A constructed block of 100 trades with exactly this mix.
50 gross wins · 50 gross losses, before costs. A model with this win probability need not produce this exact count.
75.00R won − 50.00R lost − 5.00R costs = +20.00R net. Bar height shows payout, not win count.
Expected net result per trade
+0.20R
Expected net over 100 trades
+20.00R
At 80% wins paying +0.25R and 20% losses costing −1R, gross winnings and losses cancel. Any cost makes the net negative. These are arithmetic expectations under the selected payouts and cost. Changing a real target can also change the win probability.
A constructed example. Change the inputs to explore the relationship; these are not suggested trade settings.
The idea
You do not need to win every trade for the arithmetic to work. You need the combined value of the winners to exceed the combined cost of the losers and execution.
Consider a deliberately simple example. Eight trades win a quarter of one R each. Two trades lose one R each. The winners earn +2R in total. The losers cost −2R. An 80% win rate has produced zero before trading costs.
Another collection of trades could win less often and earn more per winner. Its result would depend on that whole combination. The percentage of green trades cannot answer the question alone.
The useful quantity is expectancy: the average result per trade under a particular distribution of outcomes. A measured positive expectancy after costs gives repetition something worthwhile to repeat. An assumed positive expectancy gives a model a starting condition to explore.
Those are different levels of evidence. Your target and stop help shape the payout distribution, but moving a target farther away also changes how often it is reached. You cannot claim a larger average winner while automatically keeping the old win rate.
Win rate becomes useful when you know what the wins pay, what losses cost, and what execution takes.
How this experiment works
Change the win rate, payout, and cost in the example. Watch the average result, rather than only the number of winners.
Then ask what evidence would support that combination in a real market. These controls describe possible arithmetic. They do not make the chosen performance achievable.
How we use this
Our target and runner studies tested attractive-looking trade shapes against a no-information baseline. Many impressive hit rates were explained by the distances between price barriers. After spread, the tested unconditioned entries lost money.
That finding improved how we interpret a result. A high hit rate needs to be compared with what the same trade shape would produce without a useful read. The research did not establish that every strategy has the same result.
Show the maths
With win probability p, an average gross winner of b R, losses fixed at 1R, and an additional cost of c R per trade:
Expected R = p × b − (1 − p) − c
Break-even win probability = (1 + c) ÷ (b + 1)
If average losses differ from 1R, use their measured size. If the recorded wins and losses already include costs, do not subtract those costs again. Timeouts, scratches, and partial exits belong in the actual distribution too.
What this does not establish
A positive average from a small sample is not a guaranteed future advantage. Changing market conditions, uncertain estimates, and overlapping trades affect how much trust the result deserves. Start with the cost calculation, then examine skill versus a good run.