Expectancy decides, and the win rate on its own does not
Expectancy is what one trade is worth on average, before anything is known about the order the trades arrive in. It is the win rate multiplied by the reward-to-risk ratio, minus the loss rate multiplied by the one unit a loss costs, and it comes out in R: units of the risk taken. A system that wins 45 trades in 100 at two units of reward for one of risk returns 0.45 times 2 minus 0.55, which is 0.35 R. The win rate alone says nothing, because it never says what the wins and the losses are worth.
That is why the break-even win rate sits next to it. At a reward to risk of two, one trade in three is enough to come out level, so 45 per cent is comfortably ahead. At a reward to risk of one it needs half, and 45 per cent is now a losing system. What decides is the pair, never one half of it. None of this settles whether the win rate typed in is real or the residue of a short and lucky sample, and our Luck or Edge? calculator is the page that asks that.
Compounding runs on the capital that is there
Compounding enters the moment risk is a percentage of the account rather than a fixed amount of money. One per cent of 20,000 is 200; after a good stretch takes the account to 30,000, one per cent is 300, and the same trade carries half as much again. After losses it works the other way, and the position shrinks with the account funding it. Every trade is applied to the capital standing at that moment, which is why a hundred trades at 0.35 R do not add up to 35 R of growth.
The difference is not a rounding detail. Multiplying an average trade by the number of trades treats the account as though it never changed size, and the gap between that and the compounded figure widens with every trade in the run. What feeds all of it is that average trade, and where it comes from matters more than the arithmetic built on top: a list of closed trades put through our expectancy calculator gives a measured figure instead of an assumed one.
What the distance between the worst and the best runs shows
The smooth path is a convenience. Deal the same trades in a different order and the account travels a different route to a different place, because each trade is sized off what the ones before it left behind. Six losses at the start compound downwards and every trade after them is smaller; six wins do the opposite. The page runs that experiment over and over, holding the win rate and the reward to risk fixed throughout, and reports where the runs finished: the worst five in a hundred, the middle, and the best five.
The distance between the first and the last is the whole point of the exercise. It is not error, and it is not noise to be averaged away. It is what a single edge, applied over a limited number of trades, actually produces. Two accounts running the identical system can finish far apart on order alone. Reading the middle figure by itself and treating it as the outcome is the most expensive mistake this page can be used to make, which is why it is never shown without the worst five per cent beside it.
The bad run is part of the deal
The same reasoning covers the losing streak. A system that wins 45 per cent of the time loses 55 per cent of the time, and those losses do not arrive politely spaced out. Six in a row is not a malfunction and it is not evidence that the edge has stopped working; at that win rate it turns up inside a run of a hundred trades more often than most people expect. The deepest drawdown of the median run is on the page for that reason: it is the ordinary bad stretch, not the disaster case.
What that stretch costs is worth sitting with before the run starts rather than during it, because a loss and the gain that undoes it are not the same size, and our drawdown and recovery calculator turns one into the other. The share of runs that fell under a fifth of the starting capital is there for the same reason: at some combinations of risk per trade and win rate, an edge that is genuinely positive still ruins a slice of the accounts that run it, and the size of that slice is decided by the risk per trade rather than by the system.
