Mean R of +0.32 but a median of minus 1: an 11 trade list and one 6R winner

[Fairman]

Mean R of +0.32 but a median of minus 1: an 11 trade list and one 6R winner

Here is a made up list of 11 trades in R, not my results: -1, -1, +1.5, -1, +6, -1, +1.5, -1, +1.5, -1, -1.

The total is +3.5R, so the mean is 3.5 / 11 = +0.32R per trade. That looks like a decent system. Now sort the list: seven trades at minus 1, then three at plus 1.5 and one at plus 6. The median, the middle value of the sorted list, is minus 1R. Seven of the 11 trades lost, a win rate of 36%.

Take out the best trade, the single 6R winner, and the remaining 10 trades sum to minus 2.5R, an average of minus 0.25R. So the whole positive result comes from one trade. If that trade had been closed at 1.5R like the others, the month would be at minus 1.0R in total.

None of this means the system is bad. Trend and breakout styles often earn their money in a few big trades. The point is that the mean alone can hide how fragile the result is, and 11 trades can't tell the two cases apart.

So I report three figures in a journal: mean R, median R, and mean R without the best trade. When the third is far below the first, I treat the result as unproven until the sample is larger, and I check what the big winner had in common with the others before assuming it will repeat.

[Fairman]

How big a sample do you need for a skewed system? The standard deviation of this list is around 2.2R, so the error on the mean of 11 trades is about 0.66R, which is double the mean itself. To get the error down to 0.1R you'd need about 480 trades with the same spread. This is why a trend style takes so long to judge, and why a few good weeks tell you little about it. The more skewed the payoffs, the more trades before the average stabilises, and the lower the win rate, the longer it takes.

[Fairman]

There's a practical side to the median being minus 1R. If seven of eleven trades lose, a trader has to take losses most of the time to collect the few winners, and that has a psychological cost the mean doesn't show. Over a typical stretch of ten trades here, you'd expect around six or seven losses, and runs of four or five in a row are routine. If you can't stand that experience, a system with the same mean and a higher win rate and a smaller top trade would suit you better, even at the same expected profit.

[Fairman]

For a check on your own list, a bootstrap works without any theory. Draw 11 trades at random with replacement from the list, compute the mean, and repeat 20,000 times. For the list above I got a 5th percentile mean of minus 0.55R, and about 34% of the resamples came out negative. So a list like this can't separate a real edge from luck, which agrees with the best trade being removed and the average turning to minus 0.25R. It's about ten lines of Python, or a spreadsheet with random picks.

[Fairman]

Another point about the 6R trade is whether it was a rule-following trade. If it was a position held for a bigger move because the plan allowed it, it's part of the system and you should expect more of them over time at an unknown rate. If it was a trade that went wrong in a good way, like a moved stop or an oversized entry, it's luck and shouldn't count toward your expected value. Read that trade on its chart and its notes and decide, and then compute the mean with and without it. Both numbers are useful.