This is kinda confusing me.

The formula for profit factor is pf = sum of wins / sum of losses

However, this can be misleading as our account balance will fluctuate over time, meaning the size of our winners and losers will change as well. Lets say you have $10,000 in your account, you risk 1% at 1:1 R:R and win $100. You then withdraw $10,000, leaving $100 behind. You then risk 1% of $100 and lose, losing $1. Your profit factor will be $100 / $1 = 100, which is absurd.

So in order to get an accurate profit factor, we need to normalise our winners and losers. We can normalise our winners and losers with respect to the size of our stop loss, or risk, in each trade. If you use a fixed stop loss (fixed risk), then the size of your normalised loser is always 1. If you use a fixed 2-to-1 reward-to-risk, then the size of your normalised winner is 2. If you use a variable R:R, then you can find the size of your average winner and normalise that.

We then add our % chance of winning a trade and % chance of losing a trade to get our accurate profit factor.

The formula becomes:

pf = (winrate% * normalised average size of winner) / (loserate% * normalised average size of loser)

I hope my maths is correct so far.

Assuming it is, I’ve been backtesting two versions of a mechanical system.

The first version uses a 2-to-1 reward-to-risk and has a profit factor of 1.33. The second version uses a 0.5 reward-to-risk and has a profit factor of 1.49.

You assume the system with the higher profit factor would have a steeper equity curve. But this is not the case.

Equity curve for 2-to-1 reward-to-risk, profit factor = 1.33, risking 1% equity per trade.

Equity curve for 0.5-to-1 reward-to-risk, profit factor = 1.49, risking 1% equity per trade.

The version with the higher profit factor ends up making less money. I always assumed a higher profit factor = steeper equity curve. But this doesn’t seem to be the case? I’m frakken confused. Either my maths is off or I’ve misinterpreted the meaning of profit factor.