The depreciation/appreciation of an account trading one single system or plan is determined by three factors: amount of equity risked per trade (i.e. position sizing), accuracy (i.e. winners vs losers) of the system, and the risk:return ratio of each trade made by the system. (NB I know I'm ignoring market volatility which affects the accuracy element, as well as the distribution of winners vs losers in any given 10-(or indeed any other number)-trade streak, but humour me.)

So my point is: There must be some magic combination of equity risk per trade, accuracy, and risk vs return for a given system. This question is often cast in terms of 'drawdown you are comfortable with' but what I'm getting at is that, psychology aside, there must be a 'sweet spot'.
Or, put another way, once you know the accuracy and R:R you should be able to calculate the optimum equity risk per trade.

The question is: how? I'm sure this must be a straightforward maths question but I haven't managed to figure it out (yet). Anyone got any thoughts, whether on how to work out this formula or in general?

Consider the impact of the following scenarios on recovery time (say 1:1 SL:TP, ignore margin/leverage etc for the sake of convenience):

Risking 10% of USD 100 account on each trade:
1. lose 10 of 100, then gain:
2. 90+9=99
3. 99+9.90=108.90.
recovery complete
4. 108.90+10.89=119.79
USD 111: point at which another SL doesn't take you below initial balance

Risking 50% of USD 100 account on each trade:
1. lose 50 of 100, then gain:
2. 50+25=75
3. 75+37.5=112.5.
recovery complete
4. 112.5+56=168.5
5. 168.5+84.25=252.75
USD 200: point at which another SL doesn't take you below initial balance

Risking 90% of USD 100 account on each trade:
1. lose 90 of 100, then gain:
2. 10+9=19
3. 19+17.1=36.1
4. 36.1+32.49=68.59
5. 68.59+61.73=130.32
recovery complete
6. 130.32+117.29=247.61
7. 247.61+222.85=470.46
8. 470.46+423.41=893.87
9. 893.87+804.48=1698.34
USD 1000: point at which another SL doesn't take you below initial balance

The longer it takes to recover, the greater the risk of another SL trade before recovery complete.
On the other hand, the greater the return, the quicker the account will appreciate (once you're out of recovery).

Thoughts welcomed....
Cheers
Mark