You've completely misinterpreted the formula. There is no absolute P&L. The NOBF is based on percent returns, not absolute returns. No need for me to "experiment" further. The formula you posted looks pretty much the same as the SQN with all the same flaws.
Ok, let's try your latest version of the formula, with the percent returns. System A: [-8, -8, -8, +25, +25] System B: [-1, +1, +1, +21, +50] SPS(A) = 0.450763 SPS(B) = 0.446332 So, according to your formula, system A is better than system B, while everyone with common sense would agree that system B is way better. My own formula rates system B at about 2.3 times better than system A. Additionally, Sharpe's, Sortino, SQN, Kelly, Profit Factor, Max DD, Net profit, and pretty much every other performance measure would also rate system B higher.
All you've proven is that the NOBF can't handle ridiculous extremes like your system B, which never occur IRL. Calculating the true Kelly fractions gives the correct order for the SPS relationships. Kelly(A) = .026 NOBF(A) = .018 = about 70% of the true Kelly NOBF(B) = .0245 = about 3% of the true Kelly Kelly(B) = .734 SPS(A) = 0.65 SPS(B) = 13.4 That's quite a lot more than your 2.3 ratio.
In fact, system B is so out of phase with reality that higher-order polynomial approximations of the Kelly fraction get farther away from the exact value rather than the norm of getting closer. Linear approximation = 0.0245 Cubic approximation = 0.0225 Quintic approximation = 0.0217 :eek:
Bottomline: SPS is a "bust"...correct ? It's just some sort of statistic, but does not correlate to true performance....right ?
Fail. One key characteristic of a good performance measure should be its universality. For example, horsepower, a widely accepted measure of engine performance, is universal: its measurement does not vary from user to user or from year to year. But the Sortino ratio, the Sharpe ratio, and similar ratios all depend on something called "risk-free return", which is wildly open to interpretation. This risk-free return varies from year to year and probably from user to user as well, making it very unreliable, and by extension, making the Sortino ratio unreliable as well. We want a measure of performance that leaves no value open to misinterpretation because of different benchmarks among users, just as horsepower is not open to misinterpretation by those who know its definition.