age of winning trades? To answer that question, you need to apply the following
piece of math to your trading statistics:
P(r) [N! / (r! * (N r)!] * p^r * (1p)^(Nr)
Where:
P(r) Probability for exactly rprofitable trades
N Total number of trades
r Profitable trades
p Probability for trade to be profitable
In Excel, the formula can look something like this:
(FACT($G$2)/(FACT(ROUND($B5/100*$G$2,0))*FACT($G$2ROUND($B
5/100*$G$2,0)))*(C$4/100)^ROUND($B5/100*$G$2,0)*(1C$4/100)^($G$2
ROUND($B5/100*$G$2,0)))*100
Where:
Cell G2 Total number of trades
Cell B5 Profitable trades
Cell C4 Probability for trade to be profitable
Figure 3.1 shows how this formula can be used to create a matrix, with the
data in the matrix indicating the likelihood for a specific amount of profitable
trades, given the historical profitability and your estimate of how likely it is for
each trade to be profitable in the future. Using the data in the matrix, you also can
produce a chart like that in Figure 3.2, which shows the same thing in a graphic
way. Looking at Figure 3.2 we can, for example, see that if the historical prof-
itability is 60 percent, and you estimate the likelihood for a future trade to be a
winner at 50 percent, there is only a 1 percent likelihood that the number of prof-
itable trades will be 60 percent over a large number of trades.
Figure 3.3 shows the cumulative likelihoods for a certain percentage amount
of trades to be profitable in the future. For example, with a 60 percent historical
profitability, and the likelihood for a future trade to be profitable at 50 percent, an
almost 100 percent likelihood exists that a longer series of future trades will hold
50 percent or less profitable trades.
The point is that no matter the percentage of profitable trades you had in the
past, the likelihood to repeat that exact amount in the future is very small—not to
mention the likelihood for producing a series of trades with the winners and los-
ers in the same order as the historical or back-tested series.
The same goes for the number of winners and losers in a row. If for nothing
else, you should try to keep these numbers as low as possible (especially the los-
ers, if you like to feel comfortable with trading the system). However, for a cor-38 PART 1 How to Evaluate a System