Calculating probability of losing streaks

Any mathematicians able to help out here? Stats have never been my finest point so...

Probability of a losing streak is, in Excel speak:

=(1+(n-s)*p)*(POWER(l,s))

where n=number of trades, s=number of losing streaks, p=probability of winning, l=probability of losing.

Ok, so say I have a strat 23% successful over 220 trades, I get figures like this (written number of losses followed by probability)
10 361.21%
15 95.49%
20 25.23%
25 6.66%
30 1.76%

... something is amiss - 361%?? Any ideas?

I'm not sure if this will help as your post is in a foreign language to me, (my maths is virtually non existent), but I had a similar question before and someone was kind enough to post an excel spread sheet for me.

Hopefully this will be of some use to you. The attachment is in the below post:

http://www.forexfactory.com/showpost...3&postcount=24

Thanks Flotsom, I'm looking for a bit more than that - that tells you the probability of an individual streak, but I'm trying to calculate the chances of a streak of X losses over N number of trades.

So, for example, using simple probability, the chances of 10 losses with a 50% win rate is 1 in 1024. However, over 1,000 trades, what are the chances of it happening? Given there are multiple opportunities for that streak to start...

I think you could use a binomial distribution

You make C1000,10 * (0,5)^10*(1-0.5)^990=0 (really small)

PS: It's wrong it's give you the probability of 10 losing trade in the 1000 not in a row ,sorry

You can get an estimation of the number of consecutive losses in N trials from the following:

Consecutive LOSSES = Ln(N) /Ln(1-Win%)


1000 trades, with a 0.5% win rate would result in 10 consecutive losses

If you want to know the probability of getting a streak of x in N trials you could check out the calculator at the lnk below:

http://sbrforum.com/Betting+Tools/St...alculator.aspx

That method only valid if you want to know the probability of n losing streak for the next n trades. It does not answer the probability of x losing streak in total y trades.

Say if you have 40% win rate, then the probability for you to lose the next 10 trades in a row is 0.6^10 = 0.6047%. But no way it can tell you the probability of 10 consecutive losing trades in 50 trades.

Hanover had posted a table for the probability of losing streaks here. Basically this table tells you the probability of at least 1 time of x losing streak in total y trades. If you want to do your own calculation in excel, here is my formula:

=1 - binomdist(0, x - y + 1, z^y, false)

where,
x = number of trials
y = number of consecutive losses
z = probability of losses in single trial.

For example, x = 50, y = 10, z = 0.6, then

1 - binomdist(0, 41, 0.6^10, false) = 22%

Hope this help.

IMHO this calculate the probability of 10 losing streaks and 990 winning streaks in 1000 trades, where this scenario only happen twice in 1000 trades (The 10 losing streaks either happen at the 1st 10 trades or last 10 trades). So no doubts such a probability is infinite small.

Edit: Sorry I misunderstood the meaning of c1000,10.

Honestly I do not know the logic behind this equation. Why (1-Win%)^(consecutive losses) = N?

I cant remember the source of the equation, its long time since I studied any stats but intuitively it makes sense. As the sample size increases, the potential size of the streak increases, and as the win rate increases, the size of the streaks decrease

I usually tend to deterine these sorts of things through simulated testing, generate a bunch of random trades and then analyse the distribution. From what I remember the simulated results and the equation where pretty much the same.

Thanks both, Razzle, that's the equation I found too, but I'm suspicious of that and the calculator; both seem to return results too good to be true.
ForexQuant, just spent a few hours working with that, and it ties in with other graphs I've seen too - spot on.

My risk of ruin is now properly calculated. Long may it be a distant nightmare!

I too wanted some accurate calculator for losing streaks.
I found myself frustrated with misinformation on the WWW.

Lucky I managed to tie up with a probability "Guru" (& Coder) who helped me design
a spreadsheet for this conundrum.

I just wanted to highlight these FREE Day Trading Spreadsheets for multiple Losing streaks
to everyone here in the community.
I'll attach a sample image of the Mersenne Twister Version;

It's accurate, and really is quite useful. There isn't really anything out there from
what I can see that offers Multiple streak data within the same run series (No Of Trades).

I hope this might be of use to many traders.
There are various spreadsheets available from this webpage, including, Monte Carlo Sim,
& Mersenne Twister simulations.

I didn't password protect the spreadsheets, so any expert coders/mathematicians out there can see exactly
what's going on within these trading spreadsheets.
Enjoy.
Day Trading Losing Streak Calculator

Best regards;
DowBoy.

Every now and then, something golden turns up at FF. This spreadsheet is top notch, tight work Dow.

If anyone's got a problem with discipline, expectations are everything...

Many Thanks for the plug Triphop,,

I did spend quite a few nights formatting etc,,
I really liked the idea, the thought of wanting to create a Mersenne Twister Losing Streak Calculator

(thanks again to the guys of RiskAMP for updating their Excel Addin)

It was a bit of a journey,, without SHG & BruceZ,, the sheets wouldn't be what they are now,, so I must give credit to them also.

I hope these sheets genuinely benefits other traders out there; that was my intention, my vision driving me to create these Losing Streak Spreadsheets.

I'm working on other bits and bobs,, so bookmark the site,, maybe +1 etc) :-) if you like,, there is more to come :-)

Again, thanks for your kind words Triphop,,
your kind words do inspire me.
Best Regards;

DowBoy

(Can be downloaded from Day Trading life Website

thanks a million dowboy.

Many thanks Pemully, I really appreciate you comment.

Just to add a couple of points to wrap this up,
1. A bit more info as to why I created these.
2. Which version to choose? Try the following 1st.

1. Originally I came across a post here by a very active member (Over 4000 posts!), a great contributor called Hanover. (This was uploaded over 5 years ago).
Link;
http://www.forexfactory.com/showthre...593#post188593

The Losing Streak Probability Table can also be seen here,
http://www.schaeffersresearch.com/sc...ion.aspx?id=26

Here; an online version (Which isn't accurate also (From the lips of BruceZ)
http://www.sbrforum.com/betting-tool...ak-calculator/

I also know of a commercial version (Greg of tradingspreadsheets) that had the same table mentioned above, again the data wasn't accurate. (I emailed him some time ago about this, should be fine now.), A nice guy I must add.

I'm not sure why I read/looked into this so thoroughly, the info above, the tables just didn't quite seem right to me. I'm no probability expert, all I can say is I felt they weren’t quite right, and wanted to delve deeper to obtain accurate data if my hunch was to be proved correct.

The spread sheets that I co-created were a bit of a labour of love. I'm just quickly looking at my Hard Drive as I type this and can see somewhere in the region of 100 versions, all slightly different layouts, functions etc to get the final versions to what they are now; FREE for all to use.
(A slight perfectionist Bias in my Psychological profile I feel). :-)

Purposely I've left all the code freely available, IE NON-Password Protected, and BruceZ left a few comments in his code as pointers.
For a little more info on BruceZ's coding, please read my post on my website here;
Losing Streak Probability Spreadsheets
This is the direct link to the post with screenshots and all Excel Spreadsheet downloads.

If anybody wants to get into a very technical discussion here on the code, then I'm afraid I cannot enlighten much more than what is written on my website post. I'm no coder (certainly not at the level of the VB code within these spreadsheets).
To add; there are a lot of very clever people out there that are gifted mathematically, and can calculate probabilities etc, (it seems) with ease.

From what I've seen, read and been involved with in creating these sheets, BruceZ is the real deal, and an incredibly gifted coder.
In creating these spreadsheets I constantly read other coders/mathematicians posts/on probability (Some called EXPERTS) that were incredibly bright, but usually came into problems here and there.
BruceZ's name kept coming up, a guy generously offering help, and able to solve very complex equations and coding etc.

I was very lucky to be in contact with him (& SHG I must mention also), as these spreadsheets wouldn't be what they are now without their help.
Whilst there might be others out there that could have coded to this level of thinking, I feel there are few. BruceZ is one of those few; he just seems to think (from what I have seen/read/ and heard from others) slightly differently; a higher level of thinking within this niche.

2. My spreadsheet pick;
Name: "Multiple Losing Streak Calculator"
Here’s a direct link download to the 2010 version, Pre 2010 available on the website link above
Multiple Losing Streak Probability Calculator


I've chosen this as the de facto download mainly because of the info that is generated in its right hand table.
Briefly,
This doesn't have a simulation function for the right hand table. The right hand table cleverly (Even though I say this myself :-)) has an auto calculating Streak Matrix.
Basically depending on the (N) of trades you enter in the 'Quick Calc' & your 'Losing Percentage Probability' you enter, it will generate on the fly multiple losing streaks.
Up to 15 columns of consecutive losing streak numbers will be returned, all showing the percentages of the losing streak lengths for each of these losing streak numbers. (Up to 19) within this spreadsheet.

I'll attach a screen shot here, with a 1000 trade sample & with a 50% Losing Probability %.

You can modify as the code isn't protected, so one could choose/create even 100 (Or More) consecutive streaks; not just 15 as depicted within this spreadsheet.

I think that's about it really.
Please, if anybody really wants to give a "thumbs Up" to these sheets, feel free to either socially bookmark my webpage;
Losing Streak Probability Spreadsheets

Or add a link to this page.
The more people I feel I have helped via these spreadsheets the more worthwhile the effort has been.

This is a truly great forum, I thank you all for your kind words and
"I wish you all well in your trading."

Best regards;
Dow Boy

10 loosing trades in a row would give me 20% DD.
The probability to get those 10 bad trades in a row for me is 0,525^10=0.00159071740896

So there is 0.159% probability to get 20% DD for me

lol, I almost fell of a chair seeing that BruceZ was on this project....
it is a small world after all...

Really nice conclusion. I really needed that formula!
I`m already using it but I didn`t understand at all.
ForexQuant, can you please elaborate it?
Why the first argument is 0 and not 1?

If I`m asking to much can you just indicate me a book though?

Thanks already!

A man with patience and dedication can only work like this. I would be happy to work with you and share my profit-making trading strategies.

In case anybody's interested, the XLS used to calculate the values (using ForexQuant's formula in post #6) can be downloaded from this post.