# Thread: Probabilities and Monte-Carlo simulations - How to rank?

1. ## Probabilities and Monte-Carlo simulations - How to rank?

I'm not that statistically clued up within this particular area but it's an issue I am facing for work (bizarrely) and am having trouble of working this out.

I want to keep this very simple so that all those who are offering their help can understand what it is I am trying to accomplish.

Question: How would I go about coming up with a ranking formula with these two variables:

-Winning Percentage & Reward Ratio

Winning percentage is self-explanatory; reward ratio is what you are receiving back as a ratio of what you risked. A 1:1 Reward Ratio would be risking 1 unit for a maximum reward of 1 unit.

Here's 2 examples:

Example 1: Winning Percentage: 75% -- Reward Ratio: 0.5
Example 2: Winning Percentage: 50% -- Reward Ratio: 2.5

Of the above 2 examples, the 2nd example is better than the 1st. Using a basic monte-carlo simulation, over time (i.e. the law of large numbers) it would have yielded a better return for what you risked (reward ratio).

What I am wanting to know is how I can use a formula to place a rank on the 2 interrelating variables to tell me the best within my entire data set.

Any thoughts at all or if you wish for me to elaborate please drop a message! Massively appreciate ANY thoughts

2. ## Re: Probabilities and Monte-Carlo simulations - How to rank?

Do you just have a bunch of percentage/reward ratio scenarios, or is this real data? If real data, I am not a big MC guy, but how big of a sample are we talking? Do you need to run MC, or can you just assume they are going to converge? Given that you can just create functions to calculate each and then rank order them. I think we need a little more information to know the best approach to take.

3. ## Re: Probabilities and Monte-Carlo simulations - How to rank?

Thanks for responding!

So the monte-carlo side doesn't need to be anything fancy. I am not too concerned with the precision on making sure that the integers (or events, i.e. win or loss) are absolutely random.

Instead view this "Winning Percentage" as "x" probability of pulling a white marble over a black marble. Each event is a random but over time the distribution of wins over losses (white marbles over black) will remain tighter toward what we can expect as a winning percentage. So yes, assume they will converge over time.

So in short, I have 100's of entries:

Winning Percentage -- Reward Ratio

I am wanting to know what the best 2 complimenting variables whereby over time, they would produce the best probability relative to reward potential. Another example of this would be:

Winning Percentage: 60% -- Reward Ratio: 0.90
Winning Percentage: 40% -- Reward Ratio: 2.55 < Better of the two.

Forgive me for my lack of knowledge and or explanation on this. Hopefully this helps a little? Let me know if you need me to elaborate more.

4. ## Re: Probabilities and Monte-Carlo simulations - How to rank?

Any bright ideas ?

5. ## Re: Probabilities and Monte-Carlo simulations - How to rank?

I apologize for bumping on this thread, but I am really trumped by this.

Am wondering if someone has a fancy formula or a way to fairly say that a winning percentage of "x" with a reward ratio of "y" is better than the winning percentage of "z" and a reward ratio of "q".

The winning percentages converge over time.

Using a ranking system wouldn't work.

I could have a 40% winning rate with a reward ratio (each time I win) of 2.8. This would be better than a winning rate of 60% and a reward ratio of 1.0.

Is it possible to build a formula on this?

6. ## Re: Probabilities and Monte-Carlo simulations - How to rank?

I guess, I don't get why you just can do all of the calculations. Is there empirical data or do you just want to run all combination (huge number) or just a bunch of select combinations?

7. ## Re: Probabilities and Monte-Carlo simulations - How to rank?

I feared it might get to this level...

I suppose you have every right to tell me that I am asking in the wrong place, but my mathematics are not as advanced as this...

If this is a case of my asking too much to chew, then I understand. However, if you care to expand on what you have written there, I am confident I may well be able to digest and use this in my programming (PHP - which is what it will inevitably be incorporated into).

(UPDATE: I was referring to the formula you wrote... In response to what you have written above: there is no empirical data. It is just a case of each outcome (win or loss) being as a result of random integers dictating a win or loss (range 0-99). These integers are influenced by the "Winning percent" we can expect OVER time. The larger the data set (win and loss events), the closer the distribution of wins and losses will converge to what we can expect as a "Winning Percentage". How much we win on average is dictated by the reward ratio....)

8. ## Re: Probabilities and Monte-Carlo simulations - How to rank?

So you have a probability with a payoff ratio. I guess what you want to do is to compare the expected return of each case.

Using the example you provided in post #1, the expected return per 1 unit of investment in

case 1 is

case 2 is

Therefore case 2 yields a higher expected return and therefore is your preferred choice.

9. ## Re: Probabilities and Monte-Carlo simulations - How to rank?

Sometimes I find myself asking more than one question. The second question is aimed at myself... 'What is wrong with me sometimes'.

I have over complicated this scenario...

Thank you kindly for setting me back on my tracks.

and thank you hlsmith for your contribution too!

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