Calculating risk of ruin (sportsbetting)

Hi,

how can I calculate the risk of ruin (sportsbetting or trading) depending on the hitrate (how many %winners), winrate (average factor of winnings) and position size?

I think average winnings does not determine a unique risk of ruin, some more information about the distribution of winnings is needed.

Yes you are right, but I would like to start with standardised winnings, so to make it not too complicated.

[AaronBrown]

I'm not sure what you mean by winrate. I'm guessing it's the average payoff when you do win. Anyway, I'll start by assuming all bets are even odds, and all bets are the same size.

If your win rate is 50% or less, you are certain to lose all your money eventually. If you raise your bet size in proportion to your bankroll as you win, but don't decrease it when you lose, you are also certain to lose all your money, even if your win rate is greater than 50%.

If your win rate is exactly 50% and you keep your bet size constant, the probability that you are broke after N bets starting with a bankroll of B bets is approximately:

2*Normsdist(-B,0,N^0.5/2,true)

where Normsdist is the Excel cumulative Normal distribution function. As N goes to infinity, this approaches 1, which shows that you are certain to go broke eventually if you have no edge.

If your win rate is greater than 0.5, there is no comparably simple formula. It's not a bad approximation to use:

2*Normsdist(-B,(2*W-1)*N,(W*(1-W)*N)^0.5/2,true)

assuming W is not too far from 0.5. This will overstate your risk of ruin slightly for W > 0.5, and understate it slightly for W < 0.5.

Thx a lot. Can you give me any links or hints to how I can calculate how likely it is that I loose x% of my roll? It would be great if you can give me links to an exact calculation, because my hitrate in trading is way above 50%. I don't want to seem lazy: I can do the maths, but I don't know how to get started.

[AaronBrown]

Step 1 is to compute the expected profit and variance of each bet. If you have probability P of winning W and probability 1-P of losing L, your expected profit is:

P*W + (1-P)*L

The variance of each bet is:

P*(1-P)*(W - L)^2

If you add up all the expected profits and variances of your bets, you get your overall expected profit and variance. The square root of your variance is your standard deviation.

It is approximately correct that your probability of losing X or more is:

Normdist(-X,EP,SD,true)

where Normdist is the Excel cumulative Normal function.

For example, if you win 60% of your bets, and for each one you win $100 if you win and lose $100 if you lose, your expected profit per bet is $20 and your variance is 9,600.

If you do 150 of these bets, your expected profit is $3,000 and your variance is 144,000. The square root of the variance is $1,200. The probability of losing $1,000 or more is approximately:

Normdist(-1000,3000,1200,true) = 0.0429%

[pzhon]

[ QUOTE ]
Hi,

how can I calculate the risk of ruin (sportsbetting or trading) depending on the hitrate (how many %winners), winrate (average factor of winnings) and position size?

[/ QUOTE ]
See this post by BruceZ. It applies much more generally than the context discussed there.

It assumes you make bets of constant size, not proportinate to your bankroll. You can compute your standard deviation and win rate from the figures you mention.

[ QUOTE ]
Can you give me any links or hints to how I can calculate how likely it is that I loose x% of my roll?

[/ QUOTE ]
If you aren't changing your bet size, use the risk of ruin for x% of your bankroll to determine your probability of ever losing x% of your starting bankroll.

If you are using a proportionate betting system, there is a simple formula for the risk of dropping to a fraction of your bankroll. See section 4.1 of this paper.

[BillC]

The normal approximation is inaccurate because you might go broke before finishing the n bets. This is the classic "falling off the edge" error.

You can consult the BruceZ thread or my paper (covers both both fixed and proportional betting) as cited by pzhon below.