Adequete sample size?

[losingmyshirt]

I am looking for opinions on what is a both reasonable and realistic sample size of the results of a betting method to attain when you can start to have a relatively comfortable level of confidence in the method?

I have a method that I've been using for horse racing that over 230 races has resulted in an ROI of 12%. I know 230 is far to small to reach any solid conclusions but was thinking that if I reach the 1000 range and I am still showing a respectable ROI this would be adequete and would then be able to increase my wager size to a more substantial number as I am currently making only relatively small bets.

It is not possible for me to attain the information I require in order to backtest.

[Justin7]

Horses and sports are two different beasts. I don't know what to suggest for racing, but in sports, track the line after you bet. If the market moves agree with you (e.g. you play a team at +4, and it closes at +3), you're going to be a long-term winner.

[Peep]

Was it 230 RACES or 230 bets?

I assume not every race has a play.

If it was 230 BETS with a ROI of 12% I would feel confident in putting down "real money", but would continue to track it and keep my eyes open. If things changed over the next 230, you probably didn't have much, except statistically variation skewed by a few high prices.

[losingmyshirt]

Was it 230 RACES or 230 bets?

I assume not every race has a play.

If it was 230 BETS with a ROI of 12% I would feel confident in putting down "real money", but would continue to track it and keep my eyes open. If things changed over the next 230, you probably didn't have much, except statistically variation skewed by a few high prices.

It is 230 races, some races had multiple bets so the actual number of bets is higher. The 230 does not include races where no bets were placed and you are certainly correct in assuming that not every race has a play.

Thanks for the input guys.

[Sinister Cat]

There is a fairly recent post by Ganchrow that gives detailed instructions for calculating your z-score for a given sample of bets. That is probably the sort of thing you are looking to do, I'd think.

[accuscoresucks]

dont know about horses to much but if your talking sports
a 6,000 bet[investment] sample size will give you your answer
if it takes you over 2 years to get to this your doing something wrong its all about ROI

[Ganchrow]

I described how to calculate the significance of a set of uncorrelated bets in this post.

Using this methodology, however, would tend to overstate your variance (thereby understating significance) because many of your wagers will be negatively correlated (insofar as you're placing mutually exclusive outcome wagers on the single winner of a given race). Therefore, rather than simply summing variances to determine a total grouped variance you'd also need to include covariances in your analysis.

Given two fairly priced bets on two mutually exclusive outcome events of size x₁ and x₂, respectively the covariance between the two bets would be given by -x₁*x₂. So if we assume that the two bets are offered at decimal odds of d₁ and d₂, respectively, the total outcome variance would be given by:

σ² = x₁²*(d₁-1) + x₂²*(d₂-1) - 2*x₁*x₂

And generalizing across N mutually exclusive outcomes:

[nbtable][tr][td]σ² = [/td][td][/td][td]{x_i²*(d_i-1)} - 2*[/td][td][/td][td] [/td][td][/td][td]{x_i*x_j}[/td][/tr][/nbtable]

Of course this neglects the possibility of non-binary outcome bets (e.g. show or place bets), correlated bets that aren't mutually exclusive (e.g., a trifecta and a win bet), as well as bets known to be -EV but placed as hedge bets (as Kelly would dictate). These issues (notably the 1st, that of non-binary outcome bets) significantly complicate the problem and are probably better posed on a quantitative horse racing forum, where a suitable approximation of the solution is likely well-known.

[Peep]

dont know about horses to much but if your talking sports
a 6,000 bet[investment] sample size will give you your answer

Wow.

If I wanted for 6000 results to make a bet not only would I be confronted with rule changes like the advent of the three point shot but would be dead and buried......

[accuscoresucks]

Wow.

If I wanted for 6000 results to make a bet not only would I be confronted with rule changes like the advent of the three point shot but would be dead and buried......

i will be over 1/2 this size by years end
their are tons of over 55% advantage bets out their

[Peep]

Agree, lots of 55% (on paper) plays available.

With lots of samples.

I don't feel comfortable playing these though.

I like to find plays in the 59%/70% range. I do have to give up sample size and of course risk backfitting to do it when database mining. So there are risks, mostly that I am backfitting, with plays with this high a winning percentage.

Horses for courses, whatever turns your crank.

GL with your plays.

[losingmyshirt]

I described how to calculate the significance of a set of uncorrelated bets in this post.

Using this methodology, however, would tend to overstate your variance (thereby understating significance) because many of your wagers will be negatively correlated (insofar as you're placing mutually exclusive outcome wagers on the single winner of a given race). Therefore, rather than simply summing variances to determine a total grouped variance you'd also need to include covariances in your analysis.

Given two fairly priced bets on two mutually exclusive outcome events of size x₁ and x₂, respectively the covariance between the two bets would be given by -x₁*x₂. So if we assume that the two bets are offered at decimal odds of d₁ and d₂, respectively, the total outcome variance would be given by:

σ² = x₁²*(d₁-1) + x₂²*(d₂-1) - 2*x₁*x₂

And generalizing across N mutually exclusive outcomes:

[nbtable][tr][td]σ² = [/td][td][/td][td]{x_i²*(d_i-1)} - 2*[/td][td][/td][td] [/td][td][/td][td]{x_i*x_j}[/td][/tr][/nbtable]

Of course this neglects the possibility of non-binary outcome bets (e.g. show or place bets), correlated bets that aren't mutually exclusive (e.g., a trifecta and a win bet), as well as bets known to be -EV but placed as hedge bets (as Kelly would dictate). These issues (notably the 1st, that of non-binary outcome bets) significantly complicate the problem and are probably better posed on a quantitative horse racing forum, where a suitable approximation of the solution is likely well-known.

Thank you very much ganchrow. Reading your posts almost makes me want to brush the dust off my old stats textbooks...almost lol