Confidence & Betting Sports

[rjp]

For those of you with a more formal foundation in statistical analysis, what do you consider to be an acceptable confidence level for approximating true odds?

For the sake of discussion, assume I observe 250 successes out of 500 trials. I can construct the following confidence intervals: 95% (45.53%,54.47%); 99% (44.16%,55.84%); 99.9% (42.59%,57.41%); 99.99% (41.27%,58.73%).

This has recently become a topic of major interest for me as I do not wish to overestimate my edge when betting half Kelly. As such, I've been using the lower tail (actually just one sided) of a 99.99% confidence interval as the true probability based on an observed sample.

I guess what I really want to know is: is this the best method for estimating a probability based on a sample for betting purposes?

[craig]

I am by no means a probability expert, but unless all lines are the same you would have to have 'different' sample sizes based on the line. i.e. Separate all games based on the different lines and then you could probably estimate your probability much better.

craig

[rjp]

craig, understood, but I'm speaking more of in the general sense. Lets assume I'm flipping a biased coin, and based on a sample of 500 trials I see 250 heads and 250 tails.

Using this sample alone, what odds would I want to bet heads or tails? That's what I'm getting at.

[NajdorfDefense]

[ QUOTE ]
craig, understood, but I'm speaking more of in the general sense. Lets assume I'm flipping a biased coin, and based on a sample of 500 trials I see 250 heads and 250 tails.

Using this sample alone, what odds would I want to bet heads or tails? That's what I'm getting at.

[/ QUOTE ]

edge / odds. I'm not sure what the question is. Lower Kelly number for conservatism, and, if you wish, to reduce variance. I would think that would be the numerator, i.e. the edge, no?
[reduce the p in the b*p-q, that is. The 'b' is given by the book.]

[cboevey]

Depends on the number of trials available and what you want to use it for. For the two following questions I would use different confidence intervals:

1) Can I quit my job and bet sports professionally?
2) Did I perform better than random for the last NFL season?

Naturally I would also prefer to have as many events as possible to answer the first question whereas I wouldn't really care as to how many events I had in the second (as long as it is above 50).

If this is for something that is not life changing, you could use 95% until you get to 1,000 trials then look at both 95% and 99%. Anywhere above 10,000 trials you may as well use 99%.

Admittedly I've never seen anyone use a 99.99% confidence interval. I work with up to several million of records in my job and I still only use 99.9% CI intervals.

[rjp]

NajdorfDefense, I'm looking at estimating the probability, not the Kelly wager size. I simply mentioned Kelly because as you know overbetting is killer. [img]/images/graemlins/smile.gif[/img]

cboevey, thanks for the info. That's exactly the kind of details I was looking for.

[NajdorfDefense]

why wouldn't you use your actual record [or estimated win%] with a discount for conservatism?

[rjp]

NajdorfDefense, every game, proposition, etc. is different.