What are the chances?

[Lucky P]

Hi, my first post here and just looking for some information which I'm hoping someone can help me with, as there seem to be some knowledgeable people here. Not sure if this is the right thread but couldn't find anything more applicable. Anyway: Last season I bet on Prem-League 2 matches. Betting 1 point on each match. I was doing "draw no bet" bets. Here is what happened: Won 309 Lost 283 Drew 211 +44.47 points profit Average odds 2.65 (33/20 UK, +165USA) Basically I was wondering what are the chances of making that much profit over 803 bets if we assume that the average 2.65 odds were the "true" odds. Put another way - if something truly has a 37.7% chance of happening and you bet on it 803 times how often would you luckily come out 44.47pts or more ahead? I'm not even sure if it's possible to work this out but hopefully it is. If any more info is needed I can probably provide it. Thanks

[relf]

Re: What are the chances? Linking profits to the probabilities is not always straightforward. If the odds are mostly around 2.65, an immediate thing you can check is your strike rate. Your strike rate is 309 out of 803, or 38.5%. If something truly has a 37.7% of happening, with 803 times, it's can still be considered as 'lucky' to achieve 38.5%. The margin of error for 803 is 3.5%, either 37.7% +/- 3.5% = [34.2%, 41.2%]. This means when you bet on something with 37.7% chance for 803 times, it's 'normal' to see a result between 34.2% and 41.2%. 38.5% is well in the region. However, there is a tricky part because you have a 'Draw' option where you stake is returned. I mean, I wouldn't mind if the strike rate is only 20%, whereas the 80% goes to draw, and 0% lost. That's still a handsome profit. ;)

[Lucky P]

Re: What are the chances? Thanks relf! That 3.5% was exactly the sort of thing I was looking for. How was that worked out as I'd like to know the "wobble" for any other numbers I get in future. However would it not be more accurate to work out strike rate by wins and losses and ignore the draws as they are essentially void bets? So 309/592 = 52%. Or would that be incorrect?

[gloryhunters]

Re: What are the chances? You can find out this through using a basic binominal distribution. So if you have 803 trials and the true odds of success in each trial was 0.377, then the chances of having greater than 308 successes is 31%. So there is no reason why this doesn’t happen by random chance.

If you only have 592 trials and the true chance of success is 0.377, then the probability of having more than 308 successes is basically zero and so we would conclude that the true odds of success is higher than 0.377

[relf]

Re: What are the chances? You could wiki the term 'margin of error'. It applies only to percentages though. A handy way of remembering for 95% confidence, would be 1/sqrt(n). In your example, 1/sqrt(803) = 3.5%. Statistically speaking, 95% confidence is usually used over 90% and 99%.

Margin of error at 99% confidence

Margin of error at 95% confidence

Margin of error at 90% confidence

[Lucky P]

Re: What are the chances? Fantastic. Thanks very much! Which stats would be correct to use for this then given the type of bet that I'm placing. 309/803 or 309/592?

[relf]

Re: What are the chances? I think using 309/592 would be more useful. In saying that, I think you will need to alter the 37.7%.

[Lucky P]

Re: What are the chances? But my ave odds are 2.65. What else could I use instead of 37.7%? Should I look for the median or something?

[relf]

Re: What are the chances? I think you could eliminate the odds ended with a draw, and re-calculate the average odds. Then again, the calculations are just a guideline because your average odds are not constant. These calculations (including the Binomial mentioned) only worked if the probabilities are constant, like dice-throwing, coin-flipping.