chris001 Posted June 18, 2007 Share Posted June 18, 2007 A specific selection procedure shows a 78% s/r and a level stake ROI of 4.52% after 200 bets. From a statistical p.o.v. how many bets do you need to have some certainty that this is indicative of how it will continue at this level? Anyone know a formula? Thanks Quote Link to comment Share on other sites More sharing options...
slapdash Posted June 18, 2007 Share Posted June 18, 2007 Re: how many bets to be sure? Of course, you can never be absolutely certain. But also the answer depends on how much the odds vary. The figures you give are consistent with all bets having odds of 1.34. If this were the case, then the chance of getting a ROI of 4.52% by chance, if the long term expectation was really just to break even, would be about: 200 bets: 15.5% 400 bets: 6.6% 600 bets: 3.1% 800 bets: 1.5% 1000 bets: 0.7% 1500 bets: 0.13% 2000 bets: 0.02% If the odds actually varied, then the probabilities would be higher, depending on how much the odds varied. Quote Link to comment Share on other sites More sharing options...
chris001 Posted June 18, 2007 Author Share Posted June 18, 2007 Re: how many bets to be sure? Hi Slapdash Many thanks for your answer. Much appreciated. Average is 1.34 as you deduce Max is 1.42, min is 1.26. Does this make a great deal of difference? Would you share the calculation formula or give a reference? Quote Link to comment Share on other sites More sharing options...
slapdash Posted June 18, 2007 Share Posted June 18, 2007 Re: how many bets to be sure? Hi Slapdash Many thanks for your answer. Much appreciated. Average is 1.34 as you deduce Max is 1.42, min is 1.26. Does this make a great deal of difference? Probably not a lot if the odds only vary that much. Would you share the calculation formula or give a reference? Well, if all the odds were 1.34 and these were fair odds (so you'd break even betting in the long run), then the probability of a win is 1/1.34, or about 0.746. If the probability of winning is the same for all bets, then the number of wins over a certain number of bets is given by the binomial distribution. There are various places you can do the calculation online (probably Excel has a function to do it, but I don't know). For example: http://www.stat.tamu.edu/~west/applets/binomialdemo.html To use, this, "p" is 0.74627, the probability of each bet winning. "n" is the number of bets, say 200. A 78% strike rate over 200 bets is 156 winners, so ask it for the probability that X is at least 156, and it gives you 0.1549, or 15.49%. Quote Link to comment Share on other sites More sharing options...
slapdash Posted June 18, 2007 Share Posted June 18, 2007 Re: how many bets to be sure? If you want something a bit more complicated, but which takes account of the varying odds, then so long as the number of bets is fairly large, the yield is approximately given by the normal distribution. You'll need to calculate the standard deviation of the yield. To do this, add up the "fractional" odds (i.e., decimal odds minus one). Take the square root and divide by the number of bets. For example, if you had three bets (of course, there'll be a lot more, but this is just for an example) at odds of 1.40, 1.40 and 1.25, then 0.40 + 0.40 + 0.25 = 1.05 Square root of 1.05 is about 1.0247. Divide by 3 (number of bets): 1.0247/3 = 0.3416 So the standard deviation of the yield is 0.3416. Then you can use (for example) http://www.stat.tamu.edu/~west/applets/normaldemo.html If your actual yield was 20%, or 0.20, then give it Mean=0 Std. Dev. = 0.3416 and ask it for "Area right of" 0.20, and it gives you 0.2791, or 27.91%. Again, Excel probably has functions to do this. (Doing this for just three bets is silly, as it's not nearly enough for a normal distribution to be an accurate approximation, but that was just to give an example of calculating the standard deviation.) Quote Link to comment Share on other sites More sharing options...
chris001 Posted June 20, 2007 Author Share Posted June 20, 2007 Re: how many bets to be sure? Thanks for the calculations and explanation, slapdash. Very helpful. Cheers Chris Quote Link to comment Share on other sites More sharing options...
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