Stats Question - Negative Binomial Distribution

[Guest]

Hello! Not sure if there are any mathsy people on here that could help but thought it would be worth asking as (I think) this is a useful test for people working on strategies and systems. Essentially I want to find out the chance of your strike rate being down to luck. I used this calculator - http://easycalculation.com/statistics/negative-binomial.php to work out the negative binomial distribution for my betting so far this season. I have placed 20 bets I have won 13 bets My average odds are 1.93 The average probability of a win (as implied by the odds) is 51.59% (the reciprocal of average odds) To account for the over-round (i.e. to get a true representation of what the implied odds are) I reduced the implied probability by about 10% - a standard over-round figure for my bookmaker and the markets I bet on. Final average implied win probability 47.38% This works out at an average return of £91.40 for every £100.00 staked - this makes sense so far as it accounts for money lost on over-round SO By plugging this information into the calculator above, I get an answer of 0.0341 Which I think means There is a 3.41% chance that I just got lucky - based on the probabilities and my strike rate that would have happened randomly at that rate... Sorry if I have lost you here. Next If I double my wins and total bets (so the strike rate stays the same) I get a Negative Binomial Distribution of 0.00692 (0.692%) Again, this makes sense as if you maintain profit over more bets, chances are you are doing well. Next Take the inverse percentage of the values above, and you have a kind of confidence figure. So I can be 96.59% sure that my wins were not down to luck. If I have done anything wrong here, please let me know :) but looking through it I think that it is all correct. ------------------------------------------------------------------------------------------------------------------------------------- I think that this would be a really useful tool for people analysing their systems and own performance to get an idea of whether or not they are performing well or not, but I may be wrong! Also there is an important assumption in place that this refers to level stakes betting, there is no weighting for different stakes. Either way, if you: 1) have a high degree of confidence that you are not getting lucky and... 2) work out your strike rate * average decimal odds to be positive (after any commission) Then things should be looking good :) However I think there may be some skew due to average odds and average strike rate, if the odds vary wildly then multiplying average odds by S/R may not be an accurate way of working this out. SO if anyone can think of a better method if this is wrong, or if it is right then give me some further advice then that would be good :) Perhaps it would be better to break it down into odds ranges, i.e. 1.5-1.6 to fine tune this once you have a large data set? I know that some people on here have looked at using odds ranges as a strategy, a tool like this could be used for that. Anyway, would really appreciate some help and sorry if I seem like an absolute maniac, it's been a long day and stats are driving me mad. At least by bet on the Citeh game won.

[robkor]

Re: Stats Question - Negative Binomial Distribution Perhaps you could simulate your sample of bets via Monte Carlo simulation, and count how many simulations ended in the set target (e.g Yield>0%, >2%, >5%, ...) and so get the confidence for each target. cheers

[slapdash]

Re: Stats Question - Negative Binomial Distribution Hi, a couple of things: Firstly, the Negative Binomial Distribution isn't what I think you think it is. What you calculated was the probability that your 13th win would be on precisely your 20th bet (assuming a win probability of 47.38% for each bet). In fact, there's about about an 8.76% chance of doing at least as well as 13 wins from 20 assuming 47.38% for each bet. Secondly, you say "There is a 3.41% chance that I just got lucky - based on the probabilities and my strike rate that would have happened randomly at that rate..." OK, the 3.41% figure is wrong, but apart from that: the second part of what you wrote is fine. But that doesn't mean that there's a 3.41% chance you got lucky. You're comparing two statements: "A: I'm no better than the odds suggest at picking winners" and "B: I got 13 winners out of 20". What this kind of calculation tells you is the probability of B, given A, ("If I were no better than the odds suggest, I'd only have an 8.76% chance of doing as well as 13 out of 20"). But that's not the same as the probability of A, given B, ("If I do as well as 13 out of 20 then there's only an 8.76% chance that I'm no better than the odds suggest"). As a rather extreme example that makes the difference clear, suppose you had a system to predict the toss of a coin using astrology (or something really ridiculous, in case you believe in astrology!), and suppose your system predicted the first two tosses correctly. Then there's a 25% chance of that, assuming your system is no better than chance. But the fact that you got two out of two correct certainly doesn't mean that there's a 75% chance that your system is better than chance.

[Guest]

Re: Stats Question - Negative Binomial Distribution

Hi' date=' a couple of things:[/quote'] Thank you for replying. I had a feeling I was doing something wrong. Do you know the name of the test (I think it involves standard deviation and degrees of freedom) that would be useful for this purpose? I also want to learn a lot more about stats that can be used for modelling etc. but not really sure where to begin.

[JohnPR]

Re: Stats Question - Negative Binomial Distribution I think you are after the Chi Squared test.