Idea

[Guest przeszczepan]

Not much time to write. The situation is very simple: As usual, a child of przeszczepan's sick brain waits for an abortion(or a miraculous cure). I have made over 100 bets following a certain group of tipsters. Now, let's say, I want to apply the Kelly staking plan for the future games. It's quite easy to count my edge from the past bets so I can simply put it into the equation for every game since, as proven by Joe, it doesn't make a big difference whether I have an exact( read: unattainable) edge for each bet or just an average one. Here is where the problem begins. Say, tipster A (edge=5%) advises to bet 5/10 units on evens in one game and 10/10 units on evens in another one. The question is: how on Earth am I supposed to persuade myself to treat these games in the same way and bet the same amount of money on both of them?! What if tipster B, whose edge=10%, bet 5/10 on evens? Should I really treat it in the same way as the first game of tipster A? According to the theory: yes! According to my common sense: uh! Now imagine A bet 1/10 on odds of 3 and B bet 10/10 on the same odds! Here goes the baby: When we have tipsters data such as: units invested, no. of bets, no. of correct bets, profit, we can count some further values like average stake=units invested/no. of bets, average odds(or rather average winning odds)=(profit average stake*no. of bets)/(average stake*no. of correct bets) and the yield=(money invested profit)/money invested. Now the weakest point of the idea. We count a "virtual bank" using Kelly equation: Bank=(average stake*(average odds-1))/edge. With this "virtual bank" we are able to estimate each tipsters edge for a particular stake on particular odds: edge=(stake*(odds-1))/virtual bank Now you only have to put the edge in the equation for a particular game. I called the "virtual bank" the weakest point because I know not every tipster is using Kelly. Is it the reason why I should abandon the idea? I wouldn't hesitate for a second if the "system" would provide some unrealistic edges. But I checked it on some examples and it's doing just fine: you get higher values for higher stakes on higher odds advised by better tipsters. I just want to know if there's any better way to complete the process ( read: give yourself a mathematical grounds to bet more on better tipsters and higher odds*stake). One more question: I got a bit confused with the terms "yield" and "edge"? Could anybody explain the difference to me, please? Can you simply write edge=yield-1? Lucas

[Guest madmick]

Re: Idea Lucas I believe you will suffer from the common problem of limited data. However, what you may want to consider is to plot the record of the tipsters versus their advised stake size. This should give you some indication of whether or not the tipsters actually can estimate the edge on a particular bet - e.g. a 10 unit bet should be more likely to win than a 5 unit bet. Kelly staking advises varying stake size based on two factors - edge on that bet and odds available for that bet. What you are working on here is the first one of those two, and I think you may well get some profit (no pun intended!) out of it. Yield is the total profit/loss divided by the total amount staked. Edge is the excess of the ratio of the fair odds to the offered odds. For example, if a bookie offers 2.25 about something that should be 2.00 then the ratio is 1.125 = 112.5% which is an edge of 12.5%.

[Guest przeszczepan]

Thanks Hello Mick, Thank you for the reply. As always, I have some further comments:

what you may want to consider is to plot the record of the tipsters versus their advised stake size. This should give you some indication of whether or not the tipsters actually can estimate the edge on a particular bet - e.g. a 10 unit bet should be more likely to win than a 5 unit bet

Not sure if I got the point( I am still working on the phrase:" to plot sth versus sth"). If I am not wrong it means to take all the bets with a particular stake and count the record. Do it for each stake and check if the record is better for 2 units than for 1, for 3 better than for 2 and so on. If this is what you had on your mind than you are definitely right: I will suffer from the common problem of limited data. What's more, I am not sure but the indication may be somewhat blurred since, as in Kelly, when assigning a stake the tipster may take into consideration not only the edge but also the odds. As a result, in a group with 1 unit stake we will probably get bets with a very small estimated edge( with low odds) and those with a higher edge( higher odds). On the other hand, the si:rolleyes tuation will be similar in each group so maybe it doesn't matter after all.(?)

a 10 unit bet should be more likely to win than a 5 unit bet.

After reading this sentence I got a bit confused. I guess you meant games with the same odd, right? Thank you for the "yield/edge" explanation. Lucas

[Guest madmick]

Re: Thanks Lucas what I'd suggest is to infer the edge on each bet, based on their recommended stake size and the odds. Plot this against the returns (as noted you will suffer here from limited data) and see how well they estimate the edge for individual bets - it should be a straight line through zero.

[Guest przeszczepan]

Oh Hi Mick, Firstly, I would like to know if it's alright of me to ask so many questions? Don't you get a bit p****d off answering them? Because if you do, please, let me know or simply stop replying. You may be surprised but I would understand that ;) In the first post you wrote:

plot the record of the tipsters versus their advised stake size

and in the second one:

infer the edge on each bet, based on their recommended stake size and the odds. Plot this against the returns

My mathematical English is extremely poor so I got a bit confused here: what am I supposed to plot against the returns: the stake or the edge? Do these sentences mean the same thing? If it's the edge, then the situation is entirely clear for me. This looks quite similar to the way someone (Odds Against?) once suggested for testing correctness of systems, isn't it. The biggest difficulty for me is:

to infer the edge on each bet, based on their recommended stake size and the odds

Call me a dumbass but I actually don't know how to do it! Should I use the Kelly equation? If so, than I would also need "the starting bank", which is often different in different services. For example for a 10/10 stake on evens, where starting bank is 1000, the estimated edge would be 1% which is a bit unrealistic. I agree it wouldn't make any difference in terms of testing the tipster's ability of estimating the edge, but it would make it difficult to compare two tipsters from different services with different "banks". All in all, it's pointless to discuss it because of the "limited data" problem. The purpose of my "idea" was to find a way to compare bets with different stakes on different odds made by tipsters with different abilities. I wasn't wise enough to think about checking tipsters ability first. I thought that if somebody can generate yield of, say, 10% than it's safe enough to assume that he can determine where a smaller and where a bigger value exists. I think that I will simply check my "idea" with virtual money for the next couple of months and see whether it makes sense to use it instead of the average edge for all bets. Lucas

[Guest madmick]

Re: Oh Lucas keep asking questions - thats how we all learn. If I don't feel like answering I'm not backward about coming forward ;) IN any case some of the knowledgeable people here may have valuable contributions to make. Let me take an example to explain what I mean Lets say you have the following information from a tipster: Odds Stake Size Result 2.0 10 W 3.0 8 L 3.0 6 W 2.4 8 W 1.4 10 W 5.0 2 L 3.0 8 L Now we would really like a lot more than this in reality, but bear with me. There is a total of 52 units staked and 19.2 units profit returned. The tipsters average yield is therefore 19.2/52 = 36.9% (not very realistic!). So on average he is winning 36.9% of his stake on each bet. If we assume that the overround is 12% on the odds offered, then his average edge is 41.4%. According to Kelly, this is what he should be trying to win on each bet. So his first bet is at evens, so he is staking 10 units, so he is looking to win 10 units. So we equate the 41.4% to 10 units (we could use a scaling factor, but it doesn't really matter). His second bet is at 3.0 and for 8 units, so he is looking to win 16 units, i.e. 16/10*41.4%, so his 'relative' edge on this bet is 66%. Contnue for the other bets. These values will be the x-coordinates of your line. The y co-ordinates will be ones or zeros depending on whether the bet won or lost respectively. The line should give an indication (it will be noisy!) about how well that tipster estimates his edge on an individual bet. Hope that helps. M.

[Guest Weststander]

Re: Idea Hi Lucas,hi Mick, Lucas,if I read you correctly you want to try to find the likely probability of a certain bet winning using both the odds on offer & the recommended stake from the tipster who's given the tip. This approach may(or may not) help. Try logistic binary regression (I'm not claiming to be an expert:-)). Basically you imput the odds(decimal format should be ok) & the stake & finally whether the bet was a success or a failure(in other words whether it won or lost) You'll end up with a regression equation in terms of your 2 variables & if the tipster's any good with his selection & staking advice you will be able to imput any combination of advised bets & see how likely it is to succede based on the tipsters past record. You could also compare that probability with the odds on offer if you wanted to go your own way with the stakes. Most stats software packages should be able to do the calculation,but failing that if you post some data in the form of odds,stake,success or failure(where 1 is a winning bet & 0 is a losing bet) I'll get it done for you.Or at least the first 100 bets anyway:-). I'd certainly be interested in the results/comments.It might be a total non starter. W.

[Guest madmick]

Re: Idea logistic or probit regression, or indeed any using MLE rather than least squares would be more appropriate here, but the simplistic approach, i.e. use the Excel trendline functionality should give enough of an indication - as I interpret it the absolute accuracy is not really the issue, more the principle?