It seems reasonable, ( allbeit ironic ), to me to adjust calculated probabilities by combining them with market probabilities with a weighting constant which reflects relative accuracy. Admittedly, without many stats, deciding on c is very intuitive. With an unrealistic exactly " fair " market, this has the same effect on investment %s as fractional Kelly betting; however, in the real world, fractional Kelly betting is crude and dangerous. As well as the market being a significant indicator of probabilities, the relationship between the market and handicapper market expectation is informative. I have developed a proceedure for processing these indicators. I will post it soon when I have time. In the interim, comments on the idea/philosophy are, of course, welcome. Perhaps others are allready doing this sort of stuff.
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Yup, it's dangerous...because as Ganchrow obliquely points out, you have not figured in your Bayesian Priors for each of your "situations"...and correctly binning each "situation" is part of the problem.
...and what's worse, those priors can drift (regress) against you.Comment -
This looks like an interesting branch of mathematics, but it seems like ignoring it on this issue would cost me much less than ignoring the issue. A game with De Finetti flavour: A new sport is invented - a 2 sided game. The players are known to everyone from other sports. The rules are also exposed. The first game approaches. The bookmakers are taking bets. The bookmakers expect team A to win by 8 points. You expect team B to win by 5 points ( before you learn of the bookmakers' expectation. ) Now you are informed that you will be awarded the ultimate prize if you predict the relative score-line to within 2 points inclusive. Assuming that your expectation is based on in-depth research and calculation, you would presumably give your raw expectation some relative respect and nominate an in-between score-line. If I have done no other research, whatever you nominate becomes my expectation. Ok, this is unreal, contrived subjectivity. I do believe, however, that there is a significant limit to objectivity in the real world. Even if there is not, is not the following scenario possible: a handicapper has accumulated plenty of stats on her game ratings of league x, and has the betting stats also. She notes that the bookmakers' ratings are more accurate than hers. For the next game, her raw probability rating on team A is .65. the bookmakers' rating is .50. She scientifically factors in the bookmakers' rating and calculates a final probability of .56. The bookmakers are offering 1.90, so she has an advantage?Comment -
Hi Neil.
I have previously tried something like this. I had a very large database of horse statistics and, using some fairly advanced regression techniques, calculated a winning value for each horse. These statistics did not include the bookmakers odds. Once I had my own measure of a horses quality I combined this (lookup "multinomial logistic regression" if interested) with the bookmakers odds to form a winning probability for each horse.
As you may or may not expect, the horses which I assigned the highest probability (my favourites) actually had a slightly lower strike rate in the long run, BUT due to the fact that I was able to identify quite a few longshot winners (ie. bookmaker odds were high) the return was significantly higher than just betting on the bookmakers favourite each time.
LOJ.
PS. I should mention these "results" were simulated and I placed no actual money using this system. I do feel that it was a true reflection of what would of happened had I bet in reality - but one can never be sure
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Interesting.Hi Neil.
I have previously tried something like this. I had a very large database of horse statistics and, using some fairly advanced regression techniques, calculated a winning value for each horse. These statistics did not include the bookmakers odds. Once I had my own measure of a horses quality I combined this (lookup "multinomial logistic regression" if interested) with the bookmakers odds to form a winning probability for each horse.
As you may or may not expect, the horses which I assigned the highest probability (my favourites) actually had a slightly lower strike rate in the long run, BUT due to the fact that I was able to identify quite a few longshot winners (ie. bookmaker odds were high) the return was significantly higher than just betting on the bookmakers favourite each time.
LOJ.
PS. I should mention these "results" were simulated and I placed no actual money using this system. I do feel that it was a true reflection of what would of happened had I bet in reality - but one can never be sure
What is your theoretical ROI just betting the longshots?Comment -
After approximately 5 years I was up to 2.1 units (initial wealth 1 unit). Bets wouldn't be placed very frequently and I would need quite a neat setup to achieve this in reality.... however given my bank now offers around 4% interest maybe I should run with the 16% I could get from this......
Last edited by lukeouk; 03-06-09, 01:24 PM.Comment -
The trick (in all sports) is getting the computer to do the work for you. If you have a valid method of analysis that gives you a 25% ROR per year, it's worth the effort to automate it.After approximately 5 years I was up to 2.1 units (initial wealth 1 unit). Bets wouldn't be placed very frequently and I would need quite a neat setup to achieve this in reality.... however given my bank now offers around 4% interest maybe I should run with the 16% I could get from this......
If you are interested in pursuing this, I'll be happy to talk to you. Either steer you in the right direction, whatever else makes sense.Comment -
How do you get bookmaker odds in racing? Also, are you talking about overcoming a 20% edge by something less than 1 point? You must not be talking parimutual pools.bird bird da bird's da wordComment -
maybe he's talking about a tic-tac man?Comment -
Sorry if I was unclear - I don't have a tight grip on the lingo unfortunately. When I said "bookmaker" I meant the odds available from one of the big UK names such as Ladbrokes/William Hill etc. Once I had determined probabilities using these odds I made an, admittedly dodgy, approximation of what the Betfair Odds would have been on these horses. These odds were used to ascertain my wealth growth/shrinkage.
This approximation is clearly a major issue with the system and obviously means both profit/ROI are also approximations.
I'd never heard of a tic-tac man before today but I found the wikipedia article interesting - quite nice to know there are jobs such as this in existence
Thanks for your generous offer Justin - I'm just finishing University at the moment and am in the middle of a Job hunt but when things settle down you will most likely be hearing from me.
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Thanks, Lukeouk. I would not expect your favourites to have a slightly lower strike rate in the long run. It would seem that your probability sets would be slightly more efficient with a gentle anti-polarization manouvre. N.Hi Neil.
I have previously tried something like this. I had a very large database of horse statistics and, using some fairly advanced regression techniques, calculated a winning value for each horse. These statistics did not include the bookmakers odds. Once I had my own measure of a horses quality I combined this (lookup "multinomial logistic regression" if interested) with the bookmakers odds to form a winning probability for each horse.
As you may or may not expect, the horses which I assigned the highest probability (my favourites) actually had a slightly lower strike rate in the long run, BUT due to the fact that I was able to identify quite a few longshot winners (ie. bookmaker odds were high) the return was significantly higher than just betting on the bookmakers favourite each time.
LOJ.
PS. I should mention these "results" were simulated and I placed no actual money using this system. I do feel that it was a true reflection of what would of happened had I bet in reality - but one can never be sureComment -
Hi Neil,
Could you explain what you mean by this "anti-polarisation" procedure? I haven't come across this term before and am curious to investigate it.
Thanks,
LOJComment -
The following seems to be a reasonable polarisation proceedure: Suppose that there is a set of outcomes for an event, the probabilities of which total to 1. Symbolize these probabilities P1, P2, P3, . . . , Pn. The probabilities P1', P2', P3', . . . ,Pn' are defined as the polarised set, such that P1' = [ 1 + (P2/P1)^I + (P3/P1)^I + . . . + (Pn/P1)^I ]^-1. P2' = P1'(P2/P1)^I, P3' = P1'(P3/P1)^I, . . . ,Pn' = P1'(Pn/P1)^I. " I " is the polarisation indice. { 0 < I }. When 0 < I < 1, an anti-polarisation occurs. Hopefully, there is a vlue for " I " which generates a more statistically reflective, and more efficient set of probabilities. N.Comment -
Thanks for info Neil,
So at first glance it seems you are saying that the j'th probability is given by:
Pj' = Pj^I/(Σ(Pi^I) where the numerator is a constant (independent of j).
I see what you mean about this being an anti-polarising procedure now but surely this would have absolutely no effect on which of my probabilities is the highest. It seems that each Pj is simply enlarged due to exponent "I" and then scaled down by the summation term. I could be missing something huge, and being terribly stupid - if so I apologise and will go get another cup of coffee!
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Hi Lukeouk, Be careful with coffee! I interpreted your " lower strike rate " as meaning lower than that implied by your raw favourite probability, but you may mean lower than those of other horses.Thanks for info Neil,
So at first glance it seems you are saying that the j'th probability is given by:
Pj' = Pj^I/(Σ(Pi^I) where the numerator is a constant (independent of j).
I see what you mean about this being an anti-polarising procedure now but surely this would have absolutely no effect on which of my probabilities is the highest. It seems that each Pj is simply enlarged due to exponent "I" and then scaled down by the summation term. I could be missing something huge, and being terribly stupid - if so I apologise and will go get another cup of coffee!
Comment -
Raw probability refinement proceedure.
Refinement of an event raw probability set with ( the betting market and handicapper betting market expectation ): Suppose that there is an event for which outcome probabilities have been calculated without the betting market, and that an expected market ( set to M = 100 ( % ) ) has also been calculated. Let the raw outcome probabilities be symbolized: Pr1, Pr2, Pr3, . . . ,Prn. Symbolize the respective expected dividends: De1, De2, De3, . . . ,Den. Symbolize the respective available dividends: D1, D2, D3, . . . Dn. Let the market place relative efficiency indice be symbolized: I. ( 0 < I < 1 ). ( The greater the perceived strength of the market place relative to handicapper raw probabilities, the larger is I. ) ( The I value can vary between possible outcomes of the same event. ) Each approximate refined probability, ( Pa ), is given by: Pa = [ ( 1/Pr - 1 )(De - 1)^-I ( .01MD - 1 )^I + 1 ]^-1 Now take the excercise through another phase by calculating each balanced outcome probability ( Pb ): Pb = Pa( Pa1 + Pa2 + Pa3 + . . . + Pan )^-1 Let a perspective limitation factor be symbolized: Fl. ( 0 < Fl < 1 ). Now take the excercise through the final phase by calculating each final workable probability ( Pf ): Pf = ( 1 - Fl )Pb + 100Fl/DM ( A typical I value may well be .7 and a typical Fl value may well equal .15. With a scenario of the raw probabilities resulting from a TEAM effort, .05 may well be an appropriate Fl value. ) A handicapper may well decide that the Pb values are the final ones, especially if plenty of stats are used to generate the I value. Not only does the betting market represent information, but so does market surprise. This particular method is somewhat intuitive, but perhaps it is worthwhile until something more sophisticated comes along.Comment -
Hi Neil,
Looking back, my explanation of "lower strike rate" was slightly unclear. I meant that the horses I assigned the highest probability, in each race, won less frequently than the horses which the bookmaker assigned the lowest odds to (highest probability). I have since looked at this again and with more advanced techniques have been able to improve on this slightly.
My favourites now win approx 35% of the time, whilst the bookmaker favourites win 32.9% of the time. Given that my database contains around 80,000 races this 2.1% is significant.
Again, thanks very much for your info - I will certainly keep this in mind for future work.
LOJ.Comment -
My stats theory research is quite low, but this looks a tad misleading. Perhaps read some relevent posts by Ganchrow. It might be too massive of a task, but I would like to know the value of the weighting constant which would create a combined probability set of maximized efficiency. The owner of such of a set would generate a greater capital multiplication ( using Kelly theory ) betting on any of the other set owners' markets than the targeted owner would betting on Mr. M.E.'s markets. Let a raw probability according to the bookmakers be symbolized: Pb. Let a raw probability according to the hadicapper be symbolized: Ph. Mr. M.E.'s probability ( Pe ) is given by Pe = cPh + ( 1 - c )Pb. Depending on corelation, I suspect that if c is as high as .1, you would see the odd worthwhile bet on Betfair. 80,000 seems like a decently large sample, particularly as you apparently did enough ground-work on your proceedure to expect a significant level of efficiency.Comment -
Does your 35% win rate show a profit? To me, in the end, that is the only statistic that counts. If it does, then you have found something good.
Let me share something that has worked very well for me over the years. First, I do not subscribe to over information. That is not to say that anyone is wrong if they compile tons of data, I just don't do that. What I do is just different than what might seem logical. There is more than one way to look for an edge in gambling. Compiling tons of data is one way and using limited data in certain situations is another way (the way I do it).
In horse racing if you ask me who do you think will win the race, I would look at the tote board and pick the horse with the lowest odds. Not sophisticated, but if there was a contest to pick the most winners from each of a set of races, selecting the favorite in each of those races would give you the greatest chance of selecting the most winners compared to everyone but the very best handicappers and even then it would be close. Of course playing the favorite in each race is a losing proposition because the odds returned are not enough to make up the effect of the track take. So the answer is to find those situations where the horse you are betting on is for some reason not bet to its proper odds or underbet. If it is underbet enough, you should be able to show a profit. After looking at all kinds of races (maidens, claiming, allowance etc) I discovered different situations for the different classes of races that can create over and underbetting. Some situations only work in some of the classes and different situations work in the other classes.
Here's an example of a situation, it is a couple of minutes to post, you look up at the tote board and you notice that both the #1 and #3 horse are co-favorites at 2-1. You look at the records and you notice that the #1 is superior. It may have finished up close in better classes, it may have a better jockey/trainer combo etc. Whatever the reason (and you must know the various reasons that the public bets), you know that on paper the #1 should beat the #3 and so you place the bet. You watch the race in disbelief as the #3 easily beats the #1. You look at the records again and again decide that the #1's record is better and should have beaten the #3.
I on the other hand would have bet the #3 and here is why. First you must believe (and it is true) that the public is an expert. The public gets it right more often than any individual handicapper could when making a selection for each race (there may be very, very, very few exceptions). Since the public is expert, I know, that they know, that the #1 looks superior. If the #1 looks superior, what is the chance that the #1 is underbet? None IMO. It can't be under bet in this situation because on paper it clearly looks superior. What is the chance that the #3 is underbet? A very good chance because the #1 looks superior and even better yet it is at the same odds as a horse that looks inferior making it look like the #1 is an overlay when in reality it is an underlay. It of course does not mean you will win every time in this situation. It just means that you have a better chance of making a wager with a +EV and that is what makes profits. Enough for now. Just wanted to give you a different way of looking at things.
Joe.Comment -
Thanks Joe. Profit is, at the end of the day, the most important metric for any system of this sort. I hear what you are saying about the public and the "wisdom of crowds" etc.
This is very true, however what I am saying is that my 35% is profitable (at least in simulation) and that the 35% strike rate is above that of the bookies favourite tested on the same data - therefore I suppose you could view this system as being one of the "very best handicappers" mentioned in your post. Again you are correct in thinking that the difference in strike rate is close (2.1% in the example I gave) however given that, even in the worst case scenario, my system identified 2.1% winners that the tote-board did not; it is easy to see where the profit comes from (assuming I placed bets on these "outsiders").if there was a contest to pick the most winners from each of a set of races, selecting the favorite in each of those races would give you the greatest chance of selecting the most winners compared to everyone but the very best handicappers and even then it would be close
The system used a kelly wagering scheme and so in many cases the favourite horse was not bet on, but this is a slightly different issue I suppose.
I definetely appreciate your views on this and understand that data-mining and trying to find an underlying model are not always the best ways to do things - but, for reasons I won't go into, this was the only methodology I could look into
Do you still bet on horses in this way? I'd be interested to hear if you have moved into anything else.
I am just starting out in all this stuff and have been reading around the betfair trading forums recently - it doesn't really fall under the handicapping umbrella I suppose - but it is interesting. If anyone "trades" horses/other sports in this way I would be very interested to hear/take any advice or warnings etc..
Thanks,
Luke.Last edited by lukeouk; 03-14-09, 11:05 AM.Comment -
Hi there Lukeouk, I finally got around to looking up " multinomial logistic regression ". There are some terms that I have not learned yet, but I get the impression that the process does not corelate individual data samples to differnt trends. If this is so, you may be able to find a blending formula which generates much higher capital growth than 16% p.a. N. N.Hi Neil.
I have previously tried something like this. I had a very large database of horse statistics and, using some fairly advanced regression techniques, calculated a winning value for each horse. These statistics did not include the bookmakers odds. Once I had my own measure of a horses quality I combined this (lookup "multinomial logistic regression" if interested) with the bookmakers odds to form a winning probability for each horse.
As you may or may not expect, the horses which I assigned the highest probability (my favourites) actually had a slightly lower strike rate in the long run, BUT due to the fact that I was able to identify quite a few longshot winners (ie. bookmaker odds were high) the return was significantly higher than just betting on the bookmakers favourite each time.
LOJ.
PS. I should mention these "results" were simulated and I placed no actual money using this system. I do feel that it was a true reflection of what would of happened had I bet in reality - but one can never be sureComment -
whups, speld algothythm rong agen, shame on u!
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SYSTEM FOR UPGRADING RAW HANDICAPPER PROBABILITIES BY FACTORING THE BETTING-MARKET IN. Let "a" & "b" symbolize denotions of 2 different outcome probabilities in the same event / ( group of events ) such that the manipulative strength required to convert Pa into Pb is defined as T[a,b] = ( 1 - Pa )*Pb/( Pa*( 1 - Pb )). Tr[a,b] relates to raw handicapper probabilities. Tm[a,b] relates to probabilities indicated by the market ( set to 100% ). Tf[a,b] relates to processed probabilities to be used directly for investment ( and capital growth ) calculation. "Im" is defined as a market efficiency indice, which indicates the efficiency of market probabilities relative to raw handicapper probabilities. 0 < Im < 1. If a constant value, "c", is determined such that for a statistically large sample of events, of all of the possible constant weightings of Pr relative to Pm, the highest efficiency set is given by: P = c*Pm + ( 1 - c )*Pr for each possible outcome, then, Im ~ c. A figure of Im = 1/2, would indicate that raw handicapper probabilities have an efficiency equal to that of the probabilities implied by the market. An Im figure can be decided upon intuitively. A cautious handicapper would err on Im towards the upper limit. With n contestents in the event, calculate: Tr[1,2], Tr[1,3], Tr[1,4], . . . ,Tr[1,n], & Tm[1,2], Tm[1,3], Tm[1,4], . . . ,Tm[1,n]. For each ( Tr, Tm ) pair, calculate: Tf = Tr*( Tm/Tr )^Im, resulting in the Tf set: Tf[1,2], Tf[1,3], Tf[1,4], . . . ,Tf[1,n]. Note that Pf2 = ( ( 1/Pf1 -1 )/Tf[1,2] + 1 )^-1, Pf3 = ( ( 1/Pf1 -1 )/Tf[1,3] +1 )^-1, . . . Pfn = ( ( 1/Pf1 -1 )/Tf[1,n] +1 )^-1. Substitute these equations into this equation: Pf1 + Pf2 + Pf3 + . . . + Pfn = 1. ( This simplifies to a polynomial equation of degree n. ) Now substitute the Pf1 result into the preceeding equations to complete the Pf set. For an approximate Pf set, for each contestent/( possible outcome ), Pf = Im*Pm + ( 1 - Im )*Pr. Shortcut method for event with only 2 possible outcomes: Calculate 1/( 1 - Tf[1,2] ) ( = say Z ) Pf1 = Z +/- ( Z^2 - Z )^.5 Shortcut method for event with only 3 possible outcomes: Calculate Tf[1,2] + Tf[1,3] ( = say Z ); & Tf[1,2]*Tf[1,3] ( = say Y ). Solve this equation for Pf1: ( ( 1 - Z )/Y + 1 )*(Pf1)^3 + ( ( Z - 3 )/Y + 1 )*(Pf1)^2 + 3*Pf1/Y - 1/Y = 0. UPGRADING WITH THE BETTING MARKET & BETTING MARKET EXPECTATION. As well as formulating raw probabilities, the handicapper formulates an expected betting market; ie, a market that is most likely. This expected market is represented as a probability set ( total set to 1 ). As with the system which factors in the betting market only, calculate the sets of figures relating to Tr & Tm. Now, in the same way, calculate a Tem set of figures, relating to the expected market probabilities. Iem is defined as an expected-market efficiency indice which indicates the efficiency of expected-market probabilities relative to the market probabilities. 0 < Iem < 1. The lower the Iem figure, the more that the upgraded probability is bent towards that of the market. A handicapper may well rate Iem lower, closer to close of betting. For each ( Tr, Tm, Tem ) trio, calculate: Tf = Tr*( Tm/Tem )^( 1 - Iem ). If there is time for more betting market fluctuations before close of betting, a handicapper may also calculate a Tfem set, such that for each ( Tm, Tem ) pair, Tfem = Tem*(Tm/Tem)^( 1 - Iem ). With the former or both of these T sets, calculate the Pf set, and perhaps the Pfem set. The Pfem set represents the expected close-of-betting dividends. So, a handicapper may choose to wait before betting, and she may decide to bet on something that she expects to firm; with the intent of backing something complementary later. Note that the relationship between a Pr and the corresponding Pem, is strongly reflected in the relationship between the Pf and the Pm. Whenever either of these 2 upgrading systems are used, the indice stays constant for the calculation of the time-relevent Pf set.Comment
