General Betting
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02 Jun 11
21:10
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Date Joined:
20 Aug 05
Bear with me this isn't straightforward, but I know there are a couple of guys here that may be able to help:
I have a lay method which in testing to £100 backers stakes (assuming 5% commission) shows a 14.73% return over 336 bets (strike rate 81%, average lay odds 5.03)
When I run a reciprocal test (or A/E as Flatstats call it), I get the following calculation:
Total reciprocal odds 76.92 divided by 64 losing lays = 1.20
So far, so good.
When I use the TSM formula for calculating the 'expectation' for the purposes of Kelly staking, something doesn't quite add up:
Strike Rate: 0.81
Profit 0.95
Liability 4.03 (5.03 average odds-1)
Expectation = (0.81*.95)/((1-0.81)*4.03)
=0.77-0.77=0
Can anyone explain why the Kelly lay calculation shows a 0 expectation on this data set, when the other measures are positive? It has me baffled. I'm no maths expert by any stretch, and any help would be much appreciated before I invest. Also, I do realise this is not really a sufficient data set but it's all I can pull together.
I have a lay method which in testing to £100 backers stakes (assuming 5% commission) shows a 14.73% return over 336 bets (strike rate 81%, average lay odds 5.03)
When I run a reciprocal test (or A/E as Flatstats call it), I get the following calculation:
Total reciprocal odds 76.92 divided by 64 losing lays = 1.20
So far, so good.
When I use the TSM formula for calculating the 'expectation' for the purposes of Kelly staking, something doesn't quite add up:
Strike Rate: 0.81
Profit 0.95
Liability 4.03 (5.03 average odds-1)
Expectation = (0.81*.95)/((1-0.81)*4.03)
=0.77-0.77=0
Can anyone explain why the Kelly lay calculation shows a 0 expectation on this data set, when the other measures are positive? It has me baffled. I'm no maths expert by any stretch, and any help would be much appreciated before I invest. Also, I do realise this is not really a sufficient data set but it's all I can pull together.
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Replies: 17
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You've lost me....
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Someone'll be along in a minute now that racing's over....
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how have you derived your profit number?
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Lost myself raspberry!
Structured - using the TSM formula 1 unit -5% commission so 1.00-0.05=0.95 (TSM is the Staking Machine by the way, only place I could find the formula broken down far enough for me to understand it) |
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Your calculation above reads:
(0.81*0.95)/((1-0.81)*4.03) = 0.7695/0.7657 = ~1.005 |
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Sorry MacLovin it should read - not / so:
Expectation = (0.81*.95)-((1-0.81)*4.03) =0.77-0.77=0 |
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Yes, sorry, obviously it's impossible for the expectation to be greater than 1 (or 0.95 when subtracting commission).
From your figures if you're laying winning horses at average odds of 5.03 (you clearly aren't going by your return %) then you are showing a profit of £48 over 336 bets. This is what the expectation calculation is showing. |
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Is it because in the initial non kelly calculation you use the risk as the backers stake but in the kelly calculation you use the liability? I.e. the 14.73% return is too high an estimate and your kelly edge really is 0.38% (0.7695-0.7657). The first calculation, maybe, should give 3.7% (100*0.1473)/(100*4.03) (you're risking £403 not £100 to make £14.73). Kelly does give counter intuitive results for laying.
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Thanks for the answers guys, which have helped, but I'm still not quite there.
Maclovin's point about the price of the losing lays explains the difference. The 0 expectation is taken across the whole sample of 336 bets, when the average price of the losing lays in the sample was 3.26/1 and not 4.03/1, which is why the reciprocal calculation shows 1.20 (3.26/4.03=1.19 which is close enough for me). That's the original question answered! Pillbox your point about the % return is correct: based on liability the % falls significantly but I don't think that makes the difference as explained above. The next question, which is key in terms of whether I invest or not, is a slightly different one: To £100 backers stakes the 336 bet sample returned £4,949 after 5% commission deduction and the reciprocal calculation of 1.20 reinforces the assumption that a positive edge exists. However, given the Kelly expectation of 0.38% should I expect over time the reciprocal figure of 1.20 to fall to almost 1.00? In other words has the 336 bet sample just been 'lucky' when in reality the 0.38% figure is the correct expectation?? |
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Sorry I should have said 3.26/4.03=0.81 (the strike rate) and 1-0.81=0.19
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Any more help out there??
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Hhhhhmmmm very interesting, have just read about the kelly criterion in the last few days in this book http://www.amazon.com/Quants-Whizzes-Conquered-Street-Destroyed/dp/0307453375 and was wondering what kelly value I should be using for my laying strategy which sounds similar to yours. I am very cautious, almost always lay at around 4/1.
This site calcs kelly without the betfair commission thrown in and seems to suggest if you have a 81% hit rate, the kelly value should be 5% http://www.albionresearch.com/kelly/default.php Play around with the numbers and see you how you get on. Since reading the book the whole thing has intrigued me and I intend to run some monte-carlo simulations with the commission thrown in to try and figure out the best value to use. PM me your email address if you wanna correspond on this! |
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Hi C++,
I was beginning to lose hope of Kelly help so thanks for replying. I've looked at the site you suggested but without commission it's quite hard to assess what the staking would look like, and on balance I think I prefer the Staking Machine formula. I'm going to start a new thread with Kelly in the title to see if a few of the guys who use it on here chip in to the discussion. |
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Just search the forum with Lori and Kelly.
You will find more than enough to answer all your questions on the Kelly betting approach. And don't thank me. You don't know the half of what pain you're in for. |
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Knocked together some java code today and ran some monte-carlo / random simulations laying at 4 to 1 using pure kelly and the 5% winning commission and starting with a stake of 1000 quid in each run over 100 bets suggest that the whole approach is VERY sensitive to the strike rate.
81% strike rate implies kelly = 0.05 and average pot at the end of 10,000 sets of 100 bets is ~ 1,012 83% strike rate implies kelly = 0.15 and average pot at the end of 10,000 sets of 100 bets is ~ 1,494 85% strike rate implies kelly = 0.25 and average pot at the end of 10,000 sets of 100 bets is ~ 3,624 87% strike rate implies kelly = 0.35 and average pot at the end of 10,000 sets of 100 bets is ~ 14,195 89% strike rate implies kelly = 0.45 and average pot at the end of 10,000 sets of 100 bets is ~ 87,958 91% strike rate implies kelly = 0.55 and average pot at the end of 10,000 sets of 100 bets is ~ 810,000 Note these are average values, many of the runs woulda been above the average and many of them below it in each case! So if you can consistently lay 9 outta 10 4-1 events, you could do very well for yourself! ;-) |
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Faskinating discussion. Congratulations lads/lasses. It encourages me to have a deeper look at Kelly et al though, probably like most, maths is not a strength. Which just about sums up my betting! However, I’ve recently tried to get more disciplined and make use of Excel.
So I thought it might be contribute to the discussion and also be instructive to watch the process as experts analyse comparative data. Below are results from 2 lay systems I’ve been tracking. The obvious question is are they sound and, if so, which is better? They are fairly close and it looks like Method 1 is the way to go but I feel the lower lay and losing odds for the second method will tell in the long run (Note “feel”, which is hardly mathematical!) Average Odds Sels Lose Return Hit Rate RoI to£2 Lays Losers Method 1 720 45 £435.10 6.25% 30.22% 13.81 10.6 Method 2 811 56 £434.50 6.91% 26.79% 13.76 10.12 Incidentally, while I’ve been operating to a £2 stake, I’d really like to build the bank (£1560 at the moment) and stake accordingly, somewhere between 2 and 4% of bank. That said, the last 2 weeks have been horrendous with the hit rate on 10% and above for several days. Thus, my confidence has taken a battering but, more intuitively than scientifically, I think all will work out in the long run. Ah the optimism of the punter! |
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To Carify: the table did not come out well in the posting the last 2 columns are the average odds of (a) the selections and (b) the losing lays.
Methid 1: 720 slections; 45 losers; £435.10 return 6.25% of selections lost; 30.22% of stakes returned as winnings (RoI); lays averaged 13.81 and losers prices averaged 10.6 |