Monday, 18 April 2011

Value doesn’t pay the bills

An extremely rare guest post on my blog, from a former bookmaking colleague who has been a pro punter now for several years, Vasu Shan. You can follow him on Twitter @vasman60

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“Value doesn’t pay the bills”. I’ve always hated that expression. What does it mean?? Surely, it’s simply the ramblings of an unsuccessful punter. Is that old chestnut about finding winners being preferable to finding value rearing its ugly head? Of course, none of us can predict the outcome of an event with any certainty, nothing is “nailed on”, it’s not possible to “buy money”. We’re not in the business of prediction, we’re in the business of probability. A successful punter backs both winners and losers, ensuring that the rewards from the winners outweigh the cost of the losers. Value is what it’s all about, isn’t it?? If you need a winner so badly in order to ensure your electricity doesn’t get cut off, you probably shouldn’t be betting at all. If you need a bit of luck on the punt to pay for dinner tonight, you clearly don’t understand the long-term nature of betting. And if the value simply doesn’t seem to be paying, even in the long-term, well, likely you’re not actually getting value at all!

“Value doesn’t pay the bills”? Nonsense!

So, we’re agreed, we want value from our bets. We want 6/4 about the toss of a coin. We want Even-money about Man Utd at home to some average Premier League side next weekend. We want 33/1 that Tiger Woods wins the Open Championship. Yep, value. Maybe the above are too good to be true, but some kind of value.

And we want as much value as possible. 2/1 about the toss of a coin, even better.

Let’s crunch a few numbers. 6/4 about an Even-money chance represents 25% of value (if I spent my whole career betting Even-money chances at 6/4, my Return on Investment, or ROI, would be 25%). 2/1 about an Even-money chance is better, with Expected ROI on such a bet 50%. Betting 50/1 about a 25/1 chance is a stonking 96% of value. And it gets better, a career betting 1,000,000,000/1 about a 1,000,000/1 chance would yield an Expected ROI of 99,900%. But hold on, back in the real world, are we really saying that betting million-to-1 chances at a billion-to-1 is the gold-paved path to betting glory? After all, even after a consistent outlay, there’s every possibility that you’ll never see a return in your lifetime. Such bets may be astonishing “value”, but in terms of tangible reward are arguably not great bets at all.

Let’s get back to basics. If I offered you the following sets of annual gross profit figures, which would you prefer, as a punter? £200,000 (@ 16%ROI), or £400,000 (@ 4%ROI). Those who would prefer the latter are what economists refer to as “rational”. Winning as much as possible, as quickly as possible, is of course the ultimate betting objective. We want to maximise our Expected Wealth. Which doesn’t mean maximising Expected ROI (aka Value).

Incidentally, when we talk about maximising Expected Wealth, be sure not to confuse that with maximising Expected Profit. If you want to maximise Expected Profit, you should bet your entire bankroll on the next value selection that you come across. A strategy of betting your life savings on an Even-money chance at 11/10 (or any price for that matter) will inevitably end in disaster. Of course, a no-betting strategy will show zero profit. There is, however, an optimal stake between all and nothing...

The Kelly Criterion dictates that you should try to maximise the Expected Rate of Bank Growth rather than trying to maximise the Expected Bankroll itself. Google it for historical details. Dust off those A-Level maths books... in order to ensure Expected Rate of Bank Growth is maximised, our logarithmic utility function is differentiated and set to zero. Google again for details of the boring calculus, but the result is a formula that is able to recommend an optimal stake for each betting opportunity that is a function of the size of your bankroll and the value that you’re getting, with respect to the price that you’re taking.

The uses for Kelly don’t end there. Ever wondered what you should do if you’ve backed a 500/1 Superbowl finalist, with the 50/50 big match now priced at 10/11 pick’em. Though I suspected some economic hedging argument, the absence of a mathematical justification led me to believe that with no remaining value, simply holding the position was the right thing to do. I was wrong. There is an optimal hedge that will see the expected rate of your bank growth maximised, even though you may be accepting negative value on that hedge. Or you’re on Benfica @ 20/1 for the Europa League, and now you make them short favs in the final, and 2/1 is available. How much should you optimally press, if at all? Kelly can help you calculate how best to trade most effectively, based on how much you’ve already risked, the size of your bank and your level of risk aversity. Overstaking, re-assessment, market moves, arbitrage?? Ask Kelly. Accept no substitutes.

As the number of bets you make increases, the chance that Kelly betting will beat other systems approaches 100%. The Kelly Criterion is endorsed by no-less-an-investor as Warren Buffett, but it should be noted that while it is economically and mathematically sound, it is not to everyone’s tastes. A common complaint is that it is far too aggressive. Given that we each have a natural level of risk aversity, and knowing that we generally deal with odds estimations with a margin for error (rather than “true” odds), this seems to be a fair grievance. A fraction of Kelly is therefore recommended (30% to 50% seems to be a “happy medium” within the professional punting community), the important thing is that a suitable ratio between your bigger bets and smaller bets remains. Full-Kelly staking should be optimal, but it is certainly volatile. As you reduce your Kelly%, your bank will tend to grow less rapidly, though less volatility will be attached.

The fact is even the best odds compilers in the world would unknowingly be on the road of bankruptcy if they were to mismanage their money, by consistently overstaking. On the other hand, understaking would see a failure to fulfil punting potential (a preferable failure, admittedly).

In an earlier example, we pointed out that a career betting Even-money chances at 6/4 would yield 25%ROI, and a career betting 25/1 chances at 50/1, 96%ROI. However, more significantly, at optimal stakes, the former would on average grow your bank by 2.06% per bet, while the latter would only have an expectation of 0.73% bank growth per bet. And if you’re making a large number of bets, cumulatively, that differential can turn out to be enormous. It should be clear which is the truly productive cash cow and which is merely the efficient red herring.

Those who’ve spent a lifetime maximising ROI, I guess you’ve now realised that in a punting context, those who are able to grow their bank balance more significantly are, by most people’s definition, the more successful.

So, in summary...Return on Investment for show, Rate of Bank Growth for dough. £, not %. As I’ve always said, “Value doesn’t pay the bills”.

11 comments:

  1. What a super post. One of the best I have read in a long time. http://green-all-over.blogspot.com/2011/04/value-kelly-and-roi-blog-post-of-year.html

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  2. many thanks Cassini. Vasu will be suitably chuffed.

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  3. Silly question from one who operates on a plane much lower than you guys, can a staking plan a la Kelly be applied to strict trading. Is there a way to calculate the optimum stake size and entry/exit prices for optimum bank growth ? You guys obviously have a much greater understanding of mathematics than I have and I was wondering how to apply it? ps I also posted this query on Cassini's blog to maximise chances of a solution, don't be offended.

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  4. This is a good post but the truth is kelly isn't for most punters. This is because most will overestimate there edge more often than not and go (virtually) bankrupt.

    Kelly looks great to start with but this is simply because you are overstaking and 9 times out of ten if you took your average kelly stake and bet it each time you would find you would be in more profit and have much less risk.

    Of course kelly is the ideal but should only be used for mathematical models that have a proven history of estimating odds in my opinion. Most people will overestimate their edge at some point to devastating effect and even if you didn't and were to find an even money shot that is 99% certain to win in reality, there's still a 1% chance you will lose nearly all your money and wipe out all that hard work....

    And even though you don't actually lose all your money, you will find that in reality there's not consistently enough inaccuracy in enough sporting markets to take your bank (now 2% of what it was, back to where it was.

    Tread very carefully.

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  5. Average Guy - for trading rather than standard punting, that's a tricky one. I would cautiously say no but I'm sure some boffin will eventually come up with something.

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  6. Brian - good point. Using the Kelly criterion properly does require a good knowledge of how to assess markets accurately. Part of the reason why using a fraction of what Kelly determines is used by most followers.

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  7. Reading another BLOG last night the author painstakingly proved that for horse racing bets round the 2.0 mark that the exchanges were really efficient and ROI was nearly 0% if backing all selections in this range. My simple understanding of the Kelly method is that the stake % of the bank should be = (Offered Odds - Actual likelyhood odds). In the case hereby I.m getting Even Money (=2.0 = 50%) about a 4/5 shot (=1.8 = 55.55%) that my stake should be 5.55% of my bank. If the market is nearly 100% efficient round the 2.0 mark then this means our stake should be 0% ? Am I raving and just displaying my ignorance ?

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  9. Brian makes a very good point. The theory is wonderful, it's sound and it works. But it's certainly no magic secret to punting success.

    I guess the conclusion of the piece was that "value doesn't pay the bills" after all, but the truth is VALUE IS A PREREQUISITE. As is being able to quantify that value adequately. The old adage of "Garbage in, Garbage out" applies. All Kelly does is optimise your wealth from punting, it can make a good punter a better one. It can't, however, turn a bad punter into a good one.

    For me, the theory is the easy bit. Going out there and finding and assessing value is much harder.

    Let me give an example that may help with a few queries raised (forgive me, it's a football example, it's all I know!). Let's say MU and Chelsea were to meet in the FA Cup final, and I was happy with my 50/50 estimation of the game (admittedly, not as happy as I would be with a toss of a coin, but happy enough to proceed with 40%Kelly). On the same day, Skonto Riga (of Latvia) were at home to Omonia Nicosia (of Cyprus) in an Intertoto Cup tie, which I also made a 50/50 match (Draw No Bet). Let's say 6/4 DNB is available for both MU and Skonto. Kelly's objective formula recommends I have a similarly-sized bet on both matches. However, I know that’s nonsense, I'd be much more confident of my Even-money estimation of the former than I would that of the latter. My Intertoto Cup match odds have a much bigger "margin for error" (in maths terms, the mean doesn't mean nearly as much without a standard deviation/variance). It is for this reason that I've introduced a subjective element to my Kelly betting, that accounts for my "confidence" in a bet. In the case of this Intertoto bet, I might bet 25% of my 40% Kelly (10%Kelly).

    It's often said that successful punters require discipline. They also need to be honest with themselves. In this case, honest about their potential profitability. If you've been doing consistently well on the punt for a period of time, try Kelly, you'll be very pleased with the results. If you’re not so confident, feel free to scale down your Kelly% further. One thing that Kelly shows above anything else is that understaking is MUCH more preferable than overstaking.

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  10. Average Guy - the stakes to which you bet don't matter. Kelly works as a % of your bank. And yes, it is certainly possible to use Kelly to optimise your trading. Let's say you already have a position on a two-way market. I think the relevant parameters to determine your next bet are the size of your bank, your level of risk aversity, your current position, your re-assessed odds, your level of confidence in that re-assessment and the prevailing odds that you can bet. It's a few numbers to crunch, that's for sure!

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  11. Average guy - re your 2nd comment...I guess you have a decision to make in your example. Do you trust your assessment? Do you believe in the lack of profitability at such prices on the exchanges? As is often the case perhaps the truth is in the middle...personally I'm loathe to just dismiss an assessment I've spent time on...maybe a bet at half-stakes??

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