[Hulu]

Originally Posted by Ganchrow

Probably the two books that best demonstrate basic quantitiave analysis technique in sportsbetting are Fixed Odds Sports Betting: Statistical Forecasting and Risk Management by Jospeh Buchdahl and Sharp Sports Betting by Stanford Wong.

Thank you sir. Those 2 books are winging their way to me as we speak (along with several CDs...damn you Amazon!)

[Ganchrow]

Originally Posted by trustbutverify

Does the fact that the stock market and the sports wagering market are- to certain degrees- fluid and self correcting have any impact on the predictability of such models?

To some extent ... as the market adjusts itself the predictive strength of any given forecast will, in general, decay over time. This will tend to manifest itself in one of two ways.

Firstly, there might be a decrease in the number and strength of forecasts that meet your hurdle rate.

Secondly, and potentially more harmful to a market participant, the forecasting power of the model might decrease, resulting in biased forecasts. The problem is that the player would be overestimating his edge on any given bet, meaning that not only would he make less money (as in the "firstly"), but also he'd be unable to optimally manage his risk. But ultimately, it would just be up to the player to create a robust enough model to properly account for this factor and a flexible enough modelling framework to rapidly adjust for changes in regime.

[Ganchrow]

Originally Posted by Dark Horse

I think we're back to sequences (aka as streaks).

I'm talking about projecting a sequence of events in advance (different from evaluating each single event). If a chance of failure is 1/75, that failure will occur with certainty. It's just a matter of time.

In simple math. The chance of failure is 1.
It just may not be this time.

I'm not sure entirely certain what you're getting at here, but I fear you might be treading dangerously close to the Gambler's Fallacy.

Just to be totally clear: assuming a 1/75 fail probability, the probability of the shuttle failing at least once at some point over the next 1,000 launches would be (1-1/75)^1000 ≈ 99.99985%.

However, given that the shuttle has not failed at any point in the last 999 launches, the probability of it failing on the thousandth launch would still be 1/75.

[Ganchrow]

Originally Posted by Dark Horse

So from that perspective, an astronaut stepping on a shuttle flight would first have to embrace his own death. Only then could he operate without fear. Only then, in real life, would the end result no longer matter. (as it doesn't in the abstract world of math).

You just lost me.

Originally Posted by Dark Horse

If I translate this (things may be lost in translation) to what Ganch said about what one's true Kelly bankroll really is (everything!), then a gambler using Kelly must either embrace bankruptcy upfront or live in a state of constant fear (controlled by math based assurances).

Well guess what ... gambling can be a bit of a gamble.

[Dark Horse]

Always good to meet someone who has truly embraced risk.

(Time still has a few mysteries. ).

[trustbutverify]

Originally Posted by Ganchrow

To some extent ... as the market adjusts itself the predictive strength of any given forecast will, in general, decay over time. This will tend to manifest itself in one of two ways.

Firstly, there might be a decrease in the number and strength of forecasts that meet your hurdle rate.

Secondly, and potentially more harmful to a market participant, the forecasting power of the model might decrease, resulting in biased forecasts. The problem is that the player would be overestimating his edge on any given bet, meaning that not only would he make less money (as in the "firstly"), but also he'd be unable to optimally manage his risk. But ultimately, it would just be up to the player to create a robust enough model to properly account for this factor and a flexible enough modelling framework to rapidly adjust for changes in regime.

My thoughts exactly. In my original post on modeling i didn't mean to imply that it was impossible to create historical models with very strong predictive results.

I meant to say that it would be a very formidable task- considering many issues- to aquire target pcts with enough stability to depend on for practical kelly implementation for sports. Like most capper/investors I've played with the idea of learning enough about modeling, probability, database design etc.. and aquiring a massive amount of reliable data to do this. It's too much for me.

If i was a card counter i would use an optimizing strategy. But most sports wagerers are doing well if they find a bunch of strategies that beat the line in the long run. IMO- the money mgmnt approach best suited for long term success for most cappers is to treat all situations/angles the same(even though they are, of course, not) and then bet flat with occasional readjustments. Along with finding the best price, this will create the largest gap between the breakeven point(avg) and the avg advantage. That gap will grind out the profit- and drive the bet level and the bankroll up.

Its not optimal- but it might be the best approach for most.

[Milkin' it Slowly]

Thanks for the info .... From what I can gather, It's more based on money management... But the inherent problems in regards to handicapping, is you never no your true chance of winning. If applied correctly, you may be withered down to micromorsels, which in gambling terms is going BROKE. On the other hand if things are goin well, you can increase your stake based on the chance you think you have ... So in other words it can keep you in the game for a while but it still can't take into consideration the actual factors of a contest (weather, injury, pshycological high and low streaks...etc) Pretty complex ....

Anyway, Thanx again...

[Ganchrow]

Even if you didn't feel comfortable making the frequent edge approximations required by Kelly and have resigned yourself to assuming an equivalent edge on each bet you placed, that doesn't necessarily mean that traditional flat-betting would be your best option. In fact, it probably won't be.

If lowering the variance of your bankroll's growth were of concern to you (and it certainly should be) and you frequently find yourself betting across a wide variety of money lines, then you might want to consider moving away from fixed unit staking towards a "fixed-profit" staking plan. Fixed-profits staking refers to betting to win a constant amount on all bets. So in other words, if a fixed-profits staker were to bet 1 unit at a line of +100, he would be betting 1.1 units on a money line of -110, and ½ of a unit on a a money line of +200.

Joseph Buchdahl in Fixed Odds Sports Betting: Statistical Forecasting and Risk Management demonstrates how a bettor engaging in fixed-profits staking can reduce both his standard deviation and his risk-of-ruin versus a flat bettor with the same average bet size.

(Fixed-profits staking, btw, is actually implicit in Kelly betting.)

[trustbutverify]

Originally Posted by Ganchrow

Even if you didn't feel comfortable making the frequent edge approximations required by Kelly and resigned yourself to assuming an equivalent edge on each bet you placed, that doesn't necessarily mean that traditional flat-betting would be your best option. In fact, it probably won't be.

If lowering the variance of your bankroll's growth were of concern to you (and it certainly should be) and you frequently find yourself betting across a wide variety of money lines, then you might want to consider moving away from fixed unit staking towards a "fixed-profit" staking plan. Fixed-profits staking refers to betting to win a constant amount on all bets. So in other words, if a fixed-profits staker were to bet 1 unit at a line of +100, he would be betting 1.1 units on a money line of -110, and ½ of a unit on a a money line of +200.

Joseph Buchdahl in Fixed Odds Sports Betting: Statistical Forecasting and Risk Management demonstrates how a bettor engaging in fixed-profits staking can reduce both his standard deviation and his risk-of-ruin versus a flat bettor with the same average bet size.

(Fixed-profits staking, btw, is actually implicit in Kelly betting.)

I see alot of people who bet fixed profit on neg payouts- not too many on pos. Greed.

Another method of getting more money in on higher expectation positions and vice-versa. I'm curious- have you ever run say, 3000 of your own bets through a test of fixed stake vs fixed profit? If so- how did it come out.

[Ganchrow]

Originally Posted by trustbutverify

I see alot of people who bet fixed profit on neg payouts- not too many on pos. Greed.

I'd say it's often as much naïveté as it is greed. The decision to bet fixed profits on payout odds less 1:1 but fixed stake on payout odds greater than 1:1 might be little more than the product of US-style lines display and an unimaginative mind.

Originally Posted by trustbutverify

Another method of getting more money in on higher expectation positions and vice-versa. I'm curious- have you ever run say, 3000 of your own bets through a test of fixed stake vs fixed profit? If so- how did it come out.

It generally comes out as Buchdahl's simulation predicts: Roughly equal return and lower standard deviation of finishing bankroll than with fixed profits.

What can't easily be determined from looking at a single sequence, however, is the fact fixed-profit staking also boasts a higher probability of being profitable over any given stretch, along with a lower risk-of-ruin probability.

[trustbutverify]

Less risk and more profit probability( probability of making A profit) is certainly appealing. And the avg break even pct should- I think (correct me if I'm wrong) be the same as fixed stake-even with varying bet sizes. Of course I'm refering to to break even translated and averaged out over the whole set of outcomes.

Maybe I should read some more and take another look at fixed odds.

[Ganchrow]

Originally Posted by trustbutverify

And the avg break even pct should I think (correct me if I'm wrong) be the same as fixed stake-even with varying bet sizes. Of course I'm refering to to break even translated and averaged out over the whole set of outcomes.

No. If you're betting more on short odds relative to long odds, then your average break-even win percentage would have to increase.

But all this really proves is that break-even win percentage is not a very meaningful statistic when considering bets of varying odds.

[ugard]

Originally Posted by Ganchrow

This is actually indicative of probably the single biggest "smart-person misconception" about Kelly -- specifically that one's bankroll only includes that which the bettor can afford to lose. This is in fact untrue. One's Kelly bankroll is actually one's entire marked-to-market cash balance (properly discounted of course). That means your bankroll would consist of the value of not just your offshore betting account, but also the value of your checking account, the value of your savings account, the equity in your house, the maximum cash advance level on each of your credit cards, the maximum amount you could borrow from your family and friends, the maximum amount you could borrow from your loan shark, the $3,000 cash your elderly neighbor keeps under her mattress, etc., etc. Of course each of these sums would need to be properly discounted to reflect the cost of obtaining them (a cost which could potentially be so great as to make the sources of cash essentially valueless, but that's beside the point), but as far as Kelly is concerned your bankroll should represent the dollar figure such that if you lost it your life would be as good as over. Another way to look at it is like this, let's say you had an even odds bet that you knew a priori would win with 100% likelihood -- how much would you bet? The logical answer would of course be, "every dollar you could safely get your hands on."

Now people might very well object when they read this, saying that this bankroll valuation just doesn't make any sense, and that no one would want to bet in this matter, etc. etc. And you know what? You'd probably be right. Kelly assumes logarithmic preferences and as I've mentioned many times before most human just don't have log prefs. So to get around this issue, people often claim (in fact I don't know anyone who doesn't) that a Kelly bankroll is only what the bettor would feel comfortable losing. That's all well and good -- but to be perfectly clear that's a compromise position and doesn't represent "true" Kelly.

In conclusion, the Kelly stake represents the optimal bet size as percentage of total bankroll that should be bet if the bettor's goal were to maximize the expected growth rate of that bankroll. (In fact, this is equivalent to saying that the bettor has log preferences.) Were that bit your goal, and it probably isn't, then strictly, strictly speaking Kelly's not for you. (The ambitious might consider implementing Kelly using a amore appropriate utility function. This actually isn't too difficult to figure computationally for well-behaved, convex preferences.) But that doesn't mean that you couldn't use a version of it with which you're sufficiently comfortable.

Although this is my first post to this forum, I have been reading for going on two years. Firstly, I, like many others I am sure, would to like to thank the many posters who spend valuable time and effort explaining matters calmly, precisely and in detail. In particular, Ganchrow.

As a economist (in training!) it is especially interesting to see mathematical rigour being applied to gambling (which, of course, as a profit maximiser, is what it's all about ).

On to my points: I have been reading Kelly's 1956 paper, and there are a few things about maximising expected utility of money and expected value of money that the above paragraphs are a little confusing about. Of course, I may be misunderstanding your terminology, or may have misunderstood Kelly altogether.

Firstly, your example of betting everything one owned in a single (certain to pay off) bet does not require Kelly. The logic to act in such a way can be derived from expected value maximisation, of the form ER=p(w+x) - (1-p)(w-x), where p is one and x>0. Admittedly, Kelly does also suggest betting everything (and confirms that you should do so repeatedly), but the point is that one does not require "log preferences"* to rationalise this behaviour, as you imply ("Kelly assumes logarithmic preferences and as I've mentioned many times before most human just don't have log preferences"). In fact (if risk were reintroduced by making p<1), log preferences would mean the individuals minimum required ER to take the gamble would have to be higher than that required without log preferences. In other words, log preferences make this behaviour harder to explain, by requiring bigger expected returns.

Secondly, a more fundamental problem, is whether Kelly actually implies "log preferences". Kelly uses logs, but these have "nothing to do with the value function he attached to his money" (Kelly (1956) p925). Logs are used solely as a mathematical device to maximise the function that determines growth rate. Does wanting to maximise growth rate, rather than expected value, in the first place assume some sort of diminishing marginal utility of wealth? But, surly this is an entirely different problem (repeated choices) to that in which the term "preferences" are normally used.

As mentioned above, I am not sure whether what you have written is misleading (or at best incomplete), or whether I have been previously mislead, and your points as guiding me back towards the light of reason, even though I don't realise it.


* By "log preferences", I take you to mean those in the standard one time period, do-I-bet-all-or-nothing EV maximisation problem (of the form above). That is, wrapping a log function around peoples wealth, to give them diminishing marginal utility of wealth.

If log preferences are used above (replacing (w+x) with log(w+x), and (w-x) with log(w-x)), the result is that the excepted return (or "edge") must be slightly greater than one to reach the point of indifference between betting and not betting.