Any statisticians out there ?

Wouldn't accept **** as abbreviation of cumulative.

Sorry meant to type bet size was 10 units each.
Too good to be true otherwise.

Froggy,

To paraphrase, The Law of Large Numbers states that the average of a population's sample size of 30 or more is approximately equal to the average of the population.

http://en.wikipedia.org/wiki/Law_of_Large_Numbers

It doesn't explicity mention the number of thirty in the link [focuses more on the stats' proofing of same]; but you should find further back-up easily available on the 'Net.

[i.e. the theorem is the first "major" topic of any first year undergrad stats/actuarial degree].

Your sample size looks fine FWIW my main soccer edge was tested using a sample of 30; this resulted in a net margin of 3.80%, which marginally exceeded the 3% [post commish] profit I had expected...Fast forward a couple of thousand bets with the same edge, and the net profit is circa the 2.9% mark.

[aided by backing Ipswich vs. Arsenal; and St. Johnstone vs. Hearts. Had Hamilton vs. Celtic, but landing that at 12.5 would've exceeded the edge thrown-up by my numbers ]

steeringjobnap
Tks. for yr reply.
I wonder if it is a coincidence that my series 1) bets are also generating circa 2.9 % net profit on turnover.
But my series 2) bets look abnormally high at circa 13.9%.
As it only took about 3 weeks to generate my 300 odd selected matches, I suppose I can easily afford to be patient and wait till my sample size at least gets into the thousand mark, to see if there is any marked deteriotation in either series of bets.
It all looks to good and too easy to be true as this moment in time.

FAFH,

Are the second set of bets placed in a less efficent market? [i.e. I/R correct score vs. pre-event 2.5 U/O goals?]

Alternatively, the 2nd data-set, placed on outcomes odds-against, may indicate greater value [vs. true price] cf. the odds-on shots [again, vs. true price] of the 1st sample.

Can't really say without seeing your data [I am not asking to do that!].

Veitch reckons 16% of turnover as a net margin % is achievable, so I wouldn't be so quick to dismiss it yet.

The 3% net margin is consistent with fixed-odds books [i.e. PP latest FY results}

Billy Mountains passed the stg£1bn turnover mark for the year 2010; it will be interesting to see what their corresponding net margin is.

It goes without saying that the net margin on the second data set should be closely monitored for future variation trends!

In the beginning I was really hung up about statistical significance but now it doesn't even cross my mind because it's almost always the wrong question. Ask yourself some different questions:

First off - ask yourself why you're asking? Is it just to make yourself feel confident? Is it so that you can dream about a future in the Caribbean? Whether or not you can show statistical significance is never going to be the test of whether you try out a strategy that you've been thinking about or continue one that you're using, that will be decided by much more basic tests - so why worry.

Next ask yourself this: If one test of SS doesn't give me the result I want - am I just going to try another one? The truth is that people are often so desperate to "prove" that their results are good that they'll go through test after test until they get the desired result. I'm sure I don't need to explain why that's not healthy. Once they've found their false confidence they then use it to confidently over-stake, and go bust.

So instead of worrying about SS ask yourself some more basic, more important questions. like these:

1: Where do these result come from? Are they real bets, and are these THE ONLY BETS I STRUCK?
Anyone can run filters on a series of bad bets to pick out the little group of winners and then say "ahhh... it only works on handicaps"

2: Am I making money? If you are then you continue, SS is not necessary, if you're not then you quit - SS or none.

3: Am I lulling myself into a false sense of security, dreaming of my private jet and staking too much on a strategy that hasn't really proven itself? For most people the answer to this is usually "yes."

Been through that? right, now just forget all your statistics and start your strategy with a £100 bank and £2 stakes, once you get to £200 you start very slowly increasing your stakes at an appropriate rate (this will depend on the strategy). If you go bust it's over. That's all the analysis you will ever need. If you have any sort of edge at all you will have plenty of money in no time, if you don't- you won't, your money will be gone in a couple of weeks. Simple.

An outstanding post aye robot.

FWIW, this is actually the latest account that I use to test new edges upon; and I always, always start with the obligatory 2 yo-yo stake.

Any "test" edge that blossoms into a full-blown out-performance strategy, then has "normal" staking applied to it. [but only after the Law of Large Number's result at €2 per go; then gradually increasing staking].

Edges come & go, as the markets react to inefficencies...thereby creating new inefficencies...

I do respectfully disagree on your use of "SS" term - you'll find most of the LT winners who aren't strictly trading off price pivot points/support-resistance, etc [be they scalping or swing trading] are using:

some form of statistical analysis; OR
multivariate regression models; OR
statistical arbitrage/implied pricing, etc.

I'd actually back that at 1.01

The football markets on here are a classic example, as are the racing.

i.e. just because the pricing is neither overbroke/overround, does not mean they are "true" prices [;)], hence the value offered.

http://www.stat.cmu.edu/~cshalizi/36-220/lecture-10.pdf

The above paper has a fair degree of maths in it, apologies.

Central Limit Theorem expanded upon [a close precurser to Law of Large Numbers], using a sample size of n = 30.

[I knew the number of 30 was pivotal, even if it is 11yrs since I first looked at this material ].

I'm postulating that if a sample of 30 is good enough to prove the most important theorem in stats [re: the normal distribution of the sample mean] => using n = 30 should be sufficent for proving the mean of a sample approachs the mean of the sample size's distribution [as n both approachs infinity AND exceeds 30.]

phew! long post

Went to sleep and came back to find these last 2 interesting posts.
The numbers I posted are derivations from actual wagers I made in another " real" system. The odds were actually obtained in real time.
The " real " system was devised by what I think is a logical, mathematical thought process, and is producing results along the lines anticipated.
These " derived " systems pose a puzzle in that they apparently seem to work but not for any logical, mathematical reasons I can think of.
Hence my question was really an attempt to ascertain whether they may just be some short term anomaly and will disappear in due course.

Also aye robot they are not filtered or back fitted in any form or manner.
Quite bluntly they are flat stake analyses of the selections my ongoing real time fluctuating stake system is working with, and I was really surprised at the somewhat unexpected results.

it's critically important imo that you can mathematically define the net margin of any edge, pre-testing.

if not quantifable, then imo, you run the risk of your fate being driven by a short-term phenom [luck]; instead of what is really required i.e. a long-term, mathematically "bomb-proof" edge.

the maths don't have to be tricky - I have always, always said that bookmaking maths are the stuff of 10 year old school-goers' fractions - but any decent edge must be quantifiable imvho.

PS I had a feeling that the second sample set results were I/R.

Some amazing value achievable in these markets if you can correctly define the true "100%" price; then simply add your margin

i.e. the 2011 PDC World Darts Final; bots/traders/hedgers/mugs were literally dropping money on this site I/R at any price you like...

steeringjobnap
I agree who;eheartedly that you should define yor strategy first and then test, not the other way round.
As I said, my " real" system was developed that way.
These other two sets of results are just an unusual and quite unexpected corollary.
But as aye robot essentially says , whilst it may be nice to understand why something is working, it's not necessary to.
I believe many successful hedge funds have implemented strategies not knowing fully, at the outset at least, exactly why thet work. And no, they have not all imploded, as far as I can make out.
You could perhaps call it the nike approach. Just do it.

"I believe many successful hedge funds have implemented strategies not knowing fully, at the outset at least, exactly why thet work. And no, they have not all imploded, as far as I can make out."

You might want to tell that to Long Term Capital Management!

I'd agree with you, tbh. Have a pal who's a fund manager, and I'm blue in the face telling him that he won't beat a combination of inflation; spread & commission on his work trades in the LT.

And yet still he persists with "broken" strategies.

LTCM thought they knew all the answers in advance.
They were so sure of their intellectual superiority, that they were arrogant to the nth degree.
So their problem was in fact the converse.
They thought they knew it all and they didn't.

It's quite ironic though that John meriwether, the real founder and driving force of LTCM, was known as the martingale man in his earlier days as a bond trader on Wall St.
The bigger the hole he found himself in, the bigger he bet.

ah, the Martingale system!

It has broken many a man [nap].

PS re: LTCM - I agree.

Nothing worse than a couple of Nobel Lauretes [sic?] thinking they had re-invented the game.

If it wasn't going to be the Russian Crisis of 1998, it would've been something else [most likely Argentina 4 years later].

My real heroes are Claude Shannon, Edward Thorp and John Kelly.
True pioneers in the ways to approach both gambling and stock investing.

Ambrose Bierce for the quote "The business known as gambling is looked upon with extreme disfavour by the gambling known as business".

After that...the author of "Reminiscences [sic?] of a Stock Operator" [Messer Jesse Livermore].

Not forgetting the utterly peerless Mark Coton [Mr. Pricewise]

Don't know the latter.
Worth investigating ?

Google "Value Betting"

It is the bible of pricing up your own racing price tissues.

Should be readily available on Amazon/Ebay for about stg£25/£30

Regrettably, I remember reading that Mark passed away a number of years ago; an absolute giant of the game.

Not into HR.
So I'll take your word for it.
Some people are however truly exceptional.
I hope he was appreciated in his lifetime.

the sot man is here.

Am I amber, red or green ?

This is really a problem of how the odds or probability p is spread
The Arithmetic mean of odds and Geometric mean of odds do say something about the spread of the odds, but is nowhere near as good a measure as the variance of odds or standard deviation. The easiest way of determining the variance to allow statistical tests to be done is to determine the variance of p (the probability corresponding to the odds)
Var(X) = E(Var(X|p) + Var(E(X|p)

Fermat
So what info do I exactly need and how do I apply it ?

Am I amber, red or green ?

Fine as Frog Hair - message me with an email, I may have time to consider this the week after next.