The Efficiency of the Bookies Market
 

With the discussion going on in some other themes about longshots, ratings etc, when considering what could be termed 'market efficiency' it has been a long-held belief by many that the bookmakers market is the best guide, but not necessarily always correct, for the real chances of each individual horse in any given race.

This is certainly true in a broad sense at the very least.

Over the last few years however with weak on-track markets that efficiency has come under strain, particularly with the bookies opening markets, albeit that by race-start time a degree of efficiency has been reached, more so in Sydney than in any other, often with over-rounds of under 110% with an average of around 115%.

While not attempting how to tell others to suck eggs, for those that might not know what an over-round is: well it is the total percentages of all the runners/participants/outcomes in any given event, e.g. in the current 2nd test match between Australia & South Africa at the close-of-play on day 3 the respective odds of the three possible outcomes are:

TAbcorp Sportsbet:
Australia: $1.55 (64.5%)
South Africa: $9.00 (11.1%)
Draw: $2.80 (35.7%)
Total Percentage/Over-round = 111.3%
(Brackets indicate odds converted to percentages)

Many would argue (including me) that in a three outcome event an over-round of 111.3% is not that efficient, and it ain't when considered to the odds offered by Betfair (a short while ago):

Betfair:
Australia: $1.63 (61.3%)
South Africa: $12.00 (8.3%)
Draw: $3.25 (30.7%)
Total Percentage/Over-round = 100.3%
(Brackets indicate odds converted to percentages)

Overall an 11% advantage to those wagering on Betfair, on which at this stage there has been just under AUD$11 million matched.

Which brings me to the main point, the one at the start of this message, which is that the long-held belief the bookmaker's markets are the most efficient. Well, if the bookmaker’s markets are substituted with Betfair's they are.

Betfair in the UK recently published the following:

"Betfair prices are actually extraordinarily accurate reflections of a horse's chance of winning a race.

And it's worth remembering that this is historical data and not a predictor of future events. It also looks at average weighted prices – which isn’t something you can know until after the event. And there's commission to take into account. The value of investments can go down as well as up and all that.

The full results are below. We’ve grouped all the horses into price ranges – averaging the expected win rate and the actual win rate:

Price Banding / Average EXPECTED win rate / Average ACTUAL win rate / Difference

1.01-2............64.38%..........4.84%.........0.46%
2.01-4............36.61%.........36.88%.........0.27%
4.01-6............20.27%.........20.66%.........0.39%
6.01-10..........12.77%..........12.60%........-0.17%
10.01-20..........6.93%............7.18%........0.25%
20.01-100.........2.64%............2.56%.......-0.08%
100.01-1000......0.30%............0.26%.......-0.04%

How did we work this out?

We grouped all the horses at various prices. As an example, if a horse was 1.5, then we said that the market was theoretically saying that it had a 66.6% chance of winning the race (100 divided by the price). This gave us the “Expected win rate”.

We then checked how often they actually did win – the “Actual win rate”.

In this example, if 1.5 shots won more than 66.6% of the time, then the “Difference” would be positive – meaning that you’d have made a profit backing all of them.

We looked at all the Win markets from UK racing, jumps and flat, from 1st January 2004. We excluded any race that hadn’t a traded volume of more than £50,000.

We took the weighted average price that each horse traded prior to the off (so not including in-play) – over 157,000 horses in total. These were then grouped into the bands you see above and averages taken."

So what this table clearly indicates is the actual win outcomes are very much in accordance with the expected win outcomes.

The favourite/longshot bias that may exist in other markets certainly do not exist in the Betfair markets.

Those figures are remarkably close. Thanks for that very interesting post.

KV

La Mer
Interesting figures indeed.
It has always astounded me that the public can get it so right over so many races.
I have seen several studies where the SP market is shown to be far more accurate than even the best ratings over a large sample. The trick for ratings people,of course, is to find the race where the public have it wrong.

I suppose an interesting question might be that although the public may be getting it right over time as proved by those averages how right do they get it race by race? If odds on offer varied a lot race by race from the actual chances of winning we could still expect to turn a nice profit by betting on the right horses in the right races.


KV

Yes, Kenny that is the question,indeed. However, "statistically" seen the result is "right" every time for Betfair, as stats ONLY work in the long run (they are viewed AFTER THE EVENT, aren't they?) ie toss a coin; 50/50 chance but STILL a 100% chance of one result being correct and the other one NOT. After the 2nd toss (if it comes down on the other side) we say "see 50/50" and so on. Even if it ends up 505 heads to 495 tails it's "close enough" There is no "stat" however, which tells you the outcome of the NEXT event. They are ALWAYS simultaneously 50/50 BUT 100% certain of not being 50% right.
While there seems no way to "predict" each occurence ONE AT A TIME with coins (ie all things REALLY are equal), it is not like this with horses (or sports). Apply the coins/roulette/dice idea to horses and what you actually need is an "error" in the "apparatus" to get an edge (with coins; if you picked up that the face was significantly heavier than the taill, for example). This means, (for the races),finding an underrated (undervalued, underestimated) horse that ON THE DAY was/is, in reality (as with stats,we look AFTER the event) 100% certain or close to it. Like the coin analogy we are looking for something "wrong" (right!!!).. Once again, we then need to discover ON THE DAY what will allow this horse to over-run the others. What "advantage" has it got?
What we want therefore is access to "total knowledge" or, failing that, every trainer's words and THOUGHTS. We want the trainer to tell us the unvarnished truth about their horse.. They should let us know that the tracktimes are "suspect" (ie slower or faster) because the jockey was taking it easy or really pushing it. Or that the favoured horse seemed "grumpy" this morning, or that D. Beadman is under instructions to do......whatever, or that the real target is next week's race; or that the trainer has put the horse over 2000 m as a "practice" etc etc. But they don't. We have to deduce it!!
Well, how do we deduce what other people (our partners, mates,business associates) are REALLY thinking?? Well??? How do we know when the "boss" is annoyed Or happy,WITHOUT THEM TELLING US? . You already know!! Cheers.

Its not just ratings people that try to find the races where the public have it wrong.

Most ratings people work through race by race waiting for a discrepency,others like myself try to locate those descrepecies before the start of the day.

It's true that odds like those above are a very acurate representation of the actual chance of horses in certain price ranges BUT what isnt so obvious is that many of the horses in say the 10 to $20 price range have a far greater chance than their odds suggest,likewise many have a far worse chance.

The winning % to odds comparison provided by La Mer is just an average taken from thousands of races,individualy the horses odds mean nothing and if you pick and choose your horses its not too hard to find descrepencies.

I'm of the opinion that these descrepencies are easier to find with longer priced horses.

A Bookies open price rankings e.g. IAS opening price ,of the top 4 rankings has a slightly greater SR than say the TAB top 4 price rankings or Pre-post market top 4 rankings.



What one can do with this is ,only bet if ones selection is also in the Bookies top 4 price rankings.
The Bookies ranking is around the 75-80% mark for their top 4 getting up.

A cute relevant UK insanity according to this Bolshy rag:

http://sport.guardian.co.uk/horsera...1676770,00.html

Apparently Betfair puts so much pressure on on-course prices that the official SP is now inching higher.

So relevant dinosaurs now want to introduce an alternate "industry friendly" SP!

The current local SP may often be a farce for the obvious reason that often there aren't that many relevant bookmakers about to produce a true market figure.

An alternative official SP based on something like the weighted average of TABs, Betfair and any other licensed outfit prepared to disclose turnover statistics within 30 seconds after race jump, would make considerably more sense.

But I won't be holding my breath for such market glasnost.

understanding probabilities
 

Punter 57 The two-factor probability brings up an interesting category of study... understanding probabilities that aren't exactly straight-forward, or are counter-intuitive. For a person wagering cash money on races, having a firm foundation in probability is a must. Yet all too many people don't! (So much the better for those that DO!
So here's a simple little probability problem to get started. (I'll post the answer later, if need be)
You are told that a family has two children. You are also told that one of those two children is a girl. Assuming that the biological probability of having either a boy or a girl baby is equal (50-50) then what is the probability that the family ALSO has a boy?

Enjoy

25%.

50%

100%

50%

50 % What do we win for the right answer?

a date but it depends what side of the fence your on

I figure the probability of the other child being a boy is 2/3. But then I'm not a consensus creature.

Woof, in the highly unlikely event that your admirable educational initiative takes off, maybe you can then start a dedicated thread.

12.5%

Woof,woof,
 

What a great teaser. To me this is horse racing all over, as we think we are told the relevant facts but in fact we know diddly squat.

How many children does the family have? We might think that it's two but you might be wrong. Even though they have eighteen kids it is still correct to say that they have two kids . Even though they have twelve girls and six boys it is still correct to say they have one girl.

Is it any wonder I bet on favourites for the place?

If the family has two kids and one of them is a girl the other must be a boy - right Kenchar?.


KV

you can have ten kids all the same sex if we are talking about the same odds as a coin being tossed,each shot is 50,50 and independent of the other..

.................cheers......slowman...........

KV,
Might be a monkey too ( just joking ).
The way I look at it Woof has just used the family as an example.
The real question is you have a 50/50 scenario and one half of the 50 has gone so we should be left with the other 50 being 100%, but I could be wrong.
Woof could you PLEASE give us the answer, I can't eat or sleep and I am having nightmares ( they are the ones that race at Mooney Valley at night ) about this.

50% chance.

Chance has no memory.

So what's the chance that the family has two girls, and what's the chance it has two boys???

:D

Each time at the well produces a 50/50 chance. one sperm in a billion getting through. However if the sire has allready produced one girl the likelihood of a repeat is higher than that of producing a boy. Atheletic types have a higher temperature and predominantly produce girls. There is all sorts of other criteria which may slightly change the odds.

A bit like horse racing.

Besides that I hope everybody had a good Christmas and has a prosperous New Year

Clearly 50%. The fact that there is a girl is just there to throw people off. It is irrelevant.



Here is the answer.

the answer is
 

Well, an interesting set of answers.
Here is the correct one:
2/3 or .667 -- the probability that the family also has a boy is 2/3. (cheers jfc)
And here's the logic:
You were told a family has two children. There are four possible ways in which a family can have two children:
#1 Girl-Girl (probability = .25)
#2 Girl-Boy (prob = .25)
#3 Boy-Girl (prob = .25)
#4 Boy-Boy (prob = .25)
Each of those four ways of having two children has an equal probability of happening, and those probabilities, of course, add up to 1.000. (as specified in the question: Assuming that the biological probability of having either a boy or a girl baby is equal 50-50).
You were told that one of the children was a girl. That only eliminates one possibility out of the four: Boy-Boy, leaving three other possibilities, (GG, GB, BG) all of equal probability. Of those three, two include a boy. Thus the probability that the family ALSO has a boy is 2/3 or .667.
The most common mistake that people make when confronted with this problem is that they try to reduce it to a simpler problem. The mistake is in thinking that the FIRST child was a girl, so what is the probability that the SECOND child is a boy. In that improperly simplified problem, you have eliminated TWO out of the four possible ways of having two children (Boy-Girl and Boy-Boy) leaving only two possibiliities, only one of which has a boy in it. And thus the mistaken 50% answer. The mistake was in eliminating Boy-Girl from the set of possible situations during the simplification.

thank you

OK. I think I misread the question. My thinking was that they were expecting another, what were the chances. I think that I missed the obvious wording of the question implying that the child was already born.
All makes sense now.

I presume that those of us that said 50% would be right provided that we were guessing the sex of the second unborn child?

I'm with you on that BJ, I must of read the question the same way you did, basing my answer on the thinking the second child was yet to be born, but I should have given it a bit more thought. I always seem to rush in without thinking things through clearly.

Beton, My offspring in order are Boy Girl Boy. If I was at my athletic peak when producing the girl then I must have been in pretty bad shape when producing the Boys. :)

At the risk of being seen as a bad loser (or looser in some circles) I consider this a badly worded question. Just the sort of question a study of statistics is likely to engender as we all know statisticians like their figures to mean what the statistician wants them to mean.

Scenario 1. A family has two children and one of them is a girl therefore it is logical to assume one of them isn't. I mean how many non statisticians would say "I have two children, one is a girl and the other is a girl."
So: Answer to the original question 100%

Scenario 2. We see a picture of the unfortunate statisticians children, they aren't attractive, in fact you can't tell what sex they are with their clothes on. The statistician points to one and says 'She is a girl'. What's the other one then we wonder and of course the answer is 50/50 it's a boy since it's a even chance either way.
So: Answer to the original question 50%

The 66% scenario is more of a play on words than a sensible question.

Well, someones gotta be controversial. Crash has dissappeared and P57 has a fortnight in the sin bin.

KV

and P57 has a fortnight in the sin bin.

KV[/QUOTE]
No wonder the longshot thread is slipping down the pecking order!!

p.s could someone please tell me how to quote only part of a post? I highlighted part of the quote but the whole thing appeared on my reply anyway.

KV
The whole point about playing our handicapping game (and a lot of the "game of life") is being forced to make decisions even when faced with incomplete or conflicting information. And a person that is better at determining those probabilities and expectations in the handicapping domain, especially with uncertain information, gets paid more money in the long haul.

Thus a person that wants to progress in the game of handicapping has to first become reasonably proficient in probability and statistics, and then move on to heuristics and biases and the study of a couple or three aspects of psychology. We're all peeling the handicapping onion so to speak!

Hi! You mean like this?

Just delete the part you don't want, or put what you want between "[QUOTE] and [QUOTE]"
As to the two children question, forget it!
He answered the wrong question.
The way it was asked there is only one answer to it, and KV got it right.

Cheers.

Yes . Thanks lomaca

The fact of what they have or don't already have, is irrelevant to the answer.

If I flip a coin and I already have one heads, I still have a 50% chance of tails next spin.

What is the difference between Girl-boy and Boy-Girl, they are the same thing.

Boy-boy is an invalid combination given the question.

There are two possible combinations

Girl Girl

Girl Boy

That's it.

Of course a mathmatician, because he wouldn't want to create confusion, would ask the question thusly: "If at least one of the children is a girl" and then might get an answer other than 100% or 50%. But Woof's point is valid in that we have to get used to using half ar sed information if we want to win at handicapping (my phrasing not his).

KV

This problem is a classic case of conditional probability. The average person has trouble understanding it. The boy/girl problem can be tested by repeatedly tossing 2 coins and recording the results(say 20 times). There are 3 possible outcomes ( 4 really) - HH,HT,TT.
Now we ask what is the probability of the other coin being a TAIL given that one of them is a HEAD? Straight away we can ignore all the TT's from our sample (cross them off the list) because the question asks "given that one of them is a head". That will leave only HH's and HT's in the list. Now put a circle around any T in the list. You should find about a 2:1 ratio or a 2/3 to 1/3 Tails to Heads.

This better illustrates conditional probability. With the coin or the boy/girl examples there are 4 possible outcomes - HH, HT, TH, TT each with a 25% chance of occuring. When we ask the question "given that one of them is a ..." we are effictively saying that one of these situations did not happen. In the above example we eliminated TT leaving HT, TH, HH. Now we are left with 2 T's and 1 H with the corresponding H which we were told existed. So the probability of the other coin being a T is 2/3 and an H is 1/3.

Well we have convincing arguments supporting 50%, 66% and 100% depending on how you read the question, what I would be interested to see now is the rationalle behind the other options offered. Nanook? La Mer? I particularly liked Kenchar's explanation. It surprised me at first but then made me realise that a standard view of statistics is absolutely not essential to being a successful punter.

KV

In my case it was by multiplying 0.5 by 0.5 which gives a result of 0.25, which would be correct other than for the issue of the prior knowledge of knowing that one of the children has already been identified as a girl.

come down
 

i would like to hear jfc's thoughts on this becouse as it stands i'm wity cp...
...................cheers....slowman.............. ....

I didn't really read the question and multiplyed 0.5x0.5x0.5.......don't really know why.......don't really care, but one thing I do know is that 98% of the population who suffer from heart disease own a colour television?

nanook