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%.