Rick B. Wrote:
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> TGJB Wrote:
> --------------------------------------------------
> -----
> > Rick, you\'re right. All favorites are created
> > equal, none are worth betting against, and the
> > public is the best handicapper. And the most
> > likely winner is always the right bet.
>
> Jeez, talk about assertions, even if coated in
> dripping sarcasm.
>
> One of them is true: the public is the best win
> handicapper, always has been. Ask your math guru,
> that Rocky fellow.
Rick B. – it’s true that in aggregate, the public gets the probabilities right, but that doesn’t mean you can’t create a probability estimate of your own that is better than the public’s (ie. one that identifies overlays and underlays, which is essentially what the ROTW analysts are doing each week).
I’ll defer to Bill Benter, who explains it much better than I ever could:
\"An important feature of the parimutuel system is that public betting tends to produce odds that conform to the public’s estimate of the horse’s probability of winning. This is sometimes referred to as market efficiency, in the sense that the public betting forms an efficient market which accurately reflects all of the available information about the horse’s chance of winning. The independent actions of the individual bettors – the invisible hand of the market you might say – cause them to effectively set odds which are an accurate reflection of the horse’s chance of winning.
[Looking at] actual Hong Kong racing data - a sample of about 6,700 races - I’ve broken down the public betting on those races into ranges. There were 4,906 cases where the public had bet between 0 and 1% of the pool on a particular horse. Those cases averaged out to have 0.007% of the pool bet on them in that case. The actual frequency of winning actually worked out to be exactly 0.007% as well, so the public in aggregate – all the horses they put in that range – their probability estimate was quite accurate. Looking right down the range, you can see that in every range the public gets the probability about right.
You could summarize this situation by saying that the fraction of the pool bet is approximately equal to the probability of winning. This then leads to the problem in horse racing – the fact that the fraction bet equals the probability of winning, and given the track take, then the expected return for a bet on any horse in any of those ranges is uniformly -17%, which is the track take.
You could state that the problem in racing is that the native expectation is minus the track take. What’s needed then to overcome that in horse racing is you need a new and different probability estimate for the horse’s chance of winning.
You could ask the question at this point, ‘Well, if we established that the public’s estimate of the probability is approximately right, how can you have a different estimate of the probability? I thought we just saw from the chart that the public had the probability right.’ Well, the truth is that there can be more than one probability estimate for the race, and they can both be ‘true’ estimates, or I prefer to use the word ‘unbiased’ estimates. It all depends on your state of knowledge, what estimate you would put on the horse’s chance of winning.
Let’s look at the exact same set of races, and let’s say you were a person that had zero knowledge of the horses or anything about them. And all you could say when you looked at a particular race, when you look at the number of entrants in the race – in this case the races all had around 12 horses in them – and you would make an estimate on each horse then that each horse’s probability of winning is 1/12, or 8.8%. So a zero knowledge person would have ranked all of the horses in all of those races as each having an 8.8% chance of winning, and if he had done a chart summarizing how he did, he would find that he was correct – the average probability he gave those horses was 8.8% and lo and behold they came in exactly 8.8% of the time. It’s not a good estimate, but it’s correct – it’s unbiased, it’s not an over or underestimate of the horse’s probability of winning.
Now let’s move to the other extreme, call it the omniscient estimate. If you were God, or the God of horse racing, and you were able to correctly estimate the winner in every race prior to the race, your probability estimates would look like this: in 6,700 races, you were able to assign a probability estimate of 100% to the winning horse, and 0% to all the other horses. This also is an exactly correct probability estimate, it’s unbiased. It’s very much different than the [prior example], or even the [first example] which showed the public’s estimate.
Obviously we’re not omniscient, and we don’t have zero knowledge, so we want to try to make another estimate that will be different from the public but also true. What we talk about doing here is making a fundamental estimate. The fundamentals that we use to predict the outcome to determine the true worth of a horse are facts about the horse – past performances, the conditions of the race, the skill of the jockey – all of the fundamental factors that go into actually presumably determining the race outcome. This is not the lazy man’s way to make money at horse racing. This is a big effort. To set out to fundamentally create a comprehensive and accurate probability estimate for a horse’s chance of winning a race is a very big project, but you’re well rewarded when you do this.\"
-- Bill Benter, 12th International Conference on Gambling & Risk-Taking
Rocky R.
