question for advanced mathmaticians
 

Reference: http://en.wikipedia.org/wiki/Poisson_distribution

In regards to the Poisson probability function in Excel which is for example
=POISSON( 1.5, 1.5, FALSE )
will show 33% if formatted to percent.

Does this formula conclude,or give further weight to the common rule of thumb that favorites win 33% of the time ?

One can play around with the 1.5, 1.5 and obtain some interesting figures.

My other question is, out of the 1.5,1.5 entry, which of the 2 is the bookie and the punter, the left or the right?

I was also thinking, if my assessed odds are 1.5 and the bookie is 1.5 ironically as well,
does this mean the formula is saying there is a 33% chance winning?

Other examples
=POISSON( 2.5, 1.5, FALSE ) = 25%
=POISSON( 1.5, 2.5, FALSE ) = 21%

Can someone explain this is plain English please.

Thanks

Sadly I can't, but I will say this. Favorites win 33% of the time overall or thereabouts because of 1 factor imho - the very thing which is present in every race, meeting, racetrack, region, country, on every day of the week and any state of going.

Human nature

Coming back to your query, how good would it be to nail the 'maths' at this level and therefore be able to crack any number puzzle that comes our way, winning favorites included? My thoughts are that it is much simpler than an equation or statistical concept or method, all the complexity still present in the underlying answer however - something to be observed but not explained with the technology and wisdom we have to hand at present!

An initial filter or lens through which to look, perhaps?

LG

Oh to know when to bet in the high and sit in the low. There in lies the Holy Grail of Punt.

Puntz I think you are a bit confused on how to use the POISSON calculation.

I will say I am not a trained statistician but I am self taught and have a better understanding then the average person.

The poisson distribution in excel is as per your post :

=POISSON( X, Y, Z )

X = Value to be tested
Y = Our Predicted Value
Z = cumulative effect (We always want FALSE).

So based on what I read you had a rating of 1.5. When you do this calculation:

=POISSON( 1.5, 1.5, FALSE )

You are basically asking "I came up with a rating of 1.5, what percentage of time is this rating correct ?". In your case it replied that your only going to get your rating correct 33% of the time.

Now you just need to work out how this can be of use in your ratings. Perhaps it would work well to find the range where your rating is likely to be correct. Perhaps its of no use at all.


In regard to your original questions:




Well it adds some weight to the argument if we assume the first number is the publics odds (their guess at the horses chances of winning) and the second is the real chance of the horse then the punters are getting the odds right for a $1.50 chance around 33% of the time. But of course the would get it above and below this number just as often and therefore give rise to the fact that they get the favourite right about 33% of the time.


If depends what your trying to figure out. If your trying to figure out how often the bookie will match your odds then the bookie is first. If your trying to figure out how often your rating will be 1.5 when the bookies is 1.50 then your the first number.


No. Its saying the probability of you getting the same rating as the bookie is 33%. Its not telling you the chance of it winning.

Does that help ?

You might still be confused after reading my post. I tried to say it in plain English as good as I could but statistics are not an easy area to understand without a lot of study.

So after reading my post you are probably going to go ... ****** ? How do I use this for making money in gambling ?

Well the only areas I know of that it is extensively used is prediction in football scores. Here is an example http://www.bettingexpert.com/blog/h...-poisson-part-2

But here are some ideas where statistics might help you with ratings and punting in general:
- Find confidence intervals for your ratings
- Find your edge using chi tests
- Using distributions to model your odd distributions.
- Using distributions to model your profit distributions
- Using distribution on odds vs finishing position to determine likely finishing chances.
- Using distribution of your rating to finishing position to likely determine finish position.

The list could go on forever. If I had to decide on what I concentrate on if I was you I would look into is understanding the confidence level of each of your ratings and coming up with a "ratings range" for each horse. If you find you rated a horse 20% and you find standard deviation is 5% then your rating of 20% is really a rating range of 15%-25%. You could come up with 1 std dev ratings and 2 std deviations ratings.

If you do this you would then have a rating system that says :

Horse A : Predicted 20% chance of winning, but range 15%-25%. (5% deviation)
Horse B : Predicted 50% chance of winning but range 38% - 62% (12% deviation).
Horse C : Predicted 30% chance of winning but range 23% - 37% (7% deviation).

Looking at the above you could be fairly certain Horse B is going to win. Its lowest rating is 38% and the highest possible rating of any other horse is 37%. The overlaps is where you are going to be able to identify the races where the favourite is likely to lose or the field is so close its too hard to pick a winner.

Hopefully someone gets something out of this.

UB, your first reply made sense.

"Predictive Modeling"

Where you quoted


How did this get discovered, is recently there is a book that has just come out. Poisson was mentioned.
In that book's book review it has a quote, "the Poisson advantage is good arsenal for any serious gambler", or words to that effect.

I have ordered the book....more to be revealed.

Lord Greystoke and beton, thanks also.

Its definitely useful in the right situation. Especially for determining the "error" rate in your ratings.

Whats the book called ? can you provide a link ?

Strewth.
And to think they closed MY mathematical System down.

Conquering Risk: Attacking Vegas and Wall Street
by Elihu D. Feustel (Author)

thanks.