The following chart converts from Starts to Odds for the favorite.





I am working on a calculator for roll-your owns and starts.

Jake.

[ This Message was edited by: jakelee on 2004-07-27 11:52 ]

Is it too much trouble to get you to put the margins on the y axis,and the prices on the x axis.
Why?.I don't see the resemblance between this curve and your earlier one.

You went to all this trouble and then abandoned it.
Where are you Jakelee?

Hi Guys,

Been away... no internet for a week!

Anyhow, I have put together a website for NRL starts/Odds conversions.

here
http://www.horologe.com.au/econtrafama/starts/

The season's almost over though! But might be useful for next season.

Jake.

[ This Message was edited by: jakelee on 2004-08-23 11:02 ]

I know jack ******** about NRL.
What data do you need for an AFL chart?

To do an AFL conversion (I already have the formula, just need the paramters). I don't follow AFL, so I'm not sure what range the starts go from (would you see a +80.5 handicap?):

I would need:

- Opening Fav/Dog Start and Opening Fav/Dog To Win Odds for quite a few values from equal favs (ie, +0.5) to a big difference (ie, +80.5). I also need the starting odds for the line (it's always 1.85 for NSW SportsTAB) Like this:

Line Odds: $1.85
Start Win Odds
-10.5 $1.70
-50.5 $1.21
+5.5 $2.00
... etc

I don't need every value, just enough so I can fill in the gaps.

If someone can provide this data for the TAB, I can calculate the

JL.

[ This Message was edited by: jakelee on 2004-08-24 09:01 ]

The most I've seen is +54.5. I doubt there has ever been anything over 60.

Jakelee.Is this any good?
With lines at $1.90

1.90 -4.5
1.80 -5.5
1.75 -4.5,-5.5
1.70 -5.5,-6.5,-7.5,-8.5
1.65 -7.5,-8.5,-9.5,-13.5
1.60 -9.5,-10.5,-11.5,-12.5,-13.5
1.55 -10.5,-13.5
1.50 -12.5,-15.5,-17.5
1.45 -15.5,-17.5,-18.5
1.40 -18.5,-20.5
1.35 -22.5
1.33 -22.5,-23.5,-24.5
1.30 -20.5,-23.5,-24.5
1.28 -24.5,-27.5
1.25 -24.5,-26.5,-27.5,-28.5
1.22 -29.5,-30.5
1.20 -31.5
1.18 -32.5
1.16 -34.5,-36.5
1.14 -36.5,-39.5,-40.5
1.12 -39.5,-42.5
1.11 -35.5
1.10 -40.5,-42.5,-43.5
1.08 -42.5,-46.5
1.06 -46.5
1.02 -71.5

Seems to be mistakes made by bookies,or more likely,minor differences due to who is playing who.

That's what I need. Give me a few days.

Come on Jakelee.
Just need the mathematical formula.
Margins to percentages.
No fancy webpage necessary.Something I could do on my calculator is fine.

AFL

OK guys, this is the formula for AFL starts/odds. You can use this formula to calculate the expected start from the odds on the favourite. It was quite different from the NRL formula, which looked more like a distribution. The AFL formula is kind of a modified exponential, with quite a bit of fudging from the line makers. I suspect the line is moved to try and maximize bookie profits, as it would be more subjective in a high-scoring game like AFL over NRL.

It seems that in AFL the bookies are a LOT more liberal with the relationship between starts and odds than the NRL. For instance, odds of $1.66 can vary from a start of -9.5 to -13.5. There is about a 3 point either-side shift in the lower starts, and in some places a 6 point movement in the higher starts.


ODDS = a / [ 1 + b * e^(-c * START) ]

OR

START = -Ln[(a / ODDS - 1) / b] / c

Where
a = 0.95
b = -0.58
c = -0.033

So for example, if the odds were 1.46

START = -Ln[ (0.95 / 1.46 - 1) / -0.58] / -0.033
= -Ln[ (0.65 - 1) / -0.58 ] / -0.033
= -Ln[ -0.35 / -0.58 ] / -0.033
= -Ln[ 0.60 ] / -0.033
= 0.51 / -0.033
= 15.55

The expected start is 15.5 +/- 3



This will work from about 1.01 to 1.90.

You might find it easier to copy this to a Excel SpreadSheet.

Jake.

Well done Jakelee,but I'm a bit lost.
Is e,that epsilon Naperian log thing?
And Ln,is that the log to the base e.

Hello Moeee,

e is the exponential function. Read boffin stuff here: http://en.wikipedia.org/wiki/Exponential_function

Most calculators have one, and it's usually labled "Exp". In excel you use the function exp(...). Basically, it's just a special number that has an infinite number of decimal places, but lucky for us the calculator has a good approximation!

So to do e^7, on the calculator you would do EXP -> 7.

And yes, Ln is Log to the base of e. Also known as the natural log.

Jakelee.
How you showed an example of working out the start from odds,Can you do an example of a margin.Say if I thought a team would win by 15 points,could you do this example step by step to show the ODDS.

Like this:


ODDS = a / [ 1 + b * e^(-c * START) ]

Where
a = 0.95
b = -0.58
c = -0.033

ODDS = 0.95 / [ 1 - 0.58 * e^(0.033 * -15) ]
= 0.95 / [ 1 - 0.58 * e^(-0.495) ]
= 0.95 / [ 1 - 0.58 * 0.61 ]
= 0.95 / [ 1 - 0.353 ]
= 0.95 / 0.64
= 1.48



Thank you Jakelee.

And if you played around with the values b and c,could it then work with the base ten?

Don't understand how e came into it.
Wasn't it supposed to be following a graph of tan?